Suppose that the utility function of an enterprise consumer for gas (G) and electricity (E) is given by

U(G,E) = a ln(G) + (1 - a) ln(E) where 0 < a < 1.

Suppose the prices of gasoline and electricity are $5 and $10 respectively and the enterprise consumer has a yearly energy budget of $100000. Suppose in addition that the government has chosen to ration Gas by allowing a maximum consumption of 10000 units (G10000).

If a = 0.25, find the optimal consumption bundle of gasoline and electricity. Does the gas rationing constraint influence consumer's choice and utility, and if so, how much?

If a = 0.75, find the optimal consumption bundle of gasoline and electricity. Does the gas rationing constraint influence consumer's choice and utility, and if so, how much?