Suppose That the Preferences a Typical American Has for Quantities

Essay

Suppose that the preferences a typical American has for quantities of electricity (E)and gasoline (G)is given by
U(E,G)= a ln(E)+ (1 - a)ln(G)
where 0 < a < 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 a maximum consumption of 50 units of electricity (E ≤ 50).
a.If a = .25,find the optimal consumption bundle of gasoline and electricity.Does the electricity rationing constraint have an influence on consumer's choice?
b.If a = .75,find the optimal consumption bundle of gasoline and electricity.Does the electricity rationing constraint of the government have an influence on the consumer?