Question

Problem 2: Consider a representative consumer whose preferences over consumption and leisure are given by the following utility function: U˜(C, l) = U(C) + V (l) (2) where U(.) and V (.) are twice differentiable functions (that is, their first and second derivatives exist). Suppose that this consumer faces lump-sum taxes, T, and receives dividend income, Π, from the 100% ownership of shares of the representative firm.

A) Write down the consumer’s optimization problem and the first-order conditions determining optimal consumption and leisure. B) Carefully explain the effect of a sudden boom in the stock market, which increases dividend income, on the optimal choice of consumption and leisure? Use the ABCDEF of Cramer’s rule to answer this question. Clearly state any assumptions you make. C) Using a carefully labeled diagram, describe the effects of this positive stock market shock characterized in (b).

Answer 1

Problem 1. Demand

Bengt’s utility function is U(x1, x2)= x1 + ln x2

x1 - stamps

x2 - beer

Bengts budget p1 x1 + p2 x2 = m

p1 – price of stamps

p2 – price of beer

m – Bengt’s budget

a) What is Bengt’s demand for beer and stamps?

b) Is it true that Bengt would spend every krona in additional income on stamps?

c) What happens to demand when Bengt’s income changes (i.e. find the income elasticity)?

d) What happens to demand when p1 and p2 increase (i.e. find the price elasticities)?

Problem 2. Demand

Jan has fallen on hard times. His income per week is 400 kr, spending 200 kr on food and 200 kr

on all other goods. However, he is also receiving a social allowance in the form of 10 food

stamps per week. The coupons can be exchanged for 10 kr worth of food, and he only has to pay

5 kr for such coupons. Show the budget line with and without the food stamps. If Jan has

homothetic preferences, how much more food will he buy when he receives the food stamps?

Problem 3. Demand

Find the demand functions for the individuals below, the budget constraint is pxx+pyy=m