Exam Number: 42424242

University of Melbourne

Department of Economics

Intermediate Microeconomics, ECON 20002

Mock Final Examination (Semester 1, 2021)

Time Allowed: Three Hours Reading Time: 30 minutes

This examination paper contributes 60 percent to the assessment in ECON 20002.

This paper consists of 6 problems. This exam has 6 pages.

Problem 1: [10 marks] Consider an individual with preferences defined over two goods,

X1 and X2. This individual has preferences that can be represented by the following

utility function:

u(X1, X2) = X1 +X

0.5

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Let P1 = 4 and P2 = 2. In addition, suppose this individual has an income of $120.

(a) [1.5 marks] Write down the expression for this consumer’s marginal rate of

substitution of X1 for X2 (MRS12). Identify the distinguishing feature of this par-

ticular MRS12.

(b) [3 marks] Calculate the optimal basket of X1 and X2 and fully illustrate this

optimal choice in a diagram with X1 on the horizontal axis.

(c) [2 marks] Suppose the government introduces a $2 tax on the consumption of

each unit of X2 but X1 remains tax-free. Calculate the new optimal basket of X1

and X2. Illustrate this new optimal choice in your diagram above.

(d) [3.5 marks] Calculate the amount of monetary transfer needed to return this

consumer to her original utility level.

Problem 2: [10 marks] Consider a firm that uses capital (K) and labour (L) to produce

output (q) according to the following long-run production function:

q =

√

L+

√

K

(a) [2 marks] Use the tangency condition to derive an expression for this firm’s

expansion path.

(b) [4 marks] Let the price of each unit of labour be w and the (rental) price for

each unit of capital be r = 1. Determine the cost-minimizing labour input and the

cost-minimizing capital input for an output of q0. (Hint: you should not assume a

particular value for w)

(c) [1 mark] Find this firm’s long-run total cost function.

(d) [3 marks] Suppose instead that this firm’s long-run production function is

q = min

{

1

3

L,K

}

Assume that wages and rental rates are w and 1 respectively. Derive the long-run

total cost function for an output of q0 in this case.

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Problem 3: [10 marks] Consider a firm that is a monopolist in the market for good X.

The demand for X is

Q = 200− 2P

where P is the price of X and Q is the total quantity demanded. The monopolist’s total

cost function is

C = Q2 + 10Q

where C represents total costs.

(a) [3.5 marks] What is the monopolist’s profit maximizing output? What is the

price at this output? Fully illustrate this optimal output and price in an appropri-

ate diagram.

(b) [3.5 marks] What output and price maximizes the sum of consumer surplus and

producer surplus? Explain your answer. Add this output and price to your diagram

in part (a).

(c) [3 marks] Suppose that the monopolist is able to charge the price in (a) rather

than the price in (b). What is the resulting difference in consumer surplus, producer

surplus, and total welfare?

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Problem 4: [10 marks] Consider a risk-averse individual with an initial wealth of 100

and a utility function of the form

u(W ) = W 0.5

where W represents the payoff from a particular outcome. Suppose that this individual

faces a loss of L with probability 0.5. To reduce her risk, she would like to purchase an

insurance policy that gives her a payment of B if she suffers the loss. Suppose that the

cost of the policy is equal to the the premium, M .

(a) [1 mark] Assuming that the insurance policy is actuarially fair, what is the

premium that insurance companies will charge?

(b) [1 mark] Use all of the information above to write down an expression for this

individual’s expected utility with the actuarially fair insurance.

(c) [3 mark] Let the individual’s objective be to choose the optimal insurance pay-

ment, B. What is the optimal B?

(d) [3.5 marks] Suppose that for each dollar of benefit paid out, an insurance com-

pany incurs an additional fraction λ > 0 as an administrative cost. The insurance

company passes this cost on to the buyer by reducing the benefit paid by a fraction

λ. What is the individual’s optimal B in this case? How does it compare to your

answer in part (c)? You can assume that the the insurance industry is competitive

and the premium will be actuarially fair.

(e) [1.5 marks] Now let L = 40. Will this individual prefer having an insurance

policy where λ is greater than zero to not having insurance at all? Explain.

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Problem 5: [10 marks] Consider an industry with only two firms. The industry demand

curve is given by:

P = 100− 2QT

where QT is the total industry output and is the sum of both firm’s output of Q1 and Q2

respectively. Suppose that both firms have a constant marginal cost of $0. Suppose also

that there are no fixed costs of production.

(a) [6 marks] Let the firms engage in Cournot strategic competition. What is the

Cournot equilibrium price?

(b) [4 marks] Now suppose that there are n > 2 firms in the industry that all have

constant marginal costs of $0. Assume that the demand curve is as stated above

and no firm faces any fixed costs. Further assume that all n firms engage in Cournot

strategic competition. What is the Cournot equilibrium price now? What is the

difference between this price and the perfectly competitive market price when n is

large?

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Problem 6: [10 marks] Recent evidence suggests that unskilled labour’s share of total

factor expenditure has been decreasing globally. In this problem you are required to

examine one explanation for this trend. Suppose that a typical firm produces output

(q) using unskilled labour (LU), skilled labour (LS), and capital (K) according to the

following long-run production function

q =

√

LU +

√

αLS +

√

αK

where α ≥ 1 is a constant.

(a) [1.5 marks] Derive this firm’s marginal product of unskilled labour, skilled labour

and capital respectively.

(b) [3.5 marks] Let this firm’s target output be q = 10. Further, assume that the

wage of unskilled labour is wU = 1, the wage of skilled labour is wS = 2, and the

rental rate of capital is r = 2. Use this information to solve for the firm’s condi-

tional demand for unskilled labour, skilled labour, and capital respectively.

(c) [1.5 marks] Suppose that α = 1. Calculate this firm’s total cost of producing

q = 10. What fraction of this total cost of production is earned by unskilled labour?

(d) [3.5 marks] Now suppose that α = 2. Repeat the calculations in (c). What

has happened to unskilled labour’s share of the firm’s total cost? Can you provide

some intuition for this change?

END OF EXAMINATION

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