Reference no: EM133047487

MAN00023M Managerial Economics - University of York

Question 1
Consider a duopoly with homogenous goods where Firm 1 has the following production function:

Q₁ = F₁(L,K) = L^1/2 K^1/2,

where Q and K are measured in units and L in hours. Firm 2 uses labour and capital as well but has a different production function, given by

Q₂ = F₂(L,K) = L^1/3 K^2/3.

You may assume that the market for labour and capital is perfectly competitive and the current wage rate is £40 and the rental rate on capital is £10. Both firms sell their products on the same market with inverse demand function

P = 52 - (Q₁ + Q₂),

where P is measured in pound sterling.

a) Which production function(s) exhibit(s) decreasing returns to scale?

b) Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1?

c) Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2?

Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently, choose their strategies. Both firms are aiming to maximise their profits.

d) For each player (firm), what are their strategies? Write the game in normal form.

e) Find each player's dominant strategy (if they exists).

f) Find all Nash equilibria.

Question 2

Consider a monopolist operating on a market with a downward sloping demand curve. The monopolist has a constant marginal cost and no fixed cost. At the current level of production and at the current price level, the price elasticity of demand is equal to -0.8. Assume the monopolist wishes to maximise profits.

a) Would we be able to say anything about whether the monopolist has chosen a price and quantity that maximise profits? Explain your answer by means of diagrams (maximum 150 words).

b) What is the price elasticity of supply in this market?

Question 3

Fang likes playing badminton with her friends. Her utility function for playing badminton every week is given by

U(t) = 11t - 2t²,

where t is measured in hours. They play on a badminton court, which they can rent per hour. Suppose the current price to play on the badminton court is £2.50 per hour.

a) How many hours should Fang play if she wishes to maximise her utility?

b) Explain what we mean by the principle of diminishing marginal utility. Does the principle apply in Fang's case? Explain why.

c) In a diagram with income in pound sterling on the horizontal axis and quantity on the vertical axis, show the relationship between Fang's budget and the number of hours that would maximise her consumer surplus.

Question 4

YorMagnets and YorMugs are two companies selling merchandise to tourists visiting the city of York. YorMagnets sells fridge magnets and YorMugs sells mugs with images of popular attractions. Assume that YorMagnets is the only company producing magnets for York and YorMugs is the only company producing local mugs. The daily demand for magnets (until 2019) is given by

D₁ = 50/9 - 200/9 P₁ + 100/9 P₂,

where P1 is the price of magnets and P2 is the price of mugs. The daily demand for mugs (until 2019) is given by

D₂ = 500/9 - 200/9 P₂ + 100/9 P₁.

The marginal cost of producing magnets is £0.50 per magnet and the marginal cost of producing mugs is £2.00 per mug. Both firms simultaneously choose their quantities. You may assume that both firms aim to maximise profits.

a) Are magnets and mugs (perfect) complements or (perfect) substitutes? Explain your answer.

b) How would you characterise this market? Explain your answer.

c) Calculate the equilibrium price for both products and quantity for both firms.

d) Calculate the total producer surplus and deadweight loss.

Due to lockdowns and travel restrictions in 2020 and 2021, the number of tourists that visit York has significantly dropped.

e) Explain how a drop in tourists will have affected the demand curves. Also, explain the effect on the equilibrium price and quantity and the resulting producer surplus.

Question 5

Consider a perfectly competitive market with a price ceiling imposed by the government. If the deadweight loss is positive and the government decides to increase the price ceiling, then the deadweight loss will

A) increase.
B) decrease.
C) stay the same.
D) disappear.

Question 6
Which of the following statements is correct?
A) In a monopolistically competitive equilibrium price is chosen such that P=AC.
B) In a duopoly, there is negative relationship between a typical Cournot firm's marginal revenue and the elasticity of the residual demand curve such a firm faces.
C) In a monopoly, strategic entry barriers are always the result of absolute cost advantages.
D) Under perfect competition, in the short run there is insufficient time for new firms to enter the industry which leads to the result that firms always make positive supernormal profits.

Question 7
Maria has a fixed weekly budget which she has been spending on goods A, B, and C. Her utility function exhibits a diminishing marginal rate of substitution. She uses the equi-marginal principle to decide how much to purchase of each product. Suppose that for Maria's current consumption bundle it holds that

MU_A/P_A > MU_B/P_B = MU_C/P_C

You may assume that she has spent her entire budget. If Maria wishes to maximise utility, next week, she should
A) buy product A only.
B) buy products B and C only.
C) buy less of A and more of B and C.
D) buy more of A and less of B and C.

Question 8
Which of the following statements is correct?
A) The law of demand is only relevant for perfectly competitive markets.
B) The cross-price elasticity of demand for inferior goods is always negative.
C) In a perfectly competitive market with perfectly inelastic demand, the introduction of an ad-valorem tax will only affect the equilibrium price but not quantity.
D) Opportunity costs only exist for durable goods.