Closed Economy IS-LM, Write equations, calculate the equilibrium interest rate and level of income. a,b,c,d,e.

1. [Closed Economy IS-LM] An economy is initially described by the following equations 5 = 500 + 0.500! T) I: 500251" a M =Y25 (P) r 6:100 T=500 M=2000 P=4 a. Write down the equations for the IS and LM curves and calculate the equilibrium interest rate and level of income. (3 p15) b. Draw a well-labeled graph of the IS and LM curve from part (a) and label the equilibrium as A. (2 pts) c. Congress votes to cut taxes to T = 200. What is the new equilibrium interest rate and level of income? Draw a graph that depicts the new equilibrium on the same graph as part (b) as B. (5 pts] d. Assume the economy was in long-run equilibrium in part (b). After the tax cuts in part (c), the government wants the economy to transition to its new long-run equilibrium without any scal or monetary policy. What is the new long-run equilibrium r, Y, and P? Depict this equilibrium on the same graph as part (b) C. Describe intuitively (and briefly) how we get from point B to C. (8 pts) e. Go back to the equilibrium in part (c). What action (calculate a specific number) must the Fed take in order to restore the level on in part (b)? Why would the Fed prefer this equilibrium over the equilibrium in part (d)? (7 pts)