Consider an IS-LM model where the central bank sets the nominal interest rate. The consumption and investment functions are given by

=200+0.25()

=150+0.251000

and suppose that government expenditures and taxes are given by =250 and =200, respectively. Let real money demand be given by

/=28000

and let the initial interest rate be ₀=0.05

(a) [2 points] Solve for the equilibrium values of output and real money supply.

(b) [2 points] Solve for the equilibrium values of and , and verify that consumption, investment and government expenditures indeed add up to output .

(c) [3 points] Now suppose that interest rate is cut to ₀=0.03. Solve for the new equilibrium values of ,/, and . What are the effects of this change on the economy? Provide brief intuition.

(d) [3 points] Set the interest rate back to ₀=0.05. Now suppose that government spending increases to =400. If the central bank keeps the interest rate unchanged, how should monetary supply respond to this expansionary fiscal policy? What are the effects of this fiscal expansion on and ? Explain.