Suppose that each consumer consumes goods X and Y with preferences represented by the utility function:
U(X, Y) = √X + 2√Y.
Each consumer has income of $150. The supply curve for good X is horizontal (perfectly elastic) at a price of $1, while the supply curve of good Y is horizontal at a price of $2.
a. With no tax, what are the competitive equilibrium prices of goods X and Y? How much of each good does each consumer purchase?
b. The government has put a specific tax of $1 on purchases of good X. What are the competitive equilibrium prices of good X and Y with the tax? How much of each good does each consumer now purchase?
c. Suppose the government decides to give each consumer an income subsidy (increasing his income above $150) so that he is exactly as well off after the tax as before the tax. Will the government's tax revenue exceed the amount of the subsidy?