Download Consumer Utility Function - Microeconomic Theory - Past Exam and more Exams Microeconomics in PDF only on Docsity!
Semester 1 Examinations 2010/
Exam Code(s) 1EE1, 1EP1, 1MEE1, 1MEM Exam(s) M.A. & M.Econ.Sc. Economic Policy Evaluation & Planning M.A. & M.Econ.Sc. Economic & Environmental Modelling Module Code(s) EC Module(s) Microeconomic Theory Paper No. 1 Repeat Paper External Examiner(s) Professor Cillian Ryan Internal Examiner(s) Professor John McHale Dr. Ruvin Gekker Instructions: Please answer any FOUR questions. Duration 3 No. of Pages 3 Discipline Economics Course Co ordinator(s) Dr. Ruvin Gekker Requirements : MCQ Release to Library: Yes √ No Handout Statistical Tables Graph Paper Log Graph Paper Other Material
Please answer any FOUR questions.
- A consumer’s utility function is given by: U = xy 2 with budget constraint pxx + pyy = Y. (a) Derive the Marshallian demand functions for x and y. (6 marks) (b) Derive the indirect utility function as a function of px, py and Y. (6 marks) (c) Derive the Hicksian compensated demand functions for x and y. (7 marks) (d) Derive the expenditure function as a function of px, py and U. (6 marks)
- Given preferences € on a set X, a numerical representation for these preferences is any function U with domain X and range the real line such that x € y if and only if U(x) > U(y). (a) Prove that for € to admit a numerical representation, it is necessary that € is asymmetric and negative transitive. (12 marks) (b) Suppose that U is a numerical representation of preferences € . Prove that U is quasi-concave if and only if preferences € are convex. (13 marks)
- Given a preference relation € on a set X and non-empty subset A of X, the set of acceptable alternatives from A according to € is defined to be c(A, € ) = {x € ∈ A: there is no y € ∈ A such that y € x}. (a) Prove that for any € , c(A, €
€ ⊆ A. (8 marks) (b) Assume that € is asymmetric and negative transitive. Establish that for every finite set A, c (A, € ) is not empty. (8 marks) (c) Suppose that both x and y are in both A and B, and x € ∈ c(A, € ) and y € ∈ c(B, € ). Establish then that x € ∈ c(B, € ) and y € ∈ c(A, € ). (9 marks)
- Suppose that three oligopolists operate in a market with the following demand and cost conditions: P – 200 – q, and MC = 20 for all firms. (a) State and explain the Cournot-Nash equilibrium for this model. (8 marks) (b) Assume now that the firms choose their quantities as follows: (i) first firm 1 chooses q 1 ; (ii) firms 2 and 3 observe q 1 and then simultaneously choose q 2 and q 3 , respectively. Find the backwards induction outcome of this dynamic game. (9 marks) (c) Compare profits of firm 1 in parts (a) and (b). Does firm 1 have the first move advantage? Explain your answer. (8 marks)
