In this question we'll use the traditional method of comparative statics to determine

the impact of a change in a tax rate on input demand for a profit-maximizing firm

operating in a competitive environment. Assume that the firm's production function is

specified generally as = (, ), where q is output, k is capital and l is labour.

Denote the prices of output, capital, and labour as p, r, and w.

Now assume that the government has levied a per-unit tax on capital of t so that in

addition to price of capital r, the firm must also pay an amount t for every unit of

capital used.

a) Set up the profit-maximization problem and derive the first-order conditions.

Provide intuition for the first-order conditions.

b) Derive the second-order conditions.

c) Rewrite the first-order conditions as implicit functions of the optimal

solutions.

Question4