Two period model with investment. Suppose a firm operates for two periods. Output is produced every period according to Y4 = KN), where a and y are both positive and sum to less than one. The firm owns capital and pays a wage w for labour hired in each period. The evolution of capital is Kt+1 = (1-0)K+ +It, where d E (0,1) is the depreciation rate and It > 0 is the amount invested in period t. Assume that investment expenditure is subsidized at a rate s (0,1) by the government. The future period is discounted at a rate 1+r. a. (5 marks) Assuming the firm operates for two periods, write down the value of the firm and find the capital stock chosen by the firm for period t +1 (i.e. find optimal Kt+1). b. (4 marks) In order to fund public expenditure the government can tax firms either via a lump-sum tax or a proportional tax on profit earned. Write down the problem of the firm for each of these scenarios. Explain which tax policy is least distorting to firm investment (you are not required to solve for investment under each policy though you are welcome to - but rather make your case with a concise intuitive argument). Two period model with investment. Suppose a firm operates for two periods. Output is produced every period according to Y4 = KN), where a and y are both positive and sum to less than one. The firm owns capital and pays a wage w for labour hired in each period. The evolution of capital is Kt+1 = (1-0)K+ +It, where d E (0,1) is the depreciation rate and It > 0 is the amount invested in period t. Assume that investment expenditure is subsidized at a rate s (0,1) by the government. The future period is discounted at a rate 1+r. a. (5 marks) Assuming the firm operates for two periods, write down the value of the firm and find the capital stock chosen by the firm for period t +1 (i.e. find optimal Kt+1). b. (4 marks) In order to fund public expenditure the government can tax firms either via a lump-sum tax or a proportional tax on profit earned. Write down the problem of the firm for each of these scenarios. Explain which tax policy is least distorting to firm investment (you are not required to solve for investment under each policy though you are welcome to - but rather make your case with a concise intuitive argument)