EC201 Problem Set
宏观经济练习题代写 Problem Set 1: Preferences and Utility Exercises to be prepared before class The purpose of these exercises is to help you reflect on the
Problem Set 1: Preferences and Utility
Exercises to be prepared before class
The purpose of these exercises is to help you reflect on the assumptions we have in our models for consumer theory and for you to get used to how we model preferences.
There will be further discussion beyond these questions in the class.
1.(Based on past paper questions). When answering the following questions take care to spell out your logical argument carefully and to make use of notation accurately. 宏观经济练习题代写
(i) What is the transitivity assumption in consumer theory?
(ii) Is it possible that preferences are not transitive but can be represented by a utility function?
(iii) Assume that non-satiation and transitivity hold. Can indifference curves cross Explain using a diagram.
2.Which of the following utility functions satisfy non-satiation and convexity? Explain your answer. If these are not satisfied, then consider what shape the indifference curves have and what this implies about preferences over the two goods.
Problem Set 2: Utility maximisation and uncompensated demand 宏观经济练习题代写
These exercises will give you practice finding uncompensated demand for different
types of consumer preferences, and from there to examine elasticities of demand. Take care to explain every step of your reasoning when compiling your answers.
1.Tommaso has income m and preferences described byu(x1,x2)=x1+lnx2, where
X1≥0 and X2≥1. Prices are fixed at p1 and p2.
(i) Find Tommaso’s uncompensated demands x1(p1,p2,m) and x2(p1,p2,m).
How do these depend on the level of Tommaso’s income m?
(ii) Assume m ﹥ p1. Find the income elasticity and cross-price elasticity of demand for good 2. Sketch Tommaso’s demand curve for good 2.
Problem Set 3: Expenditure minimization and compensated demand 宏观经济练习题代写
(i) Define compensated demand and the expenditure function. What variables do these depend on?
(ii) Find Kenan’s compensated demands h1(p1,p2,u) and h2(p1,p2,u).
(iii) Find the own price elasticity of Kenan’s compensated demand for good 1; what does this capture?
(iv) Find Kenan’s expenditure function E(p1,p2,u). By how much must Kenan’s expenditure have to rise in order for him to double the level of utility he receives from u to 2u, assuming he chooses consumption in a cost minimising way? 宏观经济练习题代写
2.Azhar’spreferences over goods 1 and 2 are described by u(x1,x2) = min[5x1,x2]and she faces fixed prices p1 and p2.
(i) Find Azhar’s compensated demands h1(p1,p2,u) and h2(p1,p2,u). Explain how Azhar’s demands are affected by prices and p1 and p2.
(i) Find Azhar’s expenditure function E(p1,p2,u).
(ii) The price of good 2 rises. Use a diagram to illustrate the effect on Azhar’s consumption of the two goods. Decompose the impact of the price change into an income and substitution effect using a diagram.
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