Explain your answer. c)[20 marks] Nowthe game is repeated for infinite times. What would be the mechanism to reachany other equilibrium than Q5 b)?
1 ECM190 – MICROECONOMICS II ECM101 – MICROECONOMIC POLICY (PART 2) ASSIGNMENT
If you are registered for the 10 creditECM190module, this assignment will count40% of your final module mark.
If you are registered for the 20 creditECM101module, this assignment will count20% of your final module mark.General Guidelines:This assignment comprises four questions and you must answer all questions. Answers must be explained in full and should include any calculations relied on to arrive at the result.All diagrams should be original and not copied from other sources.
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2Q1.Sam consumes two goods x1and x2. Her utility function can be written as U(x1,x2)=x123⁄x215⁄. Suppose the price of good x1is P1, and the price of good x2is P2. Sam’s income is m. [20 marks]a)[10 marks]
Derive Sam’s Marshallian demand for each good. b)[5 marks] Derive her expenditure function using indirect utility function. c)[5 marks] Use part c) to calculate Hicksian demand function for each good.Q2.Giventhe production function = 23⁄ 13⁄and = , = [20marks]a)[10marks]Drive the equation of the total cost function.b)[10marks] Assume =1000−2 .
Find the profit maximising output level, K and L. Q3.A small island, Whiteknights, has two residents, Alex and Sarah. They consume only two goods, cake x and coffee y and in total 120 units are available for each good.
Initially Alex consumes two-third of the cake and one-third of coffee and Sarah consumes the rest of the cake and coffee. Alex and Sarah have different preferences, which are represented by the utility function. Alex’s utility function is ( , )= 25⁄ 35⁄and Sarah’s one is ( , )= 14⁄ 34⁄. [30marks]a)
[5marks] Is the initial consumption efficient in terms of consumption egalitarianism or welfare egalitarianism?
(We assume that utilities are interpersonally comparable.) b)[10marks]
Derive Alex’s and Sarah’s marginal rate of substitution of cake for coffee. Define the contract curve and draw it on the Edgeworth box. Is the initial allocation Pareto efficient? Justify your answer. c)[5 marks]
Characterize the set of allocations of cake and coffee which Pareto improve the initial allocation. d)[10marks]
Now there is a market price for each good and Alex and Sarah are price takers. The price of cake is Px=1 and the price of coffee is Py=2. Are these prices in equilibrium?
Justify your answer.Q4.Consider the following conflict game. [30marks]
Player 2No fightFight lessFight morePlayer 1No fight40, 400, 700, 60Fight less70, 030, 3010, 50Fight more60, 050, 1020, 20a)[5marks]
This is a one-shot game. What isthe best responsefunction ofeach player?
Find all the Nash equilibriaand explain.
3b)[5marks]Now, this game is repeated for 20times. What arethe sub-game perfect Nash equilibria of this repeated game?
Explain your answer. c)[20 marks] Nowthe game is repeated for infinite times. What would be the mechanism to reachany other equilibrium than Q5 b)? Explain in detail.
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