Lahore School of Economics

1. Natasha derives utility from attending rock concerts (r) and from colas (c) as follows:

U(c,r) = c^0.9r ^0.1

The marginal utility of cola (MU_c) and the marginal utility of rock concerts (MU_r) shall be:

MU_c = MU_r =

a. If the price of cola (Pc) is $1 and the price of concert tickets (Pr) is $30 and Natasha's income is $300, how many colas and tickets should Natasha buy to maximize utility? (5)

To maximize utility, Natasha (1) must be on her budget line, and (2) the marginal rate of substitution must equal the ratio of the prices of the goods. The marginal rate of substitution is equal to the ratio of the marginal utilities of the goods. Thus:

1. 
   c + 30r = 300
   

Solving these equations simultaneously for c and r yields c = 270 and r = 1.

b. Suppose that the promoters of rock concerts require each fan to buy 4 tickets or none at all. Under this constraint and given the prices and income in (a), how many colas and tickets should Natasha buy to maximize utility? (5)

b.

Without the 4 ticket constraint, Natasha would prefer to buy just 1 ticket. If required to buy 4 tickets, Natasha would maximize utility by either buying 4 tickets and consuming 180 colas, or by buying zero tickets and consuming 300 colas. The utility function may be used to determine which is preferred. In this case, Natasha will buy zero tickets and 300 colas.

c. Is Natasha better off under the conditions in (a) or (b)? Explain your answer. (3)

Natasha prefers (a). Constraining choice never leaves one better off. At best it has no effect. Otherwise, the addition of a constraint leaves one worse off.

Suppose that a consumer's increase in nominal income from the base year is exceeded by the inflation level given by a Paashe cost of living index for their level of purchases . Show that this information implies that the consumer is strictly worse-off as compared to the base year. (HINT: Use a revealed preference argument and the assumption that total expenditure = total income!) (5)

The information given above implies that This expression says that the commodity bundle purchased in the new period was affordable in the base period. However, the consumer selected a more expensive bundle in the base year. Thus, the base year commodity bundle is revealed preferred to the new commodity bundle.

Question 3

Margaret’s optimal consumption is shown in the diagram below for Hy-Vee Cola. If the price of Cola falls, show the total change in consumption of Cola. Decompose the change in Hy-Vee Cola consumption into income and substitution effects. Do the effects work in opposite directions? Explain. (5 + 3)

Normal Good

For inferior good,

Assume that Cola is a Giffen good. How would the income and substitution effects change as a result of the fall in price? (3.5 + 3.5)

(Income Effect is in Green, opposite direction to substitution effect)