1. Investment with Adjustment costs and taxes Consider a representative rm that uses capital, In, to produce output. The production function for the rm is linear given by FUQ) = A31}. The rm purchases investment good, It, at price 19,. Investment has a second cost, namely it is expensive to install. Specically, the cost of installation is given by cat) = :13. Capital does not depreciate and hence evolves as follows: If: = 1:. We assume that the initial capital stock and initial investment price are given as K9 and Pa, respectively. The output price is normalized as l. The rm maximizes the present value of prots discounted by the interest rate r. (a) Write down the rst order conditions and the transversality condition for this problem. (b) Solve for the optimal investment as a function of investment prices and parameters only. (c) Derive the Tobin's q at time t, Q:- (d) Using a phase diagram for (Kr, qr) show that there is a unique solution. What is the steady state value for 9-,? (e) Suppose that the productivity A drops to A/2. If the investment price remains the same, explain, using a phase diagram, what happens to Kr and at. Discuss which variables jump and which adjust slowly, and why