The production function for this economy is given by: Y : AKaNl-a Together the interest rate [r], the rate of depreciation [6] and the price of capital goods (pk) make up the user cost of capital. You can assume that the rm has to borrow the funds needed to nance any new investment. a] Start rst by writing out an expression for the user cost of capital and explain briey what it signies. b] Now use the above production function to nd an expression for the desired stock of capital [K'] and how it relates to the user cost of capital. In particular, derive expressions for the elasticities of the desired capital stock with respect to A and N. Which factor has the larger effect and why? [Hint: You only need to write out the desired stock of capital equation that you derived in terms of natural logs for justA and N and proceed from there.] c) Now rewrite the marginal product in terms of just output [Y] and the capital stock. As well, assume that the firms' prots are taxed at a rate I. How does the introduction of taxes affect the desired stock of capital? What is your interpretation of Y? (1] Based on the desired stock equation you derived in part c] and using the capital accumulation identity, nd an equation for investment [I]. e] Discuss how a change in depreciation would affect investment. Can you say whether investment would rise or fall? Explain why