For example, a person's utility function U=3X 1X2, then its derivative is U'=MU 1=3X2.
Read the book several times, and the most important thing is to do the exercises in the book well. These exercises can help you understand. I am also reviewing at a micro level, but it is for the postgraduate entrance examination. After you have thoroughly studied the exercises in the book, you can fully cope with the exam. Gao Hongye's practice is quite useful.
If you have any problems, you can come to me.
I'll give you the answers to the exercises behind the microscope:
Microeconomics (Gao Hongye 3rd Edition) Chapter 2 refers to the answers to exercises.
1. It is known that the demand function of a commodity in a certain period is Qd=50-5P, and the supply function is Qs=- 10+5p.
(1) Find the equilibrium price Pe and the equilibrium quantity Qe, and make a geometric figure.
(2) Assuming the supply function remains unchanged, the demand function becomes Qd=60-5P due to the improvement of consumers' income level. Find out the corresponding equilibrium price Pe and equilibrium quantity Qe, and make a geometric figure.
(3) Assuming that the demand function remains unchanged, the supply function becomes Qs=-5+5p due to the improvement of production technology. Find out the corresponding equilibrium price Pe and equilibrium quantity Qe, and make a geometric figure.
(4) Use (1)(2)(3) to explain the connection and difference between static analysis and comparative static analysis.
(5) Use (1)(2)(3) to explain the influence of demand change and supply change on the equilibrium price and quantity.
Qd=50-5P gives the solution (1).
Qs=- 10+5p
Qd=Qs
D: 50-5P=- 10+5P
So Pe=6 Qe=20.
(2) Qd=60-5P
Qs=- 10+5p
Qd=Qs
D: 60-5P=- 10+5P
So Pe=7 Qe=25.
(3) Qd=50-5P
Qs=-5+5p
Qd=Qs
50-5P=-5+5P
So Pe=5.5 Qe=22.5.
(4) The connection between static analysis and comparative static analysis: it is assumed that the adjustment time of variables is zero. In (1)(2)(3), all exogenous or endogenous variables belong to the same period. Moreover, in the process of analyzing the change of endogenous variables caused by the change of exogenous variables, it is also assumed that this adjustment time is zero.
Difference: Static analysis is an analysis method to find the endogenous variable value according to the established exogenous variable value. As shown in figure (1), the exogenous variables α, β, δ, γ are determined, and the corresponding equilibrium price Pe and equilibrium quantity Qe are obtained. In (2) and (3), exogenous variables are given different values, and the values of endogenous variables P and Q are also different. This kind of research on the influence of exogenous variables on endogenous variables and the analysis and comparison of different values of endogenous variables of exogenous variables is called comparative static analysis.
(5) Firstly, analyze the influence of demand change:
According to (1), when Qd=50-5P and Qs=- 10+5p, the equilibrium price Pe=6 and the equilibrium quantity Qe = 20. When the demand increases, such as Qd=60-5P in (2), it is concluded that P=7 and q =. Therefore, when the supply is constant, the change of demand leads to the change of equilibrium price and equilibrium quantity in the same direction.
Re-analyze the impact of supply changes;
According to (1), when Qd=50-5P and Qs=- 10+5p, the equilibrium price Pe=6 and the equilibrium quantity Qe = 20. When the supply increases, such as Qs=-5+5p in (3), P=5.5 and Q = are obtained. Therefore, when the demand is constant, the change of supply leads to the change of equilibrium price in the opposite direction and the change of equilibrium quantity in the same direction.
2 Suppose Table 2-5 is the demand table of demand function Qd=500- 100P within a certain price range:
Commodity demand table
Price (RMB) 1 2 3 4 5
Demand 400 300 200 100 0
(1) Find the price arc elasticity of demand between 2 yuan and 4 yuan.
(2) According to the given demand function, find the price elasticity of demand with P=2.
(3) Make the corresponding geometric figure according to the demand function or demand table, and calculate the price elasticity of demand when P=2 by geometric method. Is it the same as the result of (2)?
Solution (1)
(2)
(3) As shown in the figure below,
The result is the same as that of (2)
Suppose the following table is a supply table, and the supply function Qs=-3+2P within a certain price range.
Commodity supply list
Price (RMB) 2 3 4 5 6
Supply 1 3 5 7 9
(1) Find the price arc elasticity of supply between 3 yuan and 5 yuan.
(2) According to the given supply function, find the price elasticity of supply with P=4.
(3) According to the supply function or supply table, the corresponding geometric figure is made, and the price point elasticity of supply is calculated by geometric method when P=4. Is it the same as the result of (2)?
Solution (1)
(2)
(3) As shown in the figure below,
The result is the same as that of (2)
There are three linear demand curves AB, AC and AD in the following figure.
(1) Compare the price elasticity of demand at point A, point B and point C. ..
(2) Compare the demand price elasticity of A, F and E. ..
The solution (1) shows that the three points A, B and C are on a straight line, and the straight line ab is parallel to the straight line OQ. Let the straight line ab intersect with the straight line OP and the point e.
At point a,
At point b,
At point c,
So the needs of A, B and C are
The elasticity of the price point is the same.
(2) According to the figure, three points A, E and F are on a straight line, and the straight line ae is parallel to the straight line OP, so let the straight line ae intersect with the straight line OQ and point G.
At point a,
At point f,
At point e,
Due to GB
So <<
Suppose that the functional relationship between a consumer's consumption quantity Q and income M is M= 100Q2. Find the elasticity of income point of demand when income M=2500.
Solution, because M=Q2, Q=
So when M=2500, Q=5.
At this point, Em=
When M=2500 and Q=5, Em=
6 suppose the demand function is Q=MP-N, where m stands for income, p stands for commodity price, and n (n >; 0) is a constant. Seek: price point elasticity of demand and income point elasticity of demand.
Solution, because Q=MP-N
So =-MNP-N- 1, = p-n.
therefore
Em=
Suppose there are 100 consumers in a commodity market, of which 60 consumers buy13 of the commodities in the market, and the price elasticity of each consumer's demand is 3: the other 40 consumers buy 2/3 of the commodities in the market, and the price elasticity of each consumer's demand is 6. Q: According to 100 consumers, what is the price elasticity coefficient of total demand?
We assume that the total quantity of this commodity purchased by this 100 consumer is Q, and its market price is P. From the meaning of the question:
Q 1= Q2=
because
therefore
and
therefore
but
therefore
8 Suppose the price elasticity of a consumer's demand Ed= 1.3, and the income elasticity of demand Em=2.2. Q: (1) What's the effect of a 2% drop in commodity prices on the quantity demanded, other things being equal?
(2) The impact of a 5% increase in consumer income on demand, other things being equal.
The solution (1) is given by Ed= 1.3.
So if the price drops by 2%, the demand will increase by 2.6%.
(2) Because Em=2.2
Therefore, when the consumer's income increases by 5%, the consumer's demand for this commodity will increase 1 1%.
Suppose that two manufacturers A and B are competitors who produce the same different product in a certain market; The demand curve of this market for vendor A is PA=200-QA, and that for vendor B is Pb = 300-0.5 × QB; The current sales of the two manufacturers are QA=50 and QB= 100 respectively.
Q: (1) What are the price elasticities of demand of two manufacturers, A and B?
(2) If manufacturer B reduces the price, the demand of manufacturer B will increase to QB= 160, while the demand of competitor A will decrease to QA=40. So, what is the cross-price elasticity EAB of manufacturer A's demand?
(3) If firm B pursues the maximization of sales revenue, do you think that firm B's price reduction is the right choice?
The solution when QA=50 and PA=200-50= 150 (1).
When QB= 100, PB=300-0.5× 100=250.
therefore
(2) When QA 1=40, PA 1=200-40= 160 and
When Pb1= 300-0.5×160 = 220 and
therefore
(3)∵R=QB？ PB= 100？ 250=25000
R 1=QB 1？ PB 1= 160？ 220=35200
R < r 1, that is, sales revenue increases.
Manufacturer b's price reduction is the right choice.
10 graphically illustrates the relationship between the price elasticity of demand and the sales revenue of manufacturers, and illustrates it with examples.
A) when Ed >; Sales of point a 1.
Income p? Q is equivalent to the area Op 1AQ 1, point B.
Sales revenue p? Q is equivalent to the area OP2bQ2.
Obviously, the area op 1aq 1 area OP2bQ2.
Therefore, when ED < 1, the price reduction will reduce the sales revenue of the manufacturer, and the price increase will increase the sales revenue of the manufacturer, that is, the commodity price changes positively with the sales revenue of the manufacturer.
For example, suppose the ED of a commodity is 0.5, and the demand is 20 when the commodity price is 2. The sales revenue of the manufacturer is 2×20=40. When the commodity price is 2.2, that is, the price rises 10%, the demand drops by 5% because of Ed=0.5, that is, it drops to 19. At the same time, the sales revenue of the manufacturer =2.2× 1.9=4 1.8. Obviously, the sales revenue of manufacturers has increased after the price increase.
C) when Ed= 1, point a sells.
Income p? Q is equivalent to the area Op 1AQ 1, point B.
Sales revenue p? Q is equivalent to the area OP2bQ2.
Obviously, the area OP 1aQ 1= the area OP2bQ2.
Therefore, when Ed= 1, lowering or raising the price has no effect on the sales revenue of the manufacturer.
For example, suppose that the ed of a commodity =1,the price of the commodity is 2, and the demand is 20. The sales revenue of the manufacturer is 2×20=40. When the commodity price is 2.2, that is, the price rises 10%, because Ed= 1, the demand drops 10%, that is, to 18. At the same time, the sales revenue of the manufacturer =2.2× 1.8=39.6≈40. Obviously, the sales revenue of manufacturers has not changed after the price increase.
1 1 Illustrate three situations of cobweb model with graphs.
The first case: relative to the price axis,
The absolute value of the slope of the demand curve is greater than that of the slope of the supply curve.
The absolute value of the slope. When the market is disturbed
After deviating from the original equilibrium state, the actual price and
The actual output will fluctuate at the equilibrium level, but
The fluctuation range is getting smaller and smaller, and finally it will return to the original equilibrium point.
Suppose that in the first period, due to some external interference, the actual output dropped from Qe to Q 1. From the consumption curve, consumers are willing to pay the price of P 1 to buy all of Q 1. The price of P 1 is higher than that of Pe, so the producers in the second stage will increase the output of this commodity to Q2. If the supply increases and the price drops to P2, the producer with too low price will reduce the output to Q3, and the price of Q3 is P3, which determines Q4…… ........................................................................................................................................ In the diagram, the path of output and price changes forms a cobweb-like figure, so it is called cobweb diagram. Because the elasticity of supply is less than the elasticity of demand, it is called the stable condition of cobweb and the "convergent" cobweb.
The second case: relative to the price axis,
The slope of the demand curve is absolutely smaller than the supply.
Absolute value of curve slope. When the market is due to
After being disturbed and deviating from the initial equilibrium state,
The actual price and output will bypass the equilibrium water.
Up and down, but the fluctuation range is getting bigger and bigger.
The bigger it is, the farther it deviates from the equilibrium point. It can be seen that the spider web model in the figure is unstable, so the corresponding spider web is called "divergent" spider web.
The third case: relative to the price axis,
The absolute value of the slope of the demand curve is equal to the supply.
Absolute value of curve slope. When the market is due to
After being disturbed and deviating from the initial equilibrium state,
The actual price is the same as the actual output.
The degree fluctuates around the equilibrium point. corresponding
Spider webs are called "closed" spider webs.
The third chapter of Microeconomics (Gao Hongye Third Edition) refers to the answers to the exercises.
1. According to the consumption equilibrium condition of cardinal utility theory, how should consumers adjust the purchase quantity of two commodities? Why? If i= 1 and 2, how should I adjust it? Why?
Solution: can be divided into or
At this time, it shows that the marginal utility of the same dollar 1 is greater than that of the commodity 2, and rational consumers should increase the commodity 1 and decrease the commodity 2.
At this time, it shows that the marginal utility of the same dollar 1 is less than that of the commodity 2, and rational consumers should increase the commodity 2 and decrease the commodity 1.
2. According to the consumption equilibrium condition of ordinal utility theory, how should consumers adjust when or when to buy two kinds of goods? Why?
Solution: If, then, from the right side of the inequality, consumers reduce their purchases by 2 1 unit in the market, they can increase their purchases by 1 unit. From the left side of the inequality, the consumer's preference is that when the purchase amount of commodity 2 decreases by 1 unit, the original satisfaction can be maintained only by increasing the purchase amount of commodity 1 by 0.5 unit. In this way, consumers will get 0.5 unit of goods 1, which increases the total utility. Therefore, in this case, rational consumers will inevitably reduce the purchase of commodity 2 and increase the purchase of commodity 1 in order to obtain greater utility.
On the contrary, if, then, from the right side of the inequality, in the market, consumers buy less goods of 1 unit, and they can buy more goods of 1 unit. As can be seen from the left side of the inequality, consumers' preference is that when purchasing 1 unit of goods 1 is reduced, they only need to purchase 0.5 unit of goods 2 to maintain their original satisfaction. In this way, consumers will get 0.5 more units of commodity 2, thus increasing the total utility. Therefore, in this case, rational consumers will inevitably reduce the purchase of commodity 1 and increase the purchase of commodity 2 in order to obtain greater utility.
It is known that the price of a shirt is 80 yuan and the price of a KFC snack is 20 yuan. What is the marginal substitution rate of a KFC snack for a shirt at the equilibrium point where consumers maximize the utility of these two commodities?
Solution: consumer equilibrium time: Mrs12 = mu1/mu2 = p1/p2 =1/4.
The replacement rate of shirts in KFC is 1/4.
Suppose a consumer's equilibrium is as shown in Figure 3-22. Among them, the horizontal axis and the vertical axis respectively represent the quantity of commodity 1 and commodity 2, the line segment AB is the consumer's budget line, the curve U is the consumer's indifference curve, and the point E is the equilibrium point of utility maximization.
Seeking the income of consumers;
Seek the top grade price;
Write the equation of the budget line;
Find the slope of the budget line;
Find the value of point e.
Solution: (1) I = p1x1= 60.
(2) The slope of the budget line =-P 1/P2 =-2/3, and P2=3.
(3) According to I=P 1X 1+P2X2, the equation of the budget line is 2X 1+3X2=60.
(4) the slope of the budget line =-P 1/P2 =-2/3,
(5)Mrs 12 = mu 1/MU2 = p 1/P2 = 2/3
5 It is known that a consumer buys goods 1 and goods 540 yuan every year, and the prices of the two goods are =20 yuan and =30 yuan respectively. The utility function of consumers is, how much should consumers buy these two commodities every year? What is the total utility gained from it? (1) Solution: (1) Because
Equilibrium conditions:
mu 1/MU2 = p 1/P2 3x 22/6x 1x 2 = 20/30( 1)
20X 1+30X2=540 (2)
Based on the equations of (1) and (2),
X 1=9 and X2= 12 can be obtained.
(2)U=3X 1X22=3888
6. Suppose there are only two consumers A and B in a commodity market, and their demand function is sum.
List the demand table and market demand table of these two consumers;
According to (1), draw the demand curve and market demand curve of these two consumers.
Solution: (1) A consumer's demand table is:
P 5 4 3 2 1 0
QAd 0 4 8 12 16 20
B the consumer's demand table is:
P 6 5 4 3 2 1 0
QBd 0 5 10 15 20 25 30
The market demand table is:
P 6 5 4 3 2 1 0
Qd 0 5 14 23 32 4 1 50
(2) The consumer demand curve is:
B consumer demand curve is:
The demand curve of the market is:
7. Assuming that the utility function of consumers is, the price of two kinds of goods is, and the income of consumers is m, the demand functions of consumers about goods 1 and goods 2 are obtained respectively.
Mr 12 = mu 1/MU2 = p 1/P2 X2/x 1 = p 1/P2
P 1X 1=P2X2( 1)
P 1X 1+P2X2=M(2)
∴P 1X 1=M/2 P2X2=M/2
That is X 1=M/2P 1 X2=M/2P2.
8. Let a consumer's income be m and the prices of two commodities be. Assume that the indifference curve of consumers is linear and the tangent slope is-a.
Seeking: the best product mix for consumers.
Solution: Because the indifference curve is a straight line, this consumer has three optimal consumption choices.
The first case: when Mrs12 >; When P 1/P2, as shown in the figure, the position of the most effective equilibrium point e appears on the horizontal axis, which means that the optimal solution at this time is a corner solution, that is, X 1=M/P 1, X2=0. That is to say, consumers spend all their income on goods 1, thus reaching the maximum utility level, which is marked by the indifference curve represented by the solid line in the figure. Obviously, the utility level is higher than that of any other commodity combination on a given budget line, such as the utility level of the indifference curve represented by the dotted line.
The second case: when Mrs 12
In the third case, when MRS 12=P 1/P2, as shown in the figure, the indifference curve overlaps with the budget line, and the equilibrium point of utility maximization can be the commodity combination at any point on the budget line, that is, the optimal solution is X 1≥0 and X2≥0, which satisfies p1.
9. Assume that the utility function of consumers is, where q is the consumption of a commodity and m is the income. Q:
Demand function of consumers;
Anti-demand function of consumers;
Consumer surplus when q=4.
Solution: (1)
MU/P =
therefore
(2)
(3)
10, considering the substitution effect and income effect of a consumer's purchase of commodity A, assume that the consumer's demand function for commodity A is Q=0.02-2P, income m = 6,500, and price P=20. If the current price of commodity A rises to P=40.
Q: What is the total effect of the price change of commodity A? Among them, what are the substitution effect and income effect respectively?
(General project)
Solution: Q 1=0.02×6500-2×20=90.
Q2=0.02×6500-2×40=50
The total utility is 50-90=-40.
According to the definition of substitution utility, consumers should keep their real income unchanged, so they should increase their income by (40-20)×90= 1800.
q 1 = 0.02×(6500+ 1800)-2×40 = 86
Substitution effect: 86-90=-4
Income effect: -40-(-4)=-36
1 1. How do users derive the demand curve under the cardinality?
Cardinal utility theorists believe that the demand price of a commodity depends on its marginal utility. The smaller the marginal utility of a unit, the lower the price consumers are willing to pay. Due to the law of diminishing marginal utility, with the increase of consumption, the highest price that consumers are willing to pay for this commodity, that is, the demand price, will be lower and lower. Draw each consumption and its relative price on the map and you will get the consumption curve. Moreover, because the change direction of commodity demand and commodity price is opposite, the consumption curve is inclined to the lower right.
12 illustrates the analysis of consumer equilibrium conditions by ordinal utility theorists and the derivation of demand curve on this basis.
Solution: consumer equilibrium conditions:
The highest available thing
Difference curve
Tangent to the budget line,
That is MRS 12=P 1/P2.
Derivation of demand curve: From the diagram, the price and demand of each equilibrium point are in one-to-one correspondence, which are drawn on the diagram respectively, that is, the demand curve X 1=f (P 1).
13. Analyze the substitution effect and income effect of normal goods, low-grade goods and giffen goods with graphs, and further explain the characteristics of demand curves of these three kinds of goods.
Solution: the substitution effect and income effect caused by the change of commodity price and the shape of demand curve
The substitution effect of commodity types and
Price, income effect and
The relationship between price, total effect and
Relationship between price and shape of demand curve
Ordinary commodity
Low-grade commodity
Ji Fen changes in the opposite direction.
Change in the opposite direction
Change in the opposite direction
Co-directional change
Co-directional change and reverse change
Change in the opposite direction
In the same direction, tilt to the lower right.
Tilt to the lower right.
Tilt to the upper right
chapter four
Variable factor quantity, variable factor total output, variable factor average output and variable factor marginal product.
1 2 2 2
2 12 6 10
3 24 8 12
4 48 12 24
5 60 12 12
6 66 1 1 6
7 70 10 4
8 70 35/4 0
9 63 7 -7
(2) Yes. Because marginal products have the characteristics of rising first and then falling.
Variable factor input from unit 4 to unit 5.
2.
(1). The tangent slope passing through any point of the TPL curve is the value of the corresponding MPL.
(2) The slope of the line segment connecting the hot spot on the TPL curve and the coordinate origin is the corresponding APL value.
(3) when MPL >; When APL, APL curve rises.
When mpl
When MPL=APL, the APL curve reaches the maximum.
3. at point a, there is MRTS >；; W/R, it can be seen that in the factor market, manufacturers reduce labor purchase 1 unit under the condition of constant total expenditure. In the production process, the manufacturer reduces the capital investment by 1 unit, and only needs to increase the labor input by 0.25 unit to maintain the original output level. Therefore, as long as mrts >: W/R, manufacturers will continue to replace capital with labor without changing the total cost. The manufacturer's production will continue to approach from point A to point E along the equal cost line AB.
At point B, contrary to the above-mentioned manufacturer's practice at point A, as long as MRTS
(1). TPL function of total labor output =20L-o.5L2-50.
Average labor output APL function = TPL/L = 20-0.5L-50/L.
MPL function of marginal product of labor =dTPL/dL=20-L
(2) When MPL=0, TPL reaches the maximum. L=20。
When MPL=APL, APL reaches the maximum. L= 10。
When L=0, MPL reaches the maximum.
(3) According to (2), when L= 10, MPL=TPL= 10.
5. According to the meaning of the question, when the fixed input ratio of production factors is the best combination,
Q=L=4K，Q=32，
L=32，K=8
When Q= 1000, it can be obtained by the optimal combination: 100=L=4K.
L= 100，K=25
C=PLL+PKK=325
6. Let the labor price be W, the capital price be R and the cost be C..
C=WL+rK
Take a point on the expansion line and set it as the tangent of the equal cost line and the equal volume line.
MPL/MPK=W/r
( 1). 1.K/2L=W/r
2.K2/L2=W/r
3.2K/L=W/r
4.K=3L
(2). 1. 1000 = 5k 2/3l 1/3，K=2L。 K=50.2 1/3。 L= 100.2 1/3
2.K=L= 1000。
3.k=5？ 2 1/3，L= 10？ 2 1/3
4.k= 1000，L= 1000/3。
7.( 1).Q=AL 1/3K 1/3
F( λl，λK)= A(λL) 1/3(λK) 1/3 =λal 1/3k 1/3 =λf(L，K)
Therefore, this production function belongs to the production function with constant returns to scale.
(2) Assuming that in short-term production, the amount of capital investment remains unchanged, expressed as; And labor force
Input variable, denoted by l.
For the production function Q=AL 1/3K 1/3, there are:
MPL= 1/3AL-2/3K 1/3，dmpl/dl =-2/9al-5/3-2/3
This shows that, under the premise of constant short-term capital investment, with the increase of variable factor labor input, the marginal product of labor is decreasing.
Similarly, under the premise of constant short-term labor input, with the increase of capital input of a variable factor, the marginal product of capital is decreasing.
8.( 1). According to the meaning of the question, c = 2l+k.
Q=L2/3K 1/3
To achieve maximum output: MPL/MPK=W/r=2.
When C=3000, we get. L=K= 1000。
Q= 1000。
(2). The same is true. 800=L2/3K 1/3.2K/L=2
L=K=800
C=2400
9. As shown in the figure, analyze the relationship between three equal income lines Q 1, Q2, Q3 and equal cost line AB. Although the equiyield line Q3 is higher than the equiyield line Q2. But the only equal cost line AB and equal output line Q3 have neither intersection nor tangent. This shows that the output represented by the equal output curve Q3 is the output that an enterprise cannot achieve at a given cost. Look at Q 1. Although it intersects with the unique isocost line at points A and B, the output represented by the isooutput curve Q 1 is relatively low. Therefore, it is only necessary to change the combination of elements from point A to the right or from point B to the left along the established equal cost line AB to increase the output. Therefore, only at the tangent point E of the unique equal cost line AB and the equal output curve Q2 is the combination of factors that can achieve the maximum output at a given cost.
10 As shown in the figure, although the equal cost curve A "b" represents low cost, it has neither intersection nor tangent with the established yield curve Q, so the yield represented by the equal cost curve Q cannot be realized. Although the equal cost curve AB intersects with the established yield curve Q at points A and B, it represents high cost, and the same result can be obtained by moving from point A to point E or from point B to point E along the equal yield curve Q. Therefore, only at the tangent point e is the combination of elements that can achieve the minimum cost under the given output conditions.