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.
Diagrams can be drawn electronically or by hand and scanned in. You can scan diagrams which can be added to your word document:http://www.reading.ac.uk/web/FILES/its/Scanning.pdf. When drawing diagrams/graphs, you should make sure the axes, curves/lines and any other relevant information is clearly labelled. The diagrams should be clear and all information contained in them should be legible. Marks will be deducted for unclear or poorly labelled diagrams.Submission:Coursework should be submitted electronically through the
Assignment submission folder on the module Blackboard page. You should submit your work as a single document–including any diagrams. Instructions for the electronic submission of coursework can be found in the Assignment submission folder on Blackboard.Work can either be typed or handwritten. If it is handwritten you should be able to scan it and submit it as a pdf document. If submitting handwritten work, please ensure this is clear and legible.
Do not submit work done in pencil. Make sure that your work is anonymised.
Do not put your name in the header or footer or front page of your work. Don’t use your own name in the filename: Blackboard will identify your work by your Blackboard username, so your essay will not get lost in the system. FeedbackYou can expect to receive electronic feedback on your assignments along with a mark within 15 working days of the assignment submission date. You will be able to access your mark and feedback through the My Grades folder on the module Blackboard page.
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 𝑄=𝐾23⁄𝐿13⁄and 𝑃𝐾=𝑟,𝑃𝐿=𝑤[20marks]a)[10marks]Drive the equation of the total cost function.b)[10marks] Assume 𝑝=1000−2𝑄.
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 𝑈𝐴(𝑥,𝑦)=𝑥25⁄𝑦35⁄and Sarah’s one is 𝑈𝑠(𝑥,𝑦)=𝑥14⁄𝑦34⁄. [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.