EC2066 : A Firm Hires Workers from a Competitive labor Market The firm Faces the Problem that Employees Might shirk x: Microeconomics Assignment, UOL, Singapore

SECTION A
Answer all FIVE questions from this section

1. A firm hires workers from a competitive labor market. The firm faces the problem that employees might shirk (avoid working hard). The firm’s policy is to monitor the workers occasionally and fire any worker caught shirking. This policy does not reduce shirking if the firm pays its workers the market-clearing wage. However, if the firm pays a wage greater than the market-clearing wage, this policy is effective in reducing shirking. Is this true or false? Explain your answer.

2. Short-run average cost exceeds long-run average cost only when there are economies of scale. Is this true or false? Explain your answer.

3. If the wage rate falls in a competitive labor market, demand for leisure by workers must increase. Is this true or false? Explain your answer.

4. A monopolist faces a constant marginal cost c and sets a price p = λc where λ > 1. The absolute value of market demand elasticity is given by |ε| = 3. Calculate the profit-maximizing value of λ.

5. u(x, y) = x 2+ y2 . The price of x is 3 and the price of y is 2. The consumer’s income is 18. What is the optimal consumption bundle? [Hint: Compare interior bundles to corner solutions.]

SECTION B

Answer THREE questions from this section

6. Consider the following extensive-form game with two players, 1 and 2.

(a) Find the pure-strategy Nash equilibria of the game. [8 marks]

(b) Find the pure-strategy subgame-perfect equilibria of the game. [6 marks]

(c) Derive the mixed strategy Nash equilibrium of the subgame. If players play
this mixed Nash equilibrium in the subgame, would 1 play In or Out at the
initial node? [6 marks]

[Hint: Write down the normal form of the subgame and derive the mixed strategy Nash equilibrium of the subgame. Next, compare the payoff of player 1 from the mixed strategy equilibrium with 1’s payoff from playing Out.]

7. Suppose there are two identical firms in an industry. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by q2. The cost function of firm 1 is given by C(q1) =q2 1/2 and the cost function of firm 2 is given by C(q2) = q22/2. Let Q denote total output, i.e. Q = q1 + q2. The inverse demand curve in the market is given by P = 420 − Q

(a) Find the Cournot-Nash equilibrium quantity produced by each firm andthe market price.

(b) What would be the quantities produced by each firm and market priceunder
Stackelberg duopoly if firm 1 moves first?

(c) Suppose the firms can collide and produce a total quantity Q. Suppose firm 1 produces a fraction α of Q (so q1 = αQ) and firm 2 produces a fraction (1 − α) of
Q (so q2 = (1 − α)Q). What value of α minimizes the total cost of producing Q?

[Hint: Write the expression for C(q1)+ C(q2) and minimize with respect to α.]

(d) Using the cost-minimizing value of α from part (c), find the quantity produced by each firm under collusion and the market price.

8. (a) Lee does not have insurance against car theft. His car is worth 45. He can park his car on the street or pay to park in a garage. If parked on the street, the car is stolen with a probability of 1/3. If parked in a garage, the car is safe from theft. Including the value of his car, Lee has a wealth of 81. His utility from wealth W isu.

i. Calculate the maximum amount that Lee is willing to pay to park in a garage.

ii. Now suppose Lee’s risk preference changes so that he becomes
risk-neutral, The utility function representing his preference over wealth levels is given by u(W) = W. In this case, what is the maximum amount that Lee is willing to pay to park in a garage?

(b) Rachel has 100 to invest. Two assets, 1 and 2, are available for investment. An amount y invested in asset 1 yields a total return of 1.1y. An amount x invested in asset 2 yields a risky total return of x with a probability of 0.5 and
1.21x with probability 0.5. Rachel’s utility function is given by U(w) = ln(w)
where w is wealth after investing.

Let any portfolio be denoted by (x, y) where x is the amount invested in the risky
asset (asset 2) and y = 100 − x is the amount invested in the safe asset (asset 1).
How much should Rachel invest in the risky asset?

9. A monopolist has two customers with the following demand functions:
Q1 = 70 − P1 (Demand of customer 1)
Q2 = 110 − P2 (Demand of customer 2)

Here Pi is the price charged to customer i, i ∈ {1,2}. The monopolist has a constant marginal cost of 10 and no fixed costs.

(a) Suppose the monopolist can differentiate between the customers, and
the customers cannot trade between themselves, allowing the monopolist to engage in third-degree price discrimination. What is the price charged to each consumer?

(b) Now suppose the monopolist cannot differentiate between the customers and must charge them the same price. Calculate the monopolist’s optimal single price P as well as the quantity sold to each customer.

(c) Is the total surplus (consumer surplus plus profit) higher under a single price or underprice discrimination? Explain.

(d) Suppose, as, in part (b), the monopolist cannot differentiate between the customers. However, in addition to a per-unit price P, the monopolist can also charge a fixed fee F. A customer must pay this fee irrespective of the quantity purchased when a positive amount is purchased. Derive the monopolist’s optimal price and fee.