Consider the following sequential game between a government, G and a firm, F. The government announces a per unit tax t, where 0 1, and it is paid by the firm. After observing the government's choice, the firm then chooses the quantity q of a good to be sold in order to maximize its profits. The marginal revenue of the firm when it sells output is = 1 2. The tax paid to the government is the firm's only marginal cost.

a) Derive the optimal output of the firm as a function of the tax, t, set by the government.

b) Suppose that the government's objective is to maximize its tax revenue. What is the optimal per unit tax? What is the consumer surplus?

c) Suppose that the government now wants to maximize consumers surplus. What should the per unit tax be?