Question

1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per
unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro.
a) What is the marginal utility of good X (MUx) for the consumer? ( Answer: MUx = 10)
b) What is the marginal utility of good Y (MUy) for the consumer? ( Answer: MUy = 1)
c) Find the optimal qyantity of good x and good y for this consumer (assuming that the consumer’s
aim is to maximize his/her utility). (Answer: X*= 8 ; Y* = 0)
2. The consumer’s utility function is U (x ; y) = min {x/5 ; y}, where x denotes the quantity of good X
that the consumer consumes and y denotes the quantity of good Y that the consumer consumes.
The price per unit of good X is 10 euros and the price per unit of good Y is 30 euros. Consumer’s
income is 1600 euros. Find the optimal quantity of good X and good Y consumed by this consumer.
(Answer: x*= 100 ;y* = 20)
3. The consumer’s utility function is U(a,b) = ab2, where a denotes the quantity of good A that the
consumer consumes and b denotes the quantity of good B that the consumer consumes. The price
per unit of good A is 2 euros and the price per unit of good B is 4 euros. Consumer’s income is 1200
euros. Find the optimal quantity of good A and good B, for this consumer. (Answer: a*= 200; b*= 200)
4. Consumer’s utility function is: U(X,Y) = (X+2)(Y+3). Thus, the marginal utility of good x is
MUx = (Y+3) and the marginal utility of good y is MUy = (X+2) . The price per unit of good x is Px=2
and the price per unit of good y is Py=4. The consumer’s income is 60 euros. Find how many units of
x and y would the consumer consume? (Answer: X*= 17, Y* = 6.5)
5. The consumer’s demand for good X is described by the following function
X (Px; Py; Pw; M) = (M – Px + Py - Pw) / Px.
a) is the good X a normal good or an inferior good? Explain why?
b) is the good X an ordinary good or a Giffen good? Explain why?
c) are the good X and Y substitutes or complements for this consumer ? Explain why?
d) are the good X and W substitutes or complements for this consumer ? Explain why?
Find the explanations yourself with the help of lecture notes and Homework 1 Solutions.
6. The consumer’s demand for good X is described by the demand function X (Px, M) = M / 4Px,
where X denotes the quantity of good X demanded by the consumer, M denotes the consumer’s
income and Px denotes the price per unit of good X. Consumer’s income is 3600 euros and the price
of good X is 30 euros. Suppose that the price of good X decreases by 10 euros (i.e. the new price will
be 20 euros), ceteris paribus.
a) Calculate the total change in the quantity of good X demanded by the consumer (associated with
the price change described). (Answer: ΔxT = 15)
b) Calculate the substitution effect according to Slutsky (denote it by ΔXS ) associated with the price
change described) (Answer: ΔxS = 11.25)
c) Calculate the income effect according to Slutsky (denote it by ΔXM ) associated with the price
change described) (Answer: ΔxS = 3.75)
7. Consumer’s income is 4000 euros in current month and 6600 euros in the next month. The interest
rate in case of borrowing and lending is 10% per month. Inflation rate is 0%. Consumer’s utility
function is U(C1,C2) = C1 × C2, where C1 denotes the consumption in current month and C2 denotes
the consumption in the next month. Let’s also assume that the consumer is rational.
a) Find the present value (PV) of incomes for this consumer. (Answer: PV = 10000 euros)
b) Find the future value (FV) of incomes for this consumer. (Answer: FV = 11000 euros)
c) How would this consumer allocate his consumption between these two months considered?
(Answer: C1*= 5000 and C2*= 5500)
8. The consumer is facing following offers:
Offer 1: receive today 4000 euros and receive exactly in one year 6600 euros
Offer 2: receive today 5000 euros and receive exactly in one year 5500 euros
Which offer would the rational person accept if the nominal annual interest rate is 25% and the
expected inflation is 0%. (Answer: Offer 2)
9. The consumer’s utility function is U(a,b) = ab2, where a denotes the quantity of good A that the
consumer consumes and b denotes the quantity of good B that the consumer consumes. The price
per unit of good A is 4 Euros and the price per unit of good B is 8 euros. Consumer’s income is 120
euros.
a) Find the marginal utility of good A (MUa) and the marginal utility of good B (MUb) for the consumer.
(Answer: MUa = b2 and MUb = 2ab )
b) Find the optimal quantity of good A and good B, for this consumer. (Answer: a* = 10, b* = 10)
c) Government is considering 2 alternative taxation schemes:
- alternative 1: a tax of 12 Euros per unit of good A
- alternative 2: a tax of 8 Euros per unit of good B
If the consumer has to choose one of the taxation schemes, then which of these taxation schemes
will the consumer choose? Provide calculations for proof.
(Answer: Since U1(2.5; 10) = U2(10; 5) (i.e. the maximum utility that the consumer can achieve
under these alternative schemes is exactly the same) => the consumer will be indifferent
between these two alternative taxation schemes).
10. What is the market demand for good X (XT) if the individual A’s demand for X is XA = 20-PX and
individual B’s demand for X is XB = 10-2PX and there are 4 A-type and 2 B-type consumers in the
economy? PX denotes the price per unit of good x.
( Answer: XT = 100 - 8Px kui Px<5 , XT = 80- 4Px kui 5≤Px<20 , XT = 0 kui Px≥20 )
11. There are 100 type-A and 200 type-B consumers in the economy. Each type-A consumer’s
demand for good X is described by the function QA=10-P. Each type-B consumer’s demand for good
X is described by the function QB=24-3P. P is the price (in euros) of good X.
a) Describe the market demand for good X (by demand functions relevant for appropriate price
ranges) (see ”Market Demand” lecture notes!)
b) What is the market demand for good X if the price of good X is 9 euros? (Answer: QMarket = 100)
12. Market demand for good Y is described by function YD = 40-PD, where PD is the consumer price
and y is the quantity of good y demanded. Market supply of good Y is given by function YS = 10+PS,
where PS is the producer price and y is the quantity of good y supplied.
a) Find the market equilibrium that exists in this market before the tax and find also the market
equilibrium that will exist in this market after the tax. (Answer: equil.price P*=15, equil.quantity
Y*=25)
b) Suppose that a tax 10 euros is applied per unit of good Y, while the rest of the factors that could
affect demand or supply remain unchanged. Find the market equilibrium (the equilibrium quantity, the
demand price PD and the supply price PS) that will exist in this market after this tax. (Answer: Y*= 20,
PD*= 20, PS*= 10 )
c) Illustrate the pre-tax and after-tax market equilibrium on the graph. (see lecture notes!)
13. Market demand for good Y is described by function YD = 80-PD, where PD is the demand price
and YD is the quantity of good y demanded. Market supply of good Y is given by function YS = 20+PS,
where PS is the supply price and YS is the quantity of good y supplied.
a) Find the market equilibrium quantity and equilibrium price. (Answer: P* = 30; Y* = 50)
b) Suppose that a tax 20 euros is applied per unit of good Y, while the rest of the factors that could
affect demand or supply remain unchanged. Find the market equilibrium (the equilibrium quantity, the
demand price and the supply price) that will exist in this market after this tax. (Answer: PS*=20;
PD*=40; Y*=40)
c) Suppose that a subsidy 10 euros is applied per unit of good Y, while the rest of the factors that
could affect demand or supply remain unchanged. Find the market equilibrium (the equilibrium
quantity, the demand price and the supply price) that will exist in this market after this subsidy.
(Answer: PD*=25; PS*=35; Y*=55)
14. The consumer’s demand for good X is described by the function x = 600 – 10Px, where x denotes
the quantity of good X demanded and Px is the price (in euros) per unit of good X.
a) Calculate the consumer’s (net) surplus (CS) in the current conditions where the market price per
unit of good x is 20 euros. Illustrate the consumer’s (net) surplus in the graph. Mark very clearly the
area that corresponds to the consumer’s (net) surplus and identify very clearly all the numerical
values that are important for calculation of the consumer’s (net) surplus. (Answer: CS=8000 euros)
b) Suppose that the price of good X increases from 20 euros to 25 euros. Calculate the change in the
consumer’s (net) surplus (ΔCS) that is associated with this price increase of good X. Illustrate the
change in the consumer’s (net) surplus in the graph. Mark very clearly the area that corresponds to
the change in the consumer’s (net) surplus and identify very clearly all the numerical values that are
important for calculation of the change of consumer’s (net) surplus. (Answer: ΔCS = -1875 euros)
15. The firm requires at least 5 units of good A and 4 units of good B in order to produce one unit of
output Y.
a) Describe this technology by mathematical function and draw the production function.
(Answer: Y = min { A/5 ; B/4 } )
b) Draw the isoquant that corresponds to 40 units of output Y. (Find the solution yourself with the
help of class and homework examples)
16. The firm requires at least 1/2 units of good A or 4 units of good B in order to produce one unit of
output Y.
a) Describe this technology by mathematical function and draw the production function.
(Answer: Y = 2A + B/4 )
b) Draw the isoquant that corresponds to 40 units of output Y. (Find the solution yourself with the
help of class and homework examples)
17. Suppose that you have 1 million euros set aside for investment and suppose that there are only 3
investment opportunities available: 1) invest in Project A, which offers 6% return; 2) invest in Project
B, which offers 8% return, or 3) invest in project C, which offers 12% return.
a) What is your economic profit if you invest in project A? (Answer: Πecon = - 60,000 euros)
b) What is your economic profit if you invest in project C? (Answer: Πecon = 40,000 euros)
18. A firm, which is operating in the conditions of perfect competition, produces good Y. The
production function of this firm is y = 20x - 2x2, where y denotes the quantity of output Y and x
denotes the quantity of input X. Suppose that the price per unit of input X is 40 euros and the price
per unit of output Y is 10 eurot.
a) Find the marginal product of input X (Answer: MPx = 20 - 4x)
b) Find the profit-maximizing level of input. (Answer: x*=4)
c) and the profit-maximizing level of output for this firm. (Answer: y*=48)
d) What is this firm’s profit in case of its profit-maximizing output level? (Answer: Π*=320)
19. Suppose that the price per unit of input A is 10 euros and the price per unit of input B is 12 euros.
What is the minimum cost of producing 60 units of output Y for the firm if the firm’s production
function is Y = 5A + B? (Answer: Cmin(60) = 120 euros
20. Suppose that the price per unit of input C is 2 euros and the price per unit of input K is 6 euros.
What is the minimum cost of producing 100 units of output y for the firm if the firm’s production
function is Y = min {C/2 ; 4K}? (Answer: Cmin(100) = 550 euros)
21. The firm’s production function is Y = min {A/2 ; 4B} + C/2. Suppose that the price per unit of input
A is 4 euros, the price per unit of input B is 12 euros, the price per unit of input C is 6 euros. What is
the minimum cost of producing 60 units of output Y for this firm? (Answer: Cmin(60) = 660 euros)
22. Firm produces good Y, whereas fiirm’s production function is Y = min { K; A + 2B } + N/2. The price
per unit of input K is 2 euros, the price per unit of input A is 3 euros, the price per unit of input B is 5
euros and the price per unit of input N is 6 euros.
a) What is the minimum cost of producing 20 units of good y? (Answer: Cmin(20) = 90 euros)
b) How many units of input K, A, B and N would the firm use for producing 20 units of output Y when
it produces the output at minimal costs? (Answer: K = 20 , A = 0 , B = 10 , N = 0 )
23. Firm’s total costs are C(x) = 5x2 + 3x + 72. What are the firm’s ...
a) total variable costs
b) total fixed costs
c) average variable costs
d) average fixed costs
e) average costs
(Find the answers yourself with the help of class example)
24. The short-run total cost function of a competitive firm is C(y) = 500 + 6y + y2 . Marginal costs
(MC) are given by the function MC(y) = 6 + 2y . The market price of a unit of output y is 46 .
a) What is the profit-maximizing level of output y ? (Answer: y*=20)
b) What are the profits associated with this level of output? (Answer: Π* = -100)
c) Would it be better for this firm to shut-down its production or to continue producing in short-run?
(Assume that the firm is a profit-maximizer). Explain and justify your answer with calculations!
(Answer: since AVC=26 < Py => it is better to continue producing in short-run; Alternatively,
since Π(20) > Π(0) => it is better to continue producing in short-run because the loss will be
smaller than the loss if the production was 0)
25. The demand for monopolist’s output Y is described by function Y = 2000 – 100P. Suppose that
the cost function of monopolist is C(y) = 4y.
a) Find the marginal cost of Y for the monopolist (Answer: MC = 4 euros).
b) Find the formula, which describes the monopolist’s marginal revenue (Answer: MR = 20 - Y/50).
c) What is the profit maximizing output for this monopolist (assuming that price discrimination is not
possible)? (Answer: Y*= 800)
d) What is the price charged per unit of output Y by the monopolist (assuming that price
discrimination is not possible)? (Answer: P*= 12 euros)
e) Find the monopolist’s profit? (Answer: Profit = 6400 euros)
26. Monopolistis producing good Y. The market demand for good Y is described by function
y = 4200 – 20Py , where y denotes the quantity of good Y demanded and Py denotes the price of
good Y in euros. The total costs of this monopolist are described by the function C(y)= y2.
a) Find the equation, which describes the marginal revenue for the monopolist
(Answer: MR = 210 – (1/10)y )
b) Find the profit maximizing output of this monopolist (assuming that price disrimination is not
possible)? (An swer: y * = 100 )
c) Find the monopolist’s profit? (Answer: Profit = 10500 euros)
27. There are only two firms in an industry: firm A and firm B. Suppose that it is known that if:
• - both firms apply “high price” for their output, then the profit of firm A is 60 m.EUR and the
profit of firm B is 60 m.EUR.
• - both firms apply “low price” for their output, then the profit of firm A is 30 m.EUR and the
profit of firm B is 30 m.EUR.
• - Firm A applies “high price” and Firm B applies “low price”, then Firm A has a loss of 20
m.EUR and Firm B has a profit of 80 m. EUR.
• - Firm B applies “high price” and Firm A applies “low price”, then Firm B has a loss of 10
m.EUR and Firm A has a profit of 70 m.EUR.
a) Describe the profits of these firms in case of different sets of pricing strategies by matrix. (Find the
solution yourself with the help of class examples)
b) What is the optimal strategy for Firm A? (Answer: low price)
c) What is the optimal strategy for Firm B? (Answer: low price)
28. A matrix that describes the profits of firm A and firm B is following:
Firm B
Firm B
High price
Low price
Firm A
High price
( 14 ; 16 )
( 10 ; 25 )
Firm A
Low price
( 45 ; 5 )
( 25 ; 30 )
a) Is there a dominant strategy for firm A ? ( Answer: Yes, regardless of the firm B’s choice, the
optimal strategy for firm A is „low price“).
b) Is there a dominant strategy for firm B ? ( Answer: Yes, regardless of the firm A’s choice, the
optimal strategy for firm B is „low price“).

Answer 1

Answers are right. You have not mentioned what you want to ask. I hope you want to know whether answers are right. The answer is yes they are right