Suppose that the production function is Y = AK1/2L1/2, where A = 1 and L = 100. Suppose further that the price of capital good (Pk) is 10, the price of output (P ) is 4, the (annual) interest rate (r) is 0.1, and the (annual) depreciation rate () is 0.1. 1. Calculate the MPK as a function of K. 2. Calculate the real cost of capital. 3. Calculate for the optimal level of capital. 4. Suppose we are currently at the optimal level of capital. How much investment per year is needed to maintain this level of capital? 5. Suppose that the interest falls to 0.05. What is the new optimal level of capital? Suppose that the current level of capital is the same as what we calculated in step 3. How does this change in the interest rate affect investment?