Suppose that autonomous consumption and planned investment in the economy described in problem 5 change to Ca = 470 - 15r and Ip = 1,700 - 60r. All other aspects of the structure of the commodity and the money markets are as described in problem 5.
(a) Derive the equation for the new IS curve and verify that the equilibrium interest rate and real output are the same as you computed in parts 5g and 5h, respectively.
(b) Calculate the slope of the new IS curve, ∆r/∆Y.
(c) Compared to problem 5, have autonomous consumption and planned investment become more or less responsive to a change in the interest rate? Is the IS curve steeper or flatter as a result? How does this change in the interest responsiveness of autonomous spending alter the amount by which real output will change following an expansionary change in fiscal or monetary policy?
(d) Compute the new equilibrium interest rate and real output if government spending increases by 160.
(e) Compute the new equilibrium interest rate and real output if G equals 1,700 but the real money supply increases by 100.
(f) How and why do the answers in parts d and e differ from problem 6a and 6b, respectively? Is your prediction in part c confirmed?