Question 2 The production function of an economy is given by: Y=[2AK]K where K is capital,Y is output, and A is total factor productivity. A) 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, the price of capital goods is Pk, and the effective tax rate is r. B) Assume A=60 , 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,K t+1.| C) Now assume there's a positive productivity shock and A increases to 67. 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 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. D) AssumeA and rare back to their values given in b) and the interest rate, r, is now unknown. Also assume a closedeconomy with K=40, G=2, Y=20, and the following consumption function: C=6+0.5Y78r i. Derive the investment function in terms of the rate of interest,r ii. Derive the saving function in terms of the rate of interest, r iii. Find the equilibrium rate of interest, r