(2) Investment and Taxes Consider a firm which operates for two periods. It does not require any labor for production. It produces output each period according to the following production function The current capital stock is exogenously given. The firm can influence its future capital stock through investment. Capital accumulates according to K, = 1 + (1-d)K The firm liquidates itself (i.e. sells off its remaining capital) at the end of the second period The firm's objective is to maximize its value, given by 1+r denotes profits, and the firm takes the interest rate as given. (a) Write down the expressions for both current and future profits, and ' b) Write down the firm's optimization problem. What are its choice variables? (c) Algebraically solve for the firm's optimal choice of investment, . (d) Now suppose that there is a proportional tax on firm profits, t, which is the same in both periods (ie, t = t'). Re-do the above, solving for the optimal investment rule. What is the effect of the tax rate on investment