Suppose that the IS and LM curves for an economy are given by: IS: Y = 2.5Ap

Suppose that the IS and LM curves for an economy are given by:
IS: Y = 2.5Aʹp - 250r
LM: Y = 5(Ms/P) + 250r
where Aʹp is initially 5,000, Ms is initially 2,000, and P = 1.
(a) Graph the IS and LM curves when the interest rate equals 3, 4, 5, 6, and 7.
(b) Use your graphs of the IS and LM curves to find the equilibrium level of income and the equilibrium interest rate.
Suppose that housing prices and the value of the dollar (the exchange rate) are both falling simultaneously, creating uncertainty as to what the future level of autonomous planned spending, Aʹp, will be.
(c) Explain which one of these two events would cause autonomous planned spending to fall and which one would cause it to rise.
(d) Monetary policymakers evaluate the possible effects of the declines in house prices and the value of the dollar and estimate that the most autonomous planned spending can either rise or fall by is $200 billion. Given a decline in autonomous planned spending equal to $200 billion, graph the new IS curve when the interest rate equals 3, 4, 5, 6, and 7 and label that IS curve ISʹ. Given an increase in autonomous planned spending equal to $200 billion, graph the new IS curve when the interest rate equals 3, 4, 5, 6, and 7 and label that IS curve ISʹ.
(e) Suppose that the level of income you found in part a equals natural real GDP. Monetary policymakers are faced with three policy options in light of the uncertainty concerning the future amount of autonomous planned spending. First, they could maintain the interest rate at its current level and allow real GDP to adjust as autonomous planned spending varies between $4,800 and $5,200. Second, they could maintain the real money supply at its current level and allow the interest rate and real GDP to adjust to variations in autonomous planned spending between $4,800 and $5,200. Third, they could raise and lower the money supply so as to maintain real GDP at its current level, which is natural real GDP. Use the new IS curves and the LM curve to evaluate how real GDP and/or the interest rate vary as autonomous planned spending varies between $4,800 and $5,200 under each policy option.
(f) Use your answers to part e to explain why, in terms of their effects on the inflation and unemployment rates, the first policy option is the least desirable choice, whereas the third policy option is the best choice.
(g) For each policy option, explain what actions policymakers would have to take in terms of open market operations if autonomous planned spending falls below its current level of $5,000 or rises above its current level of $5,000.