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?

For each case, the best approach is to solve while ignoring the rationing constraint. If the solution you find violates the constraint, you know then that the optimal bundle will be where E = 50.
a. The MRS = .25G/.75E = 1 = MRT or simply G = 3E. Using the budget constraint:
E + 3E = 100
Solving gives E = 25 and G = 75. The electricity rationing does not have an effect.
b. The MRS = .75G/.25E = 1 = MRT or simply G = E/3. The solution from the budget constraint is E = 75. However, this violates the rationing constraint and so E = 50, G = 50.