The purpose of this problem is to study how the slope of the IS curve changes as the multiplier changes and the responsiveness of autonomous planned spending to interest rate changes. Initially, use the same information as given in problem 5.
(a) Suppose that the marginal propensity to consume increases from 0.5 to 0.6. Compute the new value of the multiplier.
(b) Derive the equation for the new autonomous planned spending schedule, Ap.
(c) Derive the equation for the new IS curve Y = kAp.
(d) Using the equation for the new IS curve; calculate the new equilibrium levels of income at interest rates equal to 0, 3, and 6.
(e) Using your answers to part d, calculate the slope of the new IS curve, ∆r/∆Y.
(f) Given that c = 0.6, suppose that the equation for planned investment expenditures is now Ip = 2,350 – 45r. Derive the equation for the new autonomous planned spending schedule, Ap.
(g) Derive the equation for the new IS curve, Y =KAp.
(h) Using the equation for the new IS curve, calculate the new equilibrium levels of income at interest rates equal to 0, 3, and 6.
(i) Using your answers to part h, calculate the slope of the new IS curve, ∆r,/∆Y.
(j) Using your answers to part e of problem 5, and parts e and i of this problem, explain whether the IS curve gets flatter or steeper as (1), the multiplier increases, and (2), the responsiveness of autonomous planned spending to the interest rate increases.