Question 3: Goods market (45 marks) The marginal product of capital for the next period for this economy is given by: MPKf : A 2K,\" where Kt+1 is the next period's desired level of capital stock and A is total factor productivity. 3) Derive an algebraic expression for the next period's desired level of capital. Assume that capital depreciates at rate d, the interest rate is 'r and the tax rate is 1'. Assume A : 120, Pk : 20, T : 50%, d : 10% and r : 5%. Use the formula found in a) to compute the numerical value of the next period's desired level of capital, Kt\". Now assume there's a positive productivity shock and A increases to 134. i. Find the new numerical value for the next period's desired level of capital. ii. The government is aware of the productivity shock and decides to change its high tax rate such that the level of desired capital stays at the level found in b). Find the new tax rate and represent graphically the change. Assume A and T are back to their values given in b) and the interest rate, r, is now unknown. Also assume a closed-economy with K : 50, G : 2, Y : 20, and the following consumption function: C:5+0.5Y780*r i. Derive the investment function in terms of the rate of interest, 7'. ii. Derive the saving function in terms of the rate of interest, 1". iii. Find the equilibrium rate of interest, 7'. iv. Find Kt+1- Is it different from your answer in b)? Explain