2. Tobin's q and investment

Suppose that the production function of a fifirm is given by Y = AK1/2L1/2 , where A = 1 and

L = 100. Suppose further that the price of the capital good (Pk) is 5, the price of the fifinal

output good (P) is 2, and the real interest rate is 0.1, and the depreciation rate is 0.1.

1. What is the replacement cost of the installed capital?

2. Suppose currently we have K = 64. Calculate the market value of the installed capital

(assume that both A and L remain at the current values in the future). What is the value

of Tobin's q? Should the fifirm increase or decrease its capital stock?

3. What is the optimal level of capital? What is the value of Tobin's q under the optimal level

of capital?

4. suppose that there has been a large inflflow of migration, so L jumped to 144. What is the

new optimal level of capita?