Question

Suppose that the preferences a typical American has for quantities of electricity (E) and gasoline (G) is given by U(E, G) = αln(E) + (1 − α)ln(G) where 0 < α < 1. Suppose the prices of gasoline and electricity in the units provided are both $1/unit and the consumer has an income of $100. Suppose in addition, the government has chosen to ration electricity by allowing 2 a maximum consumption of 50 units of electricity (E ≤ 50).

a. Suppose we discard the assumption that 0 < α < 1 and assume α > 1 instead, determine whether the given utility function U(E, G) = αln(E) + (1 − α)ln(G) is still a valid utility function.

b. Find a utility function with a different functional form that represents the same ordering of bundles as the given utility function U(E, G) does

c. If α = .25, find the optimal consumption bundle of gasoline and electricity.

d. If α = .75, find the optimal consumption bundle of gasoline and electricity.

e. Find the minimum value of α such that the rationing is binding

Answer 1