The optimality condition for capital when there is a tax is (1-tax subscript t +1) MPK + pt(1-delta)=pt(1+r), (2) where pt is the price of new capital at time t, is the annual rate of depreciation, r is the net real rate of return (constant), MPK is the real marginal product of capital and is the tax rate on capital income. This extra credit assignment asks you to solve for the price of capital in an environment with time-varying prices of capital goods. (I.e., we will allow the price pt and the tax rate t to vary over time.)a.Referring to the lecture notes, derive an expression for pt in terms of future values of tax and tMPK. What is the intuition for this expression?