Reference no: EM132586722

L1061 Advanced Microeconomics Assignment - University of Sussex, UK

SECTION A - Attempt ALL questions

1. Answer all parts of this question.

a) Consider the following scenario: allocation X is socially preferred to allocation Y only if everyone prefers X to Y. This is sometimes called the Pareto ordering, since it is closely related to the idea of Pareto efficiency.

i) Firstly, explain what do we mean by a social choice rule (Maximum 75 words).

ii) Secondly, discuss the shortcomings of the rule stated in the scenario above, as a rule for making social decisions (Maximum 130 words).

b) Explain Arrow's impossibility theorem (Maximum 130 words).

c) According to Arrow's Impossibility Theorem we cannot use a welfare function to arrive at a social preference that is complete, reflexive and transitive. Do you agree with this statement? Discuss your answer (Maximum 165 words).

d) Now suppose a group of friends want to decide on a game to play. They agree to play the game that is preferred by the majority, using pairwise majority rule. Therefore, they will choose the game that defeats any other game in a pairwise vote. The preferences over the games are as follows:

Game	Voter 1's Preferences	Voter 2's Preferences	Voter 3's Preferences
Karaoke (K)	K	C	B
Cards (C)	C	B	K
Board Game (B)	B	K	C

Can these friends decide on one of these games while satisfying the transitivity condition? Discuss. You can use a graph in your discussion (Maximum 165 words. A graph would count as 20 words).

e) Would your answer in part (d) change if the preferences were as follows? Explain. You can use a graph in your discussion (Maximum 165 words. A graph would count as 20 words).

Game	Voter 1's Preferences	Voter 2's Preferences	Voter 3's Preferences
Karaoke (K)	K	C	B
Cards (C)	C	K	K
Board Game (B)	B	B	C

f) Discuss which of the four optimal properties of social choice as stated by Arrow is now restricted under the pairwise majority voting scenario in part (e) above (Maximum 100 words).

2. Answer all parts of this question.

a) Firm A faces the industry demand function p(q) = 8 - 0.2q. The constant marginal cost of producing an extra unit of output is £1.

i) Write down the firm's maximisation problem.

ii) Find the first order condition for the firm's problem and hence find the profit maximising output of this firm.

iii) What will be the industry price when the firm produces at its profit maximising capacity?

b) Now consider two firms A and B operating in the same industry and selling a homogenous product. The industry's demand is the same as in part (a) above and A's marginal cost is the same as in part (a) above. Firm B's marginal cost is £2 per extra unit of output. The two firms compete over the market share. Recall that in a Cournot competition, each firm chooses its own output to maximise its profit given the output that it expects the other firm to produce.

i) What is a best response function ? Write down the best response functions for firms A and B.

ii) Solve the two equations in part b(i) to find the Cournot equilibrium output of the two firms and hence find the Cournot equilibrium price.

c) Now consider a situation where two firms compete over prices. For instance, the firms have already set their production capacity and compete over units sold by adjusting their price. Write down the best response functions and explain how the profit of one firm is affected by the action of the other firm.

d) Firm A commits to a price match policy and assures its customers if they find the same product cheaper elsewhere they will refund the price difference. Based on the Bertrand model of oligopoly, what would be the best response of firm B to this policy? Do you think they should lower their price to gain a bigger market share? Discuss.

e) If firms A and B were to collude over the price, what collusive price will they charge and what will be the total output in this industry?

f) Suppose these two firms meet in two markets. For instance, they both sell their products in two local markets. Discuss how the multimarket contact affects the likelihood of a successful collusion (Maximum 165 words).

3. Answer all parts of this question.

Consider a firm that produces two outputs, barley (B) and milk (M). The firm uses two kinds of labour as inputs in production. Karl's labour is denoted by L_K and Carolina's is denoted by L_C. Karl and Carolina are equally productive in barley and milk production. They each can produce 5 units of milk or 25 units of barley with one hour of work. Carolina's time inputs in barley and milk production are denoted by L_C^M and L_C^B, respectively. Similarly, Karl's inputs are denoted by L_K^M and L_K^B. Moreover, the total labour input of milk production is L_m, where L_M = L_C^M + L_K^M, and the total labour input for barley production is L_B = L_C^B + L_K^B.

a) If Carolina and Karl, each supply 8 hours of work a day, write down the time constraint of the firm in terms of L_B and L_M.

b) What is the production possibility frontier (PPF) for one day of production? Hint: think of all possible combinations of B and M that can be produced with L_B and L_M, while satisfying the time constraint in part (a) above. Intuitively, can you explain what the slope of PPF measures in this case?

c) Assume the firm pays each unit of L_B and L_M, wage rates of w_B and w_M, respectively. Write down the firm's profit maximisation problem.

d) For simplicity, let L^* be the labour cost of production. Moreover, assume that the market price for one unit of milk p_M is equal to 1, and for one unit of barley the price is p_B. Write down an equation that describes the iso-profit lines of the firm, keeping only B on the left-hand side of the equation. What are the slopes and intercepts of the iso-profit lines?

e) In two or three sentences explain what is the intuition behind an iso-profit line (max 50 words).

f) The problem of the firm in this example is to find the profit maximising combinations of outputs. The problem, therefore, can be stated as reaching the highest iso-profit line subject to the production possibility frontier. This objective is satisfied when the slopes of PPF and iso-profit lines are equal. Based on your answer to parts (b) and (d), write down the profit maximising condition for this firm.

g) Carolina and Karl, are also consumers of firm's outputs. Assume Carolina's utility from consumption of milk and barley are as following: U(M,B) = M^(2/3)B^(1/3). Her endowments of milk and barley are 1 unit of milk and 15 units of barley. If we denote Carolina's demand for milk and barley by M_M^C(p_B, p_M) and M_B^C(p_B, p_M) respectively, write down her budget constraint and hence her constrained optimisation problem.

h) The solution for Karl's and Carolina's maximisation problem is where MU_B/MU_M = the price ratio. In this case, MU_B represents either agent's marginal utility of consuming barley while MU_M represents either agent's marginal utility of consuming milk. Considering both the supply and demand sides, would you say the allocation of resources in this economy is Pareto efficient? Discuss (maximum 180 words, a graph would count as 20 words).

SECTION B - Attempt ONE question

4. 'Since people can always be induced to work hard with sufficient provision of incentives, moral hazard is not a problem'. Discuss and evaluate this statement. (Maximum 650 words, in addition you can use graphs to illustrate your answer).

5. 'Educational qualifications always allow employers to separate high ability individuals from less able individuals, effectively restoring full information and making everyone better off.' Do you agree with this statement? Explain why, or why not. Is there evidence of a signal value to education? Discuss. (Maximum 650 words in addition you can use graphs to illustrate your answer).