History homework help. The marginal product of capital for the next period is given by: MPKf =100?20Kt+1 Where Kt+1 is next period’ s desired capital stock . a) Derive an analytic expression for the next period desired level of capital . Assume that capital depreciates at a rate d , the rate of interest is given by r , corporations pay taxes at rate ? and that the price of capital is Pk . b) Assume Pk = 20, ? = 50%, d = 0.01 and r = 0.05. Use this information to calculate the desired level of capital for period t + 1. Also, calculate the effect on the desired capital stock of an increase in the corporate tax rate from 50% to 55%. c) Now Assume that the level of capital stock in period t is 2 and corporate tax rate are back at 50%. Furthermore, assume you do not know the level of interest rate r . Use the desired analytical expression for the next period desired level of capital in part (a) to derive an investment function in terms of the rate of interest (r ). The equation for desired consumption in this economy is related to GDP (Y ) and the interest rate (r ) in the following way: Cd = 5 + 0.5Y ? 0.6r d) Assume this economy is closed to international trade. If government expenditure is G, use consumption expression to find the saving function in terms of interest rate r. 1 Assuming that Y = 20 and G = 3, and using goods market condition to find the equi- librium rate of interest in this economy. What are the equilibrium level of saving and consumption? Then, find out the effect of increase in government spending from 3 to 3.1 on investment and interest rate in this closed economy. e) Assume now the economy is open to international trade and the world real interest is fixed for this small open economy. What would be the level of the world interest rate in this small open economy if net export (NX) is 0.3, net factor of payment (NFP) is 0, and again value of Y and G are 20 and 3, respectively. Next suppose that government spending is raised to new level of 3.1. What variables in the model are affected and by how much?