Btc1s what currency
Publish: 2021-03-25 01:08:42
1.
第一大组(99种):CP、CQ、CR、CS、CT、CU、CW、CX、CY、CZ、EP、EQ、ER、ES、ET、EU、EW、EX、EY、EZ、GP、GQ、GR、GS、GT、GU、GW、GX、GY、GZ、IP、IQ、IR、IS、IT、IU、IW、IX、IY、IZ、
AP、AQ、AR、AS、AT、AU、AW、AX、AY、AZ、BP、BQ、BR、BS、BT、BU、BW、BX、BY、BZ、DP、DQ、DR、DS、DT、DU、DW、DX、DY、DZ、FP、FQ、FR、FS、FT、FU、FW、FX、FY、FZ、
HP、HQ、HR、HS、HT、HU、HW、HX、HY、HZ、JP、JQ、JR、JS、JT、JU、JW、JX- JZ;
第二大组(100种)：PA、PB、PC、PD、PE、PF、PG、PH、PI、PJ、RA、RB、RC、RD、RE、RF、RG、RH、RI、RJ、TA、TB、TC、TD、TE、TF、TG、TH、TI、TJ、WA、WB、WC、WD、WE、WF、WG、WH、WI、WJ、
YA、YB、YC、YD、YE、YF、YG、YH、YI、YJ、QA、QB、QC、QD、QE、QF、QG、QH、QI、QJ、SA、SB、SC、SD、SE、SF、SG、SH、SI、SJ、
UA、UB、UC、UD、UE、UF、UG、UH、UI、UJ、XA、XB、XC、XD、XE、XF、XG、XH、XI、XJ、ZA、ZB、ZC、ZD、ZE、ZF、ZG、ZH、ZI、ZJ;
第三、四大组(54种)：PK、PL PM、PN、PO、RK、RL、RM、RN、RO、TK、TL TM、TN、TO、WK、WL、WM、WN、WO、YK、YL YM、YN、YO、
QK、QL、QM、QN、QO、SK、SL、SM、SN、SO、UK、UL、UM、UN、UO、XK、XL、XM、XN、XO、ZK、ZL、ZM、ZN、ZO、AK、AL、AM、JO;
第五、六大组(0种)
第七大组(46种)：AA、AB、AC、AD、AE、AF、AG、AH、AI、AJ、CA、CB、CC、CD、CE、CF、CG、CH、CI、CJ、EA、EB、EC、ED- -EG、EH、EI、EJ、GA、GB、GC、GD、GE、GF、GG、GH、GI、GJ、IA、IB、IC、ID、IE、JH、JI、JJ;
第八大组(100种)：PP、PQ、PR、PS、PT、PU、PW、PX、PY、PZ、RP、RQ、RR、RS、RT、RU、RW、RX、RY、RZ、TP、TQ、TR、TS、TT、TU、TW、TX、TY、TZ、
WP、WQ、WR、WS、WT、WU、WW、WX、WY、WZ、YP、YQ、YR、YS、YT、YU、YW、YX、YY、YZ、QP、QQ、QR、QS、QT、QU、QW、QX、QY、QZ、
SP、SQ、SR、SS、ST、SU、SW、SX、SY、SZ、UP、UQ、UR、US、UT、UU、UW、UX、UY、UZ、XP、XQ、XR、XS、XT、XU、XW、XX、XY、XZ、ZP、ZQ、ZR、ZS、ZT、ZU、ZW、ZX、ZY、ZZ;
第九大组(22种)：KK、KL、KM、KN、KO、MK、ML、MM、MN、MO、OK、OL、OM、ON、OO、LK、LL、LM、LN、LO、NK- - - NO
共计421种
拓展资料：
一区:共发行99个冠号，其中4个是补号(JZ、JX、JW、JU)JY为样票，未发行;保定543厂：补号JW,D组后期，F组前期，H组后期，J组其他未知，补号最大流水号JW12;
西安厂：补号JU、F组后期，其他未知，补号最大流水号JU034;还有二个厂分别印制JZ,JX补号，较珍惜，此二补号都为早期冠号所补，有一厂为北京厂补号JX;另一厂为上海厂补号JZJZ的最大流水号为JZ082,JX的最大流水号为JX025,都为珍惜补号;
二区：共发行所有的100个冠号，其中2个为补号(ZJ、ZI);保定543厂：补号ZJ,1995年9月至1998年末印制，所印冠号：P组、T组、Q组前部，U组、X组前部，大约50个冠号，补号最大流水号ZJ079;
西安厂：补号ZI,1996年8月至1999年8月，所印冠号：R组、W组、Y组、Q组后部，S组、X组后部、Z组，大约50个冠号，补号最大流水号ZI121;
三区：共发行全部的50个冠号，其中2个为补号(ZO、ZN)保定543厂：补号ZO,1999年3月至11月印制，所印冠号：P组、T组后部、W组，大约12个冠号，补号最大流水号ZO003,印刷冠号稀少;
西安厂：补号ZN,1999年9月至2001年9月印刷，所印冠号：R组、T组前部、Y组、Q组、S组、U组、W组、X组、Z组，共36个冠号，补号最大流水号ZN039;
七区：共发行55个冠号，其中3个为补号(JH、JI、JJ);所印冠号有：A组、C组、E组、IA-IE、D组保定543厂：补号JJ,2000年初至2002年印制，所印冠号：A组、C组前部、E组后期、I组大约23个冠号，补号最大流水号JJ035;
南昌厂：补号JI,2001年3月至2002年，印刷冠号：C组、E组前部，大约9个冠号;西安厂：补号JH,2001年8月至2002年末，印刷冠号：G组、D组，大约20个冠号，补号最大流水号JH010;
八区：共发行全部的100个冠号，其中5个为补号(ZU、ZW、ZX、ZY、ZZ)成都厂：补号ZW,2005年3月至2009年7月，印刷冠号：PP-PS、RT-RU、TP、YP-YQ、SS-SZ、UP-US、ZP-ZR共24个冠号，补号最大流水号ZW033;
北京厂：补号ZX,2005年3月至2008年12月印制，印刷冠号：PT-PX、TR-TX、XT-XY、YT-YZ、QP-QR、XT-XY共28个冠号，补号最大流水号ZX006;
西安厂：补号ZY,2005年3月至2008年12月，印刷冠号：PY-PZ、RP-RS、RW-RZ、TZ、WP-WU、YR-YS、QS-QZ、SP-SQ、UT-UZ、、XP-XS共38个冠号，补号最大流水号ZY046;
保定543厂：补号ZZ,2009年2月，印刷冠号：ZS,ZT共2个;未发现ZU补号，及其出处;九区：共发行22个冠号(正在发行)，其中有补号1个(NO)，其中NL、NM、NN未发行
保定543厂：补号NO,2009年2月至12月印制，印刷冠号：K组、M组、O组、L组、N组共21个冠号;四区：印刷3个冠号，其中有1个补号(JO)印刷过九区后印制四区，印制四个冠号就转而印制三冠80版5角西安厂：补号JO,2009年12月印制印刷冠号:AK-AM共3个
参考资料：网络-第四套人民币
2. 1. Slatsky equation
the total change of demand for commodity 1 Δ X1 is the demand change caused by the price change while the income remains unchanged:
Δ X1 = X1 (P1 ', m) - X1 (P1, m)
we can see that this change can be decomposed into substitution effect and income effect
Δ x1 = Δ x1s + Δ X1n
X1 (P1 ', m) - X1 (P1, m) ≡ [X1 (P1', M ') - X1 (P1, M1)] + [X1 (P1', M1) - X1 (P1 ', M')]
the above identity is called "slatsky equation". It expresses that the total change of demand is equal to the substitution effect plus the income effect< According to our previous analysis, substitution effect is always negative, but income effect can change in two opposite directions. Therefore, the total effect may be positive or negative
if it is a normal commodity, the rise (fall) of price means the fall (rise) of income, then the income effect also reces (increases) the demand, so the two effects work in the same direction< br /> Δ x1 = Δ x1s + Δ X1n
symbol (-) (-)
if it is inferior goods, then the direction of the two effects is opposite, and it is even possible that the income effect exceeds the substitution effect. As a result, the total change of demand is positive after the price rises, that is, the demand increases instead. Therefore, under inferior goods, the total effect of demand is not clear< br /> Δ x1 = Δ x1s + Δ X1n
symbol (?) (-) (+)
if the demand increases on the contrary, then this inferior commodity is still Giffen commodity
(draw the total demand effect diagram of Giffen goods and non Giffen inferior goods respectively on the blackboard)
3. Rate of change
the above slatsky identity is expressed in absolute quantity, but it is more commonly expressed in rate of change
in order to express the slatsky identity more conveniently with the rate of change, we put the Δ X1m is defined as negative income effect, that is,
Δ x1m = － Δ X1n
in this way, the slatsky equation becomes:
Δ x1 = Δ x1s － Δ X1m
if we divide by Δ P1, get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ P1
recall what we have in front of us:
Δ m = x1 Δ P1
solution Δ P1, we get Δ p1 = Δ M / x, substituting it into the last term of the previous formula, we get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ m) X1
4. Law of demand
Law of demand if the demand for a commodity increases with the increase of income, then the demand for this commodity must decrease with the increase of price<
(3) examples of substitution effect and income effect (omitted)
(4) Hicks substitution effect
focuses on the difference between Hicks substitution effect and slatsky substitution effect
as we mentioned earlier, the slatsky substitution effect is the change of consumer demand after the price changes, if the consumer's purchasing power remains unchanged through income compensation (or possibly taking away). In particular, we have made it clear that constant purchasing power means that consumers can still buy the initial consumption bundle
the Hicks substitution effect emphasizes not to keep the purchasing power unchanged, but to keep the utility unchanged. That is to say, after the price changes, the income compensation (or possibly taking away) enables consumers to buy the same utility as the initial consumption bundle
(draw a picture on the blackboard)
master a point: the Hicks substitution effect, like the slatsky substitution effect, is negative. Moreover, for smaller price changes, the two substitution effects are basically the same< In the previous analysis, our analysis of consumers' choice behavior is a static analysis, or an analysis of a period. However, in fact, a person's life is always composed of a number of periods. One of the simplest ways to divide a person's life by stages is to distinguish different periods by year. Therefore, a rational consumer always needs to arrange all the money income reasonably in different periods to consume in order to maximize the utility of his life. Moreover, a person's income is also earned in different periods
therefore, the first question we need to ask is, does the same amount of money income have the same value in different periods? In other words, do they have the same purchasing power? To answer these questions, we need to introce a new concept: the time value of money< (1) principal, interest and interest rate
1. Definition of concept
if you have a monetary income, you do not intend to spend it for the time being, so you are ready to save it. Of course, there are many ways to save. You can deposit your money in a bank or buy short-term bonds. Whether banks or bond issuers, they have to promise you that they will return the money to you after a certain period of time, and also pay you a certain amount of additional monetary income. We call this money "principal", and the extra monetary income you get is called "interest"
in terms of mathematical relationship, "interest rate" is the ratio of interest and principal. For example, if 100 yuan of principal is deposited in the bank, you will get 10 yuan of interest after one year. We say the one-year interest rate of bank deposit is 10%
note: the size of the interest rate is related to the length of the period
economists' understanding of interest rate is that interest rate is the return that the owner of money gives up the current consumption of the money income, that is, the transfer of the right to use the money for a certain period of time. Therefore, interest rate is the selling price of the commodity "right to use money". In addition, the money owner gives up the consumption of a certain amount of money in the current period, and he can get more money for consumption in the future. Therefore, interest rate also reflects the "relative price" between current consumption and future consumption. Therefore, current consumption and future consumption are opportunity costs of each other<
2. The time value and discount value of money
because today's 1 yuan will increase in value in the future, today's 1 yuan is worth more than the future 1 yuan. We call this appreciation of money "time value of money"
how to measure the time value of money? In other words, how to compare the value of 1 yuan today with that of 1 yuan a year later? We need to determine how much the future one yuan is worth today. We use the concept of discounted value to express this idea
what is "present discounted value" (also known as present value) is the value of a certain amount of money in the future in the base period
formula for calculating discount value:
if we use r to represent the one-year interest rate, we need to calculate how much a certain amount of money in one year is worth at present. We can use the following formula to calculate
discount value = the amount of money in one year / (1 + R)
how to calculate the present value of bonds
if you use a sum of money to buy a bond to be repaid after n years, it will bring you annual interest income of I1, I2, I3... In, and return the principal K to you in the nth year. Assuming that the annual interest rate of the market is r, we can use the following formula to calculate the present value of the bond:
V = I1 / (1 + R) + I2 / (1 + R) 2 + I3 / (1 + R) 3 +... + in / (1 + R) n + K / (1 + R) n
(2) determination of interest rate
1. Capital market
as we have said, in the view of economists, interest rate is the price of "right to use money", Therefore, we need a market to exchange the right to use money. We call such a market "capital market" Strictly speaking, the capital market with the exchange term of the right to use money less than one year is called "money market", and the capital market with the exchange term of more than one year is called "capital market")
according to our previous analysis of the equilibrium of market supply and demand, in fact, the interest rate is the price of the capital market. The interest rate that equals the supply and demand of capital is called the equilibrium interest rate of the market, which is the result of the awesome force of the supply of funds and the demand power of funds. Its changes can also be analyzed by our previous analysis methods< 2. Inflation and real interest rate
the so-called "inflation" is a phenomenon that the price level of a society keeps rising over time. If there is inflation, then the same amount of money will not buy as much in the future as it does now. Therefore, we say that the currency has been devalued. The so-called "inflation rate" usually refers to the rate of change of price level within one year
the existence of interest rate will make the currency appreciate in the future, while inflation will make the currency depreciate. Therefore, these are two forces in opposite directions
with inflation, we have to distinguish between "real interest rate" and "nominal interest rate"
a basic relationship is: real interest rate = nominal interest rate - inflation rate
Fourth, cross period selection
we can use some of the analysis tools we learned earlier, such as budget constraints and preferences, to analyze cross period selection. In other words, we can still use static analysis tools to analyze cross period selection. In order to understand this, we might as well think about it in this way, that is, we can understand the same commodity in different periods as different commodities. At the same time, we convert the income of different periods into the income of the same period by discounting. On this basis, we can get the budget line; At the same time, we get the indifference curve reflecting the consumption combination in different periods according to the consumers' preferences< (1) the best cross period choice
1. Budget constraint
we assume that a consumer lives only two periods and consumes only one commodity. How will he choose the combination of two periods
we use (C1, C2) to represent the consumption combination of two periods, where C1 is the consumption of the first period and C2 is the consumption of the second period. Let's assume that the consumer price remains the same in each period, which is equal to 1. Moreover, the monetary income of consumers in each period is M1 and M2, and the combination of monetary income is (M1, M2)
first of all, we assume that consumers can not borrow money to spend, and that savings do not generate interest (i.e. there is no capital market). What is the budget line and budget set of consumers
(draw a picture on the blackboard)
secondly, we assume that there is a capital market, the market interest rate is r, and the consumer is ready to put part of the first period of income into the second period of consumption, that is, he is a saver. In this case, C1 is less than M1. At the same time,
C2 = M2 + (m1-c1) + R (m1-c1) = M2 + (1 + R) (m1-c1)
finally, we assume that the consumer is a borrower, which means that he consumes part of the second period's income in advance. In this case, C1 is greater than M1. At the same time,
C2 = M2 - (c1-m1) - R (c1-m1) = M2 + (1 + R) (m1-c1)
whether the consumer is a saver or a borrower, the expression of C2 is the same, in fact, this is the budget line formula
through algebraic transformation, we can also get two other budget constraint formulas, namely
(1 + R) C1 + C2 = (1 + R) M1 + m2
the total change of demand for commodity 1 Δ X1 is the demand change caused by the price change while the income remains unchanged:
Δ X1 = X1 (P1 ', m) - X1 (P1, m)
we can see that this change can be decomposed into substitution effect and income effect
Δ x1 = Δ x1s + Δ X1n
X1 (P1 ', m) - X1 (P1, m) ≡ [X1 (P1', M ') - X1 (P1, M1)] + [X1 (P1', M1) - X1 (P1 ', M')]
the above identity is called "slatsky equation". It expresses that the total change of demand is equal to the substitution effect plus the income effect< According to our previous analysis, substitution effect is always negative, but income effect can change in two opposite directions. Therefore, the total effect may be positive or negative
if it is a normal commodity, the rise (fall) of price means the fall (rise) of income, then the income effect also reces (increases) the demand, so the two effects work in the same direction< br /> Δ x1 = Δ x1s + Δ X1n
symbol (-) (-)
if it is inferior goods, then the direction of the two effects is opposite, and it is even possible that the income effect exceeds the substitution effect. As a result, the total change of demand is positive after the price rises, that is, the demand increases instead. Therefore, under inferior goods, the total effect of demand is not clear< br /> Δ x1 = Δ x1s + Δ X1n
symbol (?) (-) (+)
if the demand increases on the contrary, then this inferior commodity is still Giffen commodity
(draw the total demand effect diagram of Giffen goods and non Giffen inferior goods respectively on the blackboard)
3. Rate of change
the above slatsky identity is expressed in absolute quantity, but it is more commonly expressed in rate of change
in order to express the slatsky identity more conveniently with the rate of change, we put the Δ X1m is defined as negative income effect, that is,
Δ x1m = － Δ X1n
in this way, the slatsky equation becomes:
Δ x1 = Δ x1s － Δ X1m
if we divide by Δ P1, get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ P1
recall what we have in front of us:
Δ m = x1 Δ P1
solution Δ P1, we get Δ p1 = Δ M / x, substituting it into the last term of the previous formula, we get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ m) X1
4. Law of demand
Law of demand if the demand for a commodity increases with the increase of income, then the demand for this commodity must decrease with the increase of price<
(3) examples of substitution effect and income effect (omitted)
(4) Hicks substitution effect
focuses on the difference between Hicks substitution effect and slatsky substitution effect
as we mentioned earlier, the slatsky substitution effect is the change of consumer demand after the price changes, if the consumer's purchasing power remains unchanged through income compensation (or possibly taking away). In particular, we have made it clear that constant purchasing power means that consumers can still buy the initial consumption bundle
the Hicks substitution effect emphasizes not to keep the purchasing power unchanged, but to keep the utility unchanged. That is to say, after the price changes, the income compensation (or possibly taking away) enables consumers to buy the same utility as the initial consumption bundle
(draw a picture on the blackboard)
master a point: the Hicks substitution effect, like the slatsky substitution effect, is negative. Moreover, for smaller price changes, the two substitution effects are basically the same< In the previous analysis, our analysis of consumers' choice behavior is a static analysis, or an analysis of a period. However, in fact, a person's life is always composed of a number of periods. One of the simplest ways to divide a person's life by stages is to distinguish different periods by year. Therefore, a rational consumer always needs to arrange all the money income reasonably in different periods to consume in order to maximize the utility of his life. Moreover, a person's income is also earned in different periods
therefore, the first question we need to ask is, does the same amount of money income have the same value in different periods? In other words, do they have the same purchasing power? To answer these questions, we need to introce a new concept: the time value of money< (1) principal, interest and interest rate
1. Definition of concept
if you have a monetary income, you do not intend to spend it for the time being, so you are ready to save it. Of course, there are many ways to save. You can deposit your money in a bank or buy short-term bonds. Whether banks or bond issuers, they have to promise you that they will return the money to you after a certain period of time, and also pay you a certain amount of additional monetary income. We call this money "principal", and the extra monetary income you get is called "interest"
in terms of mathematical relationship, "interest rate" is the ratio of interest and principal. For example, if 100 yuan of principal is deposited in the bank, you will get 10 yuan of interest after one year. We say the one-year interest rate of bank deposit is 10%
note: the size of the interest rate is related to the length of the period
economists' understanding of interest rate is that interest rate is the return that the owner of money gives up the current consumption of the money income, that is, the transfer of the right to use the money for a certain period of time. Therefore, interest rate is the selling price of the commodity "right to use money". In addition, the money owner gives up the consumption of a certain amount of money in the current period, and he can get more money for consumption in the future. Therefore, interest rate also reflects the "relative price" between current consumption and future consumption. Therefore, current consumption and future consumption are opportunity costs of each other<
2. The time value and discount value of money
because today's 1 yuan will increase in value in the future, today's 1 yuan is worth more than the future 1 yuan. We call this appreciation of money "time value of money"
how to measure the time value of money? In other words, how to compare the value of 1 yuan today with that of 1 yuan a year later? We need to determine how much the future one yuan is worth today. We use the concept of discounted value to express this idea
what is "present discounted value" (also known as present value) is the value of a certain amount of money in the future in the base period
formula for calculating discount value:
if we use r to represent the one-year interest rate, we need to calculate how much a certain amount of money in one year is worth at present. We can use the following formula to calculate
discount value = the amount of money in one year / (1 + R)
how to calculate the present value of bonds
if you use a sum of money to buy a bond to be repaid after n years, it will bring you annual interest income of I1, I2, I3... In, and return the principal K to you in the nth year. Assuming that the annual interest rate of the market is r, we can use the following formula to calculate the present value of the bond:
V = I1 / (1 + R) + I2 / (1 + R) 2 + I3 / (1 + R) 3 +... + in / (1 + R) n + K / (1 + R) n
(2) determination of interest rate
1. Capital market
as we have said, in the view of economists, interest rate is the price of "right to use money", Therefore, we need a market to exchange the right to use money. We call such a market "capital market" Strictly speaking, the capital market with the exchange term of the right to use money less than one year is called "money market", and the capital market with the exchange term of more than one year is called "capital market")
according to our previous analysis of the equilibrium of market supply and demand, in fact, the interest rate is the price of the capital market. The interest rate that equals the supply and demand of capital is called the equilibrium interest rate of the market, which is the result of the awesome force of the supply of funds and the demand power of funds. Its changes can also be analyzed by our previous analysis methods< 2. Inflation and real interest rate
the so-called "inflation" is a phenomenon that the price level of a society keeps rising over time. If there is inflation, then the same amount of money will not buy as much in the future as it does now. Therefore, we say that the currency has been devalued. The so-called "inflation rate" usually refers to the rate of change of price level within one year
the existence of interest rate will make the currency appreciate in the future, while inflation will make the currency depreciate. Therefore, these are two forces in opposite directions
with inflation, we have to distinguish between "real interest rate" and "nominal interest rate"
a basic relationship is: real interest rate = nominal interest rate - inflation rate
Fourth, cross period selection
we can use some of the analysis tools we learned earlier, such as budget constraints and preferences, to analyze cross period selection. In other words, we can still use static analysis tools to analyze cross period selection. In order to understand this, we might as well think about it in this way, that is, we can understand the same commodity in different periods as different commodities. At the same time, we convert the income of different periods into the income of the same period by discounting. On this basis, we can get the budget line; At the same time, we get the indifference curve reflecting the consumption combination in different periods according to the consumers' preferences< (1) the best cross period choice
1. Budget constraint
we assume that a consumer lives only two periods and consumes only one commodity. How will he choose the combination of two periods
we use (C1, C2) to represent the consumption combination of two periods, where C1 is the consumption of the first period and C2 is the consumption of the second period. Let's assume that the consumer price remains the same in each period, which is equal to 1. Moreover, the monetary income of consumers in each period is M1 and M2, and the combination of monetary income is (M1, M2)
first of all, we assume that consumers can not borrow money to spend, and that savings do not generate interest (i.e. there is no capital market). What is the budget line and budget set of consumers
(draw a picture on the blackboard)
secondly, we assume that there is a capital market, the market interest rate is r, and the consumer is ready to put part of the first period of income into the second period of consumption, that is, he is a saver. In this case, C1 is less than M1. At the same time,
C2 = M2 + (m1-c1) + R (m1-c1) = M2 + (1 + R) (m1-c1)
finally, we assume that the consumer is a borrower, which means that he consumes part of the second period's income in advance. In this case, C1 is greater than M1. At the same time,
C2 = M2 - (c1-m1) - R (c1-m1) = M2 + (1 + R) (m1-c1)
whether the consumer is a saver or a borrower, the expression of C2 is the same, in fact, this is the budget line formula
through algebraic transformation, we can also get two other budget constraint formulas, namely
(1 + R) C1 + C2 = (1 + R) M1 + m2
3. 1. The total change of the demand for commodity 1 in the slatsky equation Δ X1 is the demand change caused by price change while the income remains unchanged Δ X1 = X1 (P1 ', m) - X1 (P1, m) we can see that this change can be decomposed into substitution effect and income effect Δ x1= Δ x1s+ Δ X1nx1 (P1 ', m) - X1 (P1, m) ≡ [X1 (P1', M ') - X1 (P1, M1)] + [X1 (P1', M1) - X1 (P1 ', M')] the above identity is called "slatsky equation". It expresses that the total change of demand is equal to the substitution effect plus the income effect. 2. According to our previous analysis, substitution effect is always negative, but income effect can change in two opposite directions. Therefore, the total effect may be positive or negative. If it is a normal commodity, the rise (fall) of price means the decrease (rise) of income, then the income effect is also the decrease (increase) of demand, then the two effects work in the same direction. Δ x1= Δ x1s+ Δ If x1n sign (-) (-) (-) is a inferior commodity, then the two effects have opposite directions. It is even possible that the income effect exceeds the substitution effect. As a result, the total change of demand is positive after the price rises, that is, the demand increases instead. Therefore, under inferior goods, the total effect of demand is not clear. Δ x1= Δ x1s+ Δ X1n symbol (?) (-) (+) If demand increases instead, then this inferior commodity is still a Giffen commodity 3. The slatsky identity on the rate of change is expressed in absolute quantity, but the more common way is to use the rate of change. In order to express the slatsky identity more conveniently by the rate of change, we put the Δ X1m is defined as negative income effect, i.e Δ x1m=－ Δ In this way, the slatsky equation becomes: Δ x1= Δ x1s－ Δ X1m if we divide it on both sides of the equation Δ P1, get Δ x1/ Δ p1= Δ x1s/ Δ p1－ Δ x1m/ Δ P1 recall that we have: Δ m=x1 Δ P1 solution Δ P1, we get Δ p1= Δ M / x, substituting it into the last term of the previous formula, we get Δ x1/ Δ p1= Δ x1s/ Δ p1－ Δ x1m/ Δ m) If the demand for a commodity increases with the increase of income, then the demand for this commodity must decrease with the increase of price 3 Examples of substitution effect and income effect (4) Hicks substitution effect focuses on the difference between Hicks substitution effect and slatsky substitution effect. As we have said before, the slatsky substitution effect is the change of consumer demand after the price changes, if the consumer's purchasing power remains unchanged through income compensation (or possibly taking away). In particular, we have made it clear that constant purchasing power means that consumers can still buy the initial consumption bundle. Hicks substitution effect emphasizes not to keep purchasing power unchanged, but to keep utility unchanged. That is to say, after the price changes, the income compensation (or possibly taking away) enables consumers to buy the same utility as the initial consumption bundle Draw a picture on the blackboard) master a point: the Hicks substitution effect is negative, just like the slatsky substitution effect. Moreover, for smaller price changes, the two substitution effects are basically the same. 3、 The time value of money in the previous analysis, our analysis of consumer choice behavior is a static analysis, or in other words, the analysis of a period. However, in fact, a person's life is always composed of several periods. One of the simplest stages is to distinguish different periods by year. Therefore, a rational consumer always needs to arrange all the money income reasonably in different periods to consume in order to maximize the utility of his life. Moreover, a person's income is also earned in different periods. So, the first question we need to ask is, does the same amount of money income have the same value in different periods? In other words, do they have the same purchasing power? To answer these questions, we need to introce a new concept: the time value of money 1 If you have a monetary income, you don't intend to spend it for the time being, so you are ready to save it. Of course, there are many ways to save. You can deposit your money in a bank or buy short-term bonds. Whether banks or bond issuers, they have to promise you that they will return the money to you after a certain period of time, and also pay you a certain amount of additional monetary income. We call this money "principal", and the extra monetary income you get is called "interest". From the perspective of mathematical relationship, "interest rate" is the ratio of interest and principal. For example, if 100 yuan of principal is deposited in the bank, you will get 10 yuan of interest after one year. We say the one-year interest rate of bank deposit is 10%. Note: the size of the interest rate is related to the length of the period. Economists' understanding of interest rate is that interest rate is the return that the owner of money gives up the current consumption of the money income, that is, the return from the transfer of the right to use the money for a certain period of time. Therefore, interest rate is the selling price of the commodity "right to use money". In addition, the money owner gives up the consumption of a certain amount of money in the current period, and the amount of money he can get will be used for consumption in the future. Therefore, interest rate also reflects the "relative price" between current consumption and future consumption. Therefore, current consumption and future consumption are opportunity costs of each other. 2. The time value and discount value of money because today's 1 yuan will increase in value in the future, so today's 1 yuan is more valuable than the future 1 yuan. We call this appreciation of money "time value of money". How to measure the time value of money? In other words, how to compare the value of 1 yuan today with that of 1 yuan a year later? We need to determine how much the future one yuan is worth today. We use the concept of discounted value to express this idea. What is "present discounted value" (also known as present value) is the future value of a certain amount of money in the base period. The formula for calculating the discount value: if we use r to represent the one-year interest rate, we need to calculate how much a certain amount of money in one year is worth at present. We can calculate the discount value by the following formula: how to calculate the discount value = the amount of money in one year / (1 + R) the present value of the bond? If you use a sum of money to buy a bond to be repaid after n years, it will bring you interest income of I1, I2, I3... In every year, and return the principal K to you in the nth year. Assuming that the annual interest rate of the market is r, we can use the following formula to calculate the present value of the bond: v = I1 / (1 + R) + I2 / (1 + R) 2 + I3 / (1 + R) 3 +... + in / (1 + R) n + K / (1 + R) n (2) the determination of the interest rate 1. As we have said in the capital market, in the view of economists, the interest rate is the price of the "right to use money", so, We need a market in exchange for the right to use money. We call such a market "capital market" Strictly speaking, the capital market in which the exchange term of the right to use money is less than one year is called "money market", and the capital market in which the exchange term of the right to use money is more than one year. According to our previous analysis of the equilibrium of market supply and demand, in fact, the interest rate is the price of the capital market. The interest rate that equals the supply and demand of capital is called the equilibrium interest rate of the market, which is the result of the awesome force of the supply of funds and the demand power of funds. Its changes can also be analyzed by our previous analysis methods Inflation and real interest rate the so-called "inflation" is a phenomenon that the price level in a society keeps rising over time. If there is inflation, then the same amount of money will not buy as much in the future as it does now. Therefore, we say that the currency has been devalued. The so-called "inflation rate" usually refers to the rate of change of price level within one year. The existence of interest rate will make the currency increase in value in the future, while inflation will make the currency devalue. Therefore, these are two forces in opposite directions. Because of inflation, we have to distinguish between "real interest rate" and "nominal interest rate". A basic relationship is: real interest rate = nominal interest rate - inflation rate 4. Intertemporal choice. We can use some of the analysis tools we learned earlier, such as budget constraints and preferences, to analyze intertemporal choice. In other words, we can still use static analysis tools to analyze intertemporal choice. In order to understand this, we might as well think about it in this way, that is, we can understand the same commodity in different periods as different commodities. At the same time, we convert the income of different periods into the income of the same period by discounting. On this basis, we can get the budget line; At the same time, we get the indifference curve reflecting the consumption combination in different periods according to the consumers' preferences 1 We assume that a consumer lives only two periods and consumes only one commodity. How will he choose the combination of two periods? We use (C1, C2) to represent the consumption combination of the two periods, where C1 is the consumption of the first period and C2 is the consumption of the second period. Let's assume that the consumer price remains the same in each period, which is equal to 1. Moreover, the monetary income of consumers in each period is M1 and M2, and the combination of monetary income is (M1, M2). First, we assume that consumers can't borrow money to spend, and that saving doesn't generate interest (i.e. there is no capital market). What is the budget line and budget set of consumers Secondly, we assume that there is a capital market, the market interest rate is r, and the consumer is ready to put part of the first period of income into the second period of consumption, that is, he is a saver. In this case, C1 is less than M1. At the same time, C2 = M2 + (m1-c1) + R (m1-c1) = M2 + (1 + R) (m1-c1) finally, we assume that the consumer is a borrower, which means that he consumes part of the second period's income in advance. In this case, C1 is greater than M1. At the same time, C2 = M2 - (c1-m1) - R (c1-m1) = M2 + (1 + R) (m1-c1) whether the consumer is a saver or a borrower, the expression of C2 is the same. In fact, this is the budget line formula. Through algebraic transformation, we can also get two other budget constraint formulas, that is, (1 + R) C1 + C2 = (1 + R) M1 + M2 (income represented by future value) and C1 + C2 / (1 + R) = M1 + m2 / (1 + R) (income represented by present value). These two equations can be expressed as: p1x1 + P2X2 = p1m1 + p2m2 (Note: different equations P1 and P2 represent different values) (draw pictures on the blackboard) According to the above, the shape of indifference curve reflects consumers' preference for consumption combination in different periods. The indifference curve of complete substitution shows that consumers don't care whether they spend in the current period or the next period. The complete complementary indifference curve shows that consumers always allocate their current and next consumption in a fixed proportion. More realistic indifference curve or good character indifference curve, that is, consumers are willing to replace part of the current consumption for the next one, and how much to replace depends on the consumer's own consumption
4. How come there's so much nonsense upstairs? If there's BT's best, it's enough to add it to 30. You have to depend on your own strength. Jiamin's principle is to see his hit, as long as the hit is no less than 138, then all the monsters in your adventure island can be hit. Jiamin is to rece miss. It's enough that the min of zakun is no less than 130. I'm also a swordsman. I don't have abnormal equipment myself. I've increased the min to 75, but the most important thing for soldiers is attack agility. It's just to rece miss. But miss has a lot to do with your level. That is to say, if you are more agile, you can skip the level to fight monsters. I'm playing with mushrooms, and I can't play with you.
5. 1. Slatsky equation
the total change of demand for commodity 1 Δ X1 is the demand change caused by the price change while the income remains unchanged:
Δ X1 = X1 (P1 ', m) - X1 (P1, m)
we can see that this change can be decomposed into substitution effect and income effect
Δ x1 = Δ x1s + Δ X1n
X1 (P1 ', m) - X1 (P1, m) ≡ [X1 (P1', M ') - X1 (P1, M1)] + [X1 (P1', M1) - X1 (P1 ', M')]
the above identity is called "slatsky equation". It expresses that the total change of demand is equal to the substitution effect plus the income effect< According to our previous analysis, substitution effect is always negative, but income effect can change in two opposite directions. Therefore, the total effect may be positive or negative
if it is a normal commodity, the rise (fall) of price means the fall (rise) of income, then the income effect also reces (increases) the demand, so the two effects work in the same direction< br /> Δ x1 = Δ x1s + Δ X1n
symbol (-) (-)
if it is inferior goods, then the direction of the two effects is opposite, and it is even possible that the income effect exceeds the substitution effect. As a result, the total change of demand is positive after the price rises, that is, the demand increases instead. Therefore, under inferior goods, the total effect of demand is not clear< br /> Δ x1 = Δ x1s + Δ X1n
symbol (?) (-) (+)
if the demand increases on the contrary, then this inferior commodity is still Giffen commodity
(draw the total demand effect diagram of Giffen goods and non Giffen inferior goods respectively on the blackboard)
3. Rate of change
the above slatsky identity is expressed in absolute quantity, but it is more commonly expressed in rate of change
in order to express the slatsky identity more conveniently with the rate of change, we put the Δ X1m is defined as negative income effect, that is,
Δ x1m = － Δ X1n
in this way, the slatsky equation becomes:
Δ x1 = Δ x1s － Δ X1m
if we divide by Δ P1, get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ P1
recall what we have in front of us:
Δ m = x1 Δ P1
solution Δ P1, we get Δ p1 = Δ M / x, substituting it into the last term of the previous formula, we get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ m) X1
4. Law of demand
Law of demand if the demand for a commodity increases with the increase of income, then the demand for this commodity must decrease with the increase of price<
(3) examples of substitution effect and income effect (omitted)
(4) Hicks substitution effect
focuses on the difference between Hicks substitution effect and slatsky substitution effect
as we mentioned earlier, the slatsky substitution effect is the change of consumer demand after the price changes, if the consumer's purchasing power remains unchanged through income compensation (or possibly taking away). In particular, we have made it clear that constant purchasing power means that consumers can still buy the initial consumption bundle
the Hicks substitution effect emphasizes not to keep the purchasing power unchanged, but to keep the utility unchanged. That is to say, after the price changes, the income compensation (or possibly taking away) enables consumers to buy the same utility as the initial consumption bundle
(draw a picture on the blackboard)
master a point: the Hicks substitution effect, like the slatsky substitution effect, is negative. Moreover, for smaller price changes, the two substitution effects are basically the same< In the previous analysis, our analysis of consumers' choice behavior is a static analysis, or an analysis of a period. However, in fact, a person's life is always composed of a number of periods. One of the simplest ways to divide a person's life by stages is to distinguish different periods by year. Therefore, a rational consumer always needs to arrange all the money income reasonably in different periods to consume in order to maximize the utility of his life. Moreover, a person's income is also earned in different periods
therefore, the first question we need to ask is, does the same amount of money income have the same value in different periods? In other words, do they have the same purchasing power? To answer these questions, we need to introce a new concept: the time value of money< (1) principal, interest and interest rate
1. Definition of concept
if you have a monetary income, you do not intend to spend it for the time being, so you are ready to save it. Of course, there are many ways to save. You can deposit your money in a bank or buy short-term bonds. Whether banks or bond issuers, they have to promise you that they will return the money to you after a certain period of time, and also pay you a certain amount of additional monetary income. We call this money "principal", and the extra monetary income you get is called "interest"
in terms of mathematical relationship, "interest rate" is the ratio of interest and principal. For example, if 100 yuan of principal is deposited in the bank, you will get 10 yuan of interest after one year. We say the one-year interest rate of bank deposit is 10%
note: the size of the interest rate is related to the length of the period
economists' understanding of interest rate is that interest rate is the return that the owner of money gives up the current consumption of the money income, that is, the transfer of the right to use the money for a certain period of time. Therefore, interest rate is the selling price of the commodity "right to use money". In addition, the money owner gives up the consumption of a certain amount of money in the current period, and he can get more money for consumption in the future. Therefore, interest rate also reflects the "relative price" between current consumption and future consumption. Therefore, current consumption and future consumption are opportunity costs of each other<
2. The time value and discount value of money
because today's 1 yuan will increase in value in the future, today's 1 yuan is worth more than the future 1 yuan. We call this appreciation of money "time value of money"
how to measure the time value of money? In other words, how to compare the value of 1 yuan today with that of 1 yuan a year later? We need to determine how much the future one yuan is worth today. We use the concept of discounted value to express this idea
what is "present discounted value" (also known as present value) is the value of a certain amount of money in the future in the base period
formula for calculating discount value:
if we use r to represent the one-year interest rate, we need to calculate how much a certain amount of money in one year is worth at present. We can use the following formula to calculate
discount value = the amount of money in one year / (1 + R)
how to calculate the present value of bonds
if you use a sum of money to buy a bond to be repaid after n years, it will bring you annual interest income of I1, I2, I3... In, and return the principal K to you in the nth year. Assuming that the annual interest rate of the market is r, we can use the following formula to calculate the present value of the bond:
V = I1 / (1 + R) + I2 / (1 + R) 2 + I3 / (1 + R) 3 +... + in / (1 + R) n + K / (1 + R) n
(2) determination of interest rate
1. Capital market
as we have said, in the view of economists, interest rate is the price of "right to use money", Therefore, we need a market to exchange the right to use money. We call such a market "capital market" Strictly speaking, the capital market with the exchange term of the right to use money less than one year is called "money market", and the capital market with the exchange term of more than one year is called "capital market")
according to our previous analysis of the equilibrium of market supply and demand, in fact, the interest rate is the price of the capital market. The interest rate that equals the supply and demand of capital is called the equilibrium interest rate of the market, which is the result of the awesome force of the supply of funds and the demand power of funds. Its changes can also be analyzed by our previous analysis methods< 2. Inflation and real interest rate
the so-called "inflation" is a phenomenon that the price level of a society keeps rising over time. If there is inflation, then the same amount of money will not buy as much in the future as it does now. Therefore, we say that the currency has been devalued. The so-called "inflation rate" usually refers to the rate of change of price level within one year
the existence of interest rate will make the currency appreciate in the future, while inflation will make the currency depreciate. Therefore, these are two forces in opposite directions
with inflation, we have to distinguish between "real interest rate" and "nominal interest rate"
a basic relationship is: real interest rate = nominal interest rate - inflation rate
Fourth, cross period selection
we can use some of the analysis tools we learned earlier, such as budget constraints and preferences, to analyze cross period selection. In other words, we can still use static analysis tools to analyze cross period selection. In order to understand this, we might as well think about it in this way, that is, we can understand the same commodity in different periods as different commodities. At the same time, we convert the income of different periods into the income of the same period by discounting. On this basis, we can get the budget line; At the same time, we get the indifference curve reflecting the consumption combination in different periods according to the consumers' preferences< (1) the best cross period choice
1. Budget constraint
we assume that a consumer lives only two periods and consumes only one commodity. How will he choose the combination of two periods
we use (C1, C2) to represent the consumption combination of two periods, where C1 is the consumption of the first period and C2 is the consumption of the second period. Let's assume that the consumer price remains the same in each period, which is equal to 1. Moreover, the monetary income of consumers in each period is M1 and M2, and the combination of monetary income is (M1, M2)
first of all, we assume that consumers can not borrow money to spend, and that savings do not generate interest (i.e. there is no capital market). What is the budget line and budget set of consumers
(draw a picture on the blackboard)
secondly, we assume that there is a capital market, the market interest rate is r, and the consumer is ready to put part of the first period of income into the second period of consumption, that is, he is a saver. In this case, C1 is less than M1. At the same time,
C2 = M2 + (m1-c1) + R (m1-c1) = M2 + (1 + R) (m1-c1)
finally, we assume that the consumer is a borrower, which means that he consumes part of the second period's income in advance. In this case, C1 is greater than M1. At the same time,
C2 = M2 - (c1-m1) - R (c1-m1) = M2 + (1 + R) (m1-c1)
whether the consumer is a saver or a borrower, the expression of C2 is the same, in fact, this is the budget line formula
through algebraic transformation, we can also get two other budget constraint formulas, namely
(1 + R) C1 + C2 = (1 + R) M1 + m2
the total change of demand for commodity 1 Δ X1 is the demand change caused by the price change while the income remains unchanged:
Δ X1 = X1 (P1 ', m) - X1 (P1, m)
we can see that this change can be decomposed into substitution effect and income effect
Δ x1 = Δ x1s + Δ X1n
X1 (P1 ', m) - X1 (P1, m) ≡ [X1 (P1', M ') - X1 (P1, M1)] + [X1 (P1', M1) - X1 (P1 ', M')]
the above identity is called "slatsky equation". It expresses that the total change of demand is equal to the substitution effect plus the income effect< According to our previous analysis, substitution effect is always negative, but income effect can change in two opposite directions. Therefore, the total effect may be positive or negative
if it is a normal commodity, the rise (fall) of price means the fall (rise) of income, then the income effect also reces (increases) the demand, so the two effects work in the same direction< br /> Δ x1 = Δ x1s + Δ X1n
symbol (-) (-)
if it is inferior goods, then the direction of the two effects is opposite, and it is even possible that the income effect exceeds the substitution effect. As a result, the total change of demand is positive after the price rises, that is, the demand increases instead. Therefore, under inferior goods, the total effect of demand is not clear< br /> Δ x1 = Δ x1s + Δ X1n
symbol (?) (-) (+)
if the demand increases on the contrary, then this inferior commodity is still Giffen commodity
(draw the total demand effect diagram of Giffen goods and non Giffen inferior goods respectively on the blackboard)
3. Rate of change
the above slatsky identity is expressed in absolute quantity, but it is more commonly expressed in rate of change
in order to express the slatsky identity more conveniently with the rate of change, we put the Δ X1m is defined as negative income effect, that is,
Δ x1m = － Δ X1n
in this way, the slatsky equation becomes:
Δ x1 = Δ x1s － Δ X1m
if we divide by Δ P1, get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ P1
recall what we have in front of us:
Δ m = x1 Δ P1
solution Δ P1, we get Δ p1 = Δ M / x, substituting it into the last term of the previous formula, we get
Δ x1 / Δ p1 = Δ x1s / Δ p1 － Δ x1m / Δ m) X1
4. Law of demand
Law of demand if the demand for a commodity increases with the increase of income, then the demand for this commodity must decrease with the increase of price<
(3) examples of substitution effect and income effect (omitted)
(4) Hicks substitution effect
focuses on the difference between Hicks substitution effect and slatsky substitution effect
as we mentioned earlier, the slatsky substitution effect is the change of consumer demand after the price changes, if the consumer's purchasing power remains unchanged through income compensation (or possibly taking away). In particular, we have made it clear that constant purchasing power means that consumers can still buy the initial consumption bundle
the Hicks substitution effect emphasizes not to keep the purchasing power unchanged, but to keep the utility unchanged. That is to say, after the price changes, the income compensation (or possibly taking away) enables consumers to buy the same utility as the initial consumption bundle
(draw a picture on the blackboard)
master a point: the Hicks substitution effect, like the slatsky substitution effect, is negative. Moreover, for smaller price changes, the two substitution effects are basically the same< In the previous analysis, our analysis of consumers' choice behavior is a static analysis, or an analysis of a period. However, in fact, a person's life is always composed of a number of periods. One of the simplest ways to divide a person's life by stages is to distinguish different periods by year. Therefore, a rational consumer always needs to arrange all the money income reasonably in different periods to consume in order to maximize the utility of his life. Moreover, a person's income is also earned in different periods
therefore, the first question we need to ask is, does the same amount of money income have the same value in different periods? In other words, do they have the same purchasing power? To answer these questions, we need to introce a new concept: the time value of money< (1) principal, interest and interest rate
1. Definition of concept
if you have a monetary income, you do not intend to spend it for the time being, so you are ready to save it. Of course, there are many ways to save. You can deposit your money in a bank or buy short-term bonds. Whether banks or bond issuers, they have to promise you that they will return the money to you after a certain period of time, and also pay you a certain amount of additional monetary income. We call this money "principal", and the extra monetary income you get is called "interest"
in terms of mathematical relationship, "interest rate" is the ratio of interest and principal. For example, if 100 yuan of principal is deposited in the bank, you will get 10 yuan of interest after one year. We say the one-year interest rate of bank deposit is 10%
note: the size of the interest rate is related to the length of the period
economists' understanding of interest rate is that interest rate is the return that the owner of money gives up the current consumption of the money income, that is, the transfer of the right to use the money for a certain period of time. Therefore, interest rate is the selling price of the commodity "right to use money". In addition, the money owner gives up the consumption of a certain amount of money in the current period, and he can get more money for consumption in the future. Therefore, interest rate also reflects the "relative price" between current consumption and future consumption. Therefore, current consumption and future consumption are opportunity costs of each other<
2. The time value and discount value of money
because today's 1 yuan will increase in value in the future, today's 1 yuan is worth more than the future 1 yuan. We call this appreciation of money "time value of money"
how to measure the time value of money? In other words, how to compare the value of 1 yuan today with that of 1 yuan a year later? We need to determine how much the future one yuan is worth today. We use the concept of discounted value to express this idea
what is "present discounted value" (also known as present value) is the value of a certain amount of money in the future in the base period
formula for calculating discount value:
if we use r to represent the one-year interest rate, we need to calculate how much a certain amount of money in one year is worth at present. We can use the following formula to calculate
discount value = the amount of money in one year / (1 + R)
how to calculate the present value of bonds
if you use a sum of money to buy a bond to be repaid after n years, it will bring you annual interest income of I1, I2, I3... In, and return the principal K to you in the nth year. Assuming that the annual interest rate of the market is r, we can use the following formula to calculate the present value of the bond:
V = I1 / (1 + R) + I2 / (1 + R) 2 + I3 / (1 + R) 3 +... + in / (1 + R) n + K / (1 + R) n
(2) determination of interest rate
1. Capital market
as we have said, in the view of economists, interest rate is the price of "right to use money", Therefore, we need a market to exchange the right to use money. We call such a market "capital market" Strictly speaking, the capital market with the exchange term of the right to use money less than one year is called "money market", and the capital market with the exchange term of more than one year is called "capital market")
according to our previous analysis of the equilibrium of market supply and demand, in fact, the interest rate is the price of the capital market. The interest rate that equals the supply and demand of capital is called the equilibrium interest rate of the market, which is the result of the awesome force of the supply of funds and the demand power of funds. Its changes can also be analyzed by our previous analysis methods< 2. Inflation and real interest rate
the so-called "inflation" is a phenomenon that the price level of a society keeps rising over time. If there is inflation, then the same amount of money will not buy as much in the future as it does now. Therefore, we say that the currency has been devalued. The so-called "inflation rate" usually refers to the rate of change of price level within one year
the existence of interest rate will make the currency appreciate in the future, while inflation will make the currency depreciate. Therefore, these are two forces in opposite directions
with inflation, we have to distinguish between "real interest rate" and "nominal interest rate"
a basic relationship is: real interest rate = nominal interest rate - inflation rate
Fourth, cross period selection
we can use some of the analysis tools we learned earlier, such as budget constraints and preferences, to analyze cross period selection. In other words, we can still use static analysis tools to analyze cross period selection. In order to understand this, we might as well think about it in this way, that is, we can understand the same commodity in different periods as different commodities. At the same time, we convert the income of different periods into the income of the same period by discounting. On this basis, we can get the budget line; At the same time, we get the indifference curve reflecting the consumption combination in different periods according to the consumers' preferences< (1) the best cross period choice
1. Budget constraint
we assume that a consumer lives only two periods and consumes only one commodity. How will he choose the combination of two periods
we use (C1, C2) to represent the consumption combination of two periods, where C1 is the consumption of the first period and C2 is the consumption of the second period. Let's assume that the consumer price remains the same in each period, which is equal to 1. Moreover, the monetary income of consumers in each period is M1 and M2, and the combination of monetary income is (M1, M2)
first of all, we assume that consumers can not borrow money to spend, and that savings do not generate interest (i.e. there is no capital market). What is the budget line and budget set of consumers
(draw a picture on the blackboard)
secondly, we assume that there is a capital market, the market interest rate is r, and the consumer is ready to put part of the first period of income into the second period of consumption, that is, he is a saver. In this case, C1 is less than M1. At the same time,
C2 = M2 + (m1-c1) + R (m1-c1) = M2 + (1 + R) (m1-c1)
finally, we assume that the consumer is a borrower, which means that he consumes part of the second period's income in advance. In this case, C1 is greater than M1. At the same time,
C2 = M2 - (c1-m1) - R (c1-m1) = M2 + (1 + R) (m1-c1)
whether the consumer is a saver or a borrower, the expression of C2 is the same, in fact, this is the budget line formula
through algebraic transformation, we can also get two other budget constraint formulas, namely
(1 + R) C1 + C2 = (1 + R) M1 + m2
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7. Definition of the concept
if you have a monetary income, you do not intend to spend it for the time being, so you are ready to save it. Of course, there are many ways to save. You can deposit your money in a bank or buy short-term bonds. Whether banks or bond issuers, they have to promise you that they will return the money to you after a certain period of time, and also pay you a certain amount of additional monetary income. We call this money "principal", and the extra monetary income you get is called "interest"
in terms of mathematical relationship, "interest rate" is the ratio of interest and principal. For example, if 100 yuan of principal is deposited in the bank, you will get 10 yuan of interest after one year. We say the one-year interest rate of bank deposit is 10%
note: the size of the interest rate is related to the length of the period
economists' understanding of interest rate is that interest rate is the return that the owner of money gives up the current consumption of the money income, that is, the transfer of the right to use the money for a certain period of time. Therefore, interest rate is the selling price of the commodity "right to use money". In addition, the money owner gives up the consumption of a certain amount of money in the current period, and he can get more money for consumption in the future. Therefore, interest rate also reflects the "relative price" between current consumption and future consumption. Therefore, current consumption and future consumption are opportunity costs of each other<
2. The time value and discount value of money
because today's 1 yuan will increase in value in the future, today's 1 yuan is worth more than the future 1 yuan. We call this appreciation of money "time value of money"
how to measure the time value of money? In other words, how to compare the value of 1 yuan today with that of 1 yuan a year later? We need to determine how much the future one yuan is worth today. We use the concept of discounted value to express this idea
what is "present discounted value" (also known as present value) is the value of a certain amount of money in the future in the base period
formula for calculating discount value:
if we use r to represent the one-year interest rate, we need to calculate how much a certain amount of money in one year is worth at present. We can use the following formula to calculate
discount value = the amount of money in one year / (1 + R)
how to calculate the present value of bonds
if you use a sum of money to buy a bond to be repaid after n years, it will bring you annual interest income of I1, I2, I3... In, and return the principal K to you in the nth year. Assuming that the annual interest rate of the market is r, we can use the following formula to calculate the present value of the bond:
V = I1 / (1 + R) + I2 / (1 + R) 2 + I3 / (1 + R) 3 +... + in / (1 + R) n + K / (1 + R) n
(2) determination of interest rate
1. Capital market
as we have said, in the view of economists, interest rate is the price of "right to use money", Therefore, we need a market to exchange the right to use money. We call such a market "capital market" Strictly speaking, the capital market with the exchange term of the right to use money less than one year is called "money market", and the capital market with the exchange term of more than one year is called "capital market")
according to our previous analysis of the equilibrium of market supply and demand, in fact, the interest rate is the price of the capital market. The interest rate that equals the supply and demand of capital is called the equilibrium interest rate of the market, which is the result of the awesome force of the supply of funds and the demand power of funds. Its changes can also be analyzed by our previous analysis methods< 2. Inflation and real interest rate
the so-called "inflation" is a phenomenon that the price level of a society keeps rising over time. If there is inflation, then the same amount of money will not buy as much in the future as it does now. Therefore, we say that the currency has been devalued. The so-called "inflation rate" usually refers to the rate of change of price level within one year
the existence of interest rate will make the currency appreciate in the future, while inflation will make the currency depreciate. Therefore, these are two forces in opposite directions
with inflation, we have to distinguish between "real interest rate" and "nominal interest rate"
a basic relationship is: real interest rate = nominal interest rate - inflation rate
Fourth, cross period selection
we can use some of the analysis tools we learned earlier, such as budget constraints and preferences, to analyze cross period selection. In other words, we can still use static analysis tools to analyze cross period selection. In order to understand this, we might as well think about it in this way, that is, we can understand the same commodity in different periods as different commodities. At the same time, we convert the income of different periods into the income of the same period by discounting. On this basis, we can get the budget line; At the same time, we get the indifference curve reflecting the consumption combination in different periods according to the consumers' preferences< (1) the best cross period choice
1. Budget constraint
we assume that a consumer lives only two periods and consumes only one commodity. How will he choose the combination of two periods
we use (C1, C2) to represent the consumption combination of two periods, where C1 is the consumption of the first period and C2 is the consumption of the second period. Let's assume that the consumer price remains the same in each period, which is equal to 1. Moreover, the monetary income of consumers in each period is M1 and M2, and the combination of monetary income is (M1, M2)
first of all, we assume that consumers can not borrow money to spend, and that savings do not generate interest (i.e. there is no capital market). What is the budget line and budget set of consumers
(draw a picture on the blackboard)
secondly, we assume that there is a capital market, the market interest rate is r, and the consumer is ready to put part of the first period of income into the second period of consumption, that is, he is a saver. In this case, C1 is less than M1. At the same time,
C2 = M2 + (m1-c1) + R (m1-c1) = M2 + (1 + R) (m1-c1)
finally, we assume that the consumer is a borrower, which means that he consumes part of the second period's income in advance. In this case, C1 is greater than M1. At the same time,
C2 = M2 - (c1-m1) - R (c1-m1) = M2 + (1 + R) (m1-c1)
whether consumers are savers or borrowers, the expression of C2 is the same, in fact, this is the budget line formula
through algebraic transformation, we can also get two other budget constraint formulas, That is to say,
(1 + R) C1 + C2 = (1 + R) M1 + M2 (income represented by future value)
and
C1 + C2 / (1 + R) = M1 + m2 / (1 + R) (income represented by present value)
these two equations can be expressed as:
p1x1 + P2X2 = p1m1 + p2m2
(Note: different processes P1 and P2 represent different values)
(drawing on the blackboard) < B R / >
2. Consumer preference
according to the above, the shape of indifference curve reflects consumers' preference for consumption combination in different periods
the indifference curve of complete substitution shows that consumers don't care whether they spend in the current period or the next period
the complete complementary indifference curve shows that consumers always allocate the consumption of the current period and the next period according to a fixed proportion
a more realistic indifference curve or a good indifference curve, that is, consumers are willing to substitute part of the current consumption for the next one, and the amount of substitution depends on the consumer's consumption pattern. In this case, preference is convex< (2) comparative static analysis
1. Determination of consumer type
under what circumstances is a consumer a borrower? Under what circumstances are consumers depositors< When C1 > M1, the consumer is the borrower
when C1 < M1, consumers are depositors< 2. The impact of interest rate changes on consumer behavior
the change of interest rate actually affects the price ratio of consumption in different periods, so it will affect the budget set and budget line of consumers, and ultimately affect the optimal consumption combination of consumers
if the interest rate rises, the depositor will continue to be the depositor
if the interest rate falls, the borrower will continue to be the borrower
(draw a picture on the blackboard to explain, which can be proved according to the display preference principle)
how the behavior of the borrower changes after the interest rate rises and how the behavior of the depositor changes after the interest rate falls, which shows what the display preference principle can't tell us
however, after the interest rate rises, if the borrower continues to be a borrower, his situation will certainly get worse; After the interest rate drops, if the depositor continues to be a depositor, his situation will certainly get worse< The change of interest rate leads to the change of consumer price and demand in different periods
changes in demand can also be decomposed into substitution effect and income effect
taking the increase of interest rate as an example, we use the budget constraint of future value to analyze that the increase of interest rate is equal to the increase of the price of the first period consumption. According to the slatsky equation, we get:
Δ c1t / Δ p1 = Δ c1s / Δ p1 +m1－c1 Δ c1m / Δ m
— +
according to the above expression, we can dece that if the consumer is a borrower, then the rise of interest rate will rece his consumption in the first period; However, for consumers as depositors, the overall effect is not obvious.
if you have a monetary income, you do not intend to spend it for the time being, so you are ready to save it. Of course, there are many ways to save. You can deposit your money in a bank or buy short-term bonds. Whether banks or bond issuers, they have to promise you that they will return the money to you after a certain period of time, and also pay you a certain amount of additional monetary income. We call this money "principal", and the extra monetary income you get is called "interest"
in terms of mathematical relationship, "interest rate" is the ratio of interest and principal. For example, if 100 yuan of principal is deposited in the bank, you will get 10 yuan of interest after one year. We say the one-year interest rate of bank deposit is 10%
note: the size of the interest rate is related to the length of the period
economists' understanding of interest rate is that interest rate is the return that the owner of money gives up the current consumption of the money income, that is, the transfer of the right to use the money for a certain period of time. Therefore, interest rate is the selling price of the commodity "right to use money". In addition, the money owner gives up the consumption of a certain amount of money in the current period, and he can get more money for consumption in the future. Therefore, interest rate also reflects the "relative price" between current consumption and future consumption. Therefore, current consumption and future consumption are opportunity costs of each other<
2. The time value and discount value of money
because today's 1 yuan will increase in value in the future, today's 1 yuan is worth more than the future 1 yuan. We call this appreciation of money "time value of money"
how to measure the time value of money? In other words, how to compare the value of 1 yuan today with that of 1 yuan a year later? We need to determine how much the future one yuan is worth today. We use the concept of discounted value to express this idea
what is "present discounted value" (also known as present value) is the value of a certain amount of money in the future in the base period
formula for calculating discount value:
if we use r to represent the one-year interest rate, we need to calculate how much a certain amount of money in one year is worth at present. We can use the following formula to calculate
discount value = the amount of money in one year / (1 + R)
how to calculate the present value of bonds
if you use a sum of money to buy a bond to be repaid after n years, it will bring you annual interest income of I1, I2, I3... In, and return the principal K to you in the nth year. Assuming that the annual interest rate of the market is r, we can use the following formula to calculate the present value of the bond:
V = I1 / (1 + R) + I2 / (1 + R) 2 + I3 / (1 + R) 3 +... + in / (1 + R) n + K / (1 + R) n
(2) determination of interest rate
1. Capital market
as we have said, in the view of economists, interest rate is the price of "right to use money", Therefore, we need a market to exchange the right to use money. We call such a market "capital market" Strictly speaking, the capital market with the exchange term of the right to use money less than one year is called "money market", and the capital market with the exchange term of more than one year is called "capital market")
according to our previous analysis of the equilibrium of market supply and demand, in fact, the interest rate is the price of the capital market. The interest rate that equals the supply and demand of capital is called the equilibrium interest rate of the market, which is the result of the awesome force of the supply of funds and the demand power of funds. Its changes can also be analyzed by our previous analysis methods< 2. Inflation and real interest rate
the so-called "inflation" is a phenomenon that the price level of a society keeps rising over time. If there is inflation, then the same amount of money will not buy as much in the future as it does now. Therefore, we say that the currency has been devalued. The so-called "inflation rate" usually refers to the rate of change of price level within one year
the existence of interest rate will make the currency appreciate in the future, while inflation will make the currency depreciate. Therefore, these are two forces in opposite directions
with inflation, we have to distinguish between "real interest rate" and "nominal interest rate"
a basic relationship is: real interest rate = nominal interest rate - inflation rate
Fourth, cross period selection
we can use some of the analysis tools we learned earlier, such as budget constraints and preferences, to analyze cross period selection. In other words, we can still use static analysis tools to analyze cross period selection. In order to understand this, we might as well think about it in this way, that is, we can understand the same commodity in different periods as different commodities. At the same time, we convert the income of different periods into the income of the same period by discounting. On this basis, we can get the budget line; At the same time, we get the indifference curve reflecting the consumption combination in different periods according to the consumers' preferences< (1) the best cross period choice
1. Budget constraint
we assume that a consumer lives only two periods and consumes only one commodity. How will he choose the combination of two periods
we use (C1, C2) to represent the consumption combination of two periods, where C1 is the consumption of the first period and C2 is the consumption of the second period. Let's assume that the consumer price remains the same in each period, which is equal to 1. Moreover, the monetary income of consumers in each period is M1 and M2, and the combination of monetary income is (M1, M2)
first of all, we assume that consumers can not borrow money to spend, and that savings do not generate interest (i.e. there is no capital market). What is the budget line and budget set of consumers
(draw a picture on the blackboard)
secondly, we assume that there is a capital market, the market interest rate is r, and the consumer is ready to put part of the first period of income into the second period of consumption, that is, he is a saver. In this case, C1 is less than M1. At the same time,
C2 = M2 + (m1-c1) + R (m1-c1) = M2 + (1 + R) (m1-c1)
finally, we assume that the consumer is a borrower, which means that he consumes part of the second period's income in advance. In this case, C1 is greater than M1. At the same time,
C2 = M2 - (c1-m1) - R (c1-m1) = M2 + (1 + R) (m1-c1)
whether consumers are savers or borrowers, the expression of C2 is the same, in fact, this is the budget line formula
through algebraic transformation, we can also get two other budget constraint formulas, That is to say,
(1 + R) C1 + C2 = (1 + R) M1 + M2 (income represented by future value)
and
C1 + C2 / (1 + R) = M1 + m2 / (1 + R) (income represented by present value)
these two equations can be expressed as:
p1x1 + P2X2 = p1m1 + p2m2
(Note: different processes P1 and P2 represent different values)
(drawing on the blackboard) < B R / >
2. Consumer preference
according to the above, the shape of indifference curve reflects consumers' preference for consumption combination in different periods
the indifference curve of complete substitution shows that consumers don't care whether they spend in the current period or the next period
the complete complementary indifference curve shows that consumers always allocate the consumption of the current period and the next period according to a fixed proportion
a more realistic indifference curve or a good indifference curve, that is, consumers are willing to substitute part of the current consumption for the next one, and the amount of substitution depends on the consumer's consumption pattern. In this case, preference is convex< (2) comparative static analysis
1. Determination of consumer type
under what circumstances is a consumer a borrower? Under what circumstances are consumers depositors< When C1 > M1, the consumer is the borrower
when C1 < M1, consumers are depositors< 2. The impact of interest rate changes on consumer behavior
the change of interest rate actually affects the price ratio of consumption in different periods, so it will affect the budget set and budget line of consumers, and ultimately affect the optimal consumption combination of consumers
if the interest rate rises, the depositor will continue to be the depositor
if the interest rate falls, the borrower will continue to be the borrower
(draw a picture on the blackboard to explain, which can be proved according to the display preference principle)
how the behavior of the borrower changes after the interest rate rises and how the behavior of the depositor changes after the interest rate falls, which shows what the display preference principle can't tell us
however, after the interest rate rises, if the borrower continues to be a borrower, his situation will certainly get worse; After the interest rate drops, if the depositor continues to be a depositor, his situation will certainly get worse< The change of interest rate leads to the change of consumer price and demand in different periods
changes in demand can also be decomposed into substitution effect and income effect
taking the increase of interest rate as an example, we use the budget constraint of future value to analyze that the increase of interest rate is equal to the increase of the price of the first period consumption. According to the slatsky equation, we get:
Δ c1t / Δ p1 = Δ c1s / Δ p1 +m1－c1 Δ c1m / Δ m
— +
according to the above expression, we can dece that if the consumer is a borrower, then the rise of interest rate will rece his consumption in the first period; However, for consumers as depositors, the overall effect is not obvious.
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