Consider the following short‐run model of the economy. C = 50 +0.9(Y‐T) , I = 50 – r , G=T=100 , M=3900, P=5, L(Y,r) = 0.8y – 2r
(a) Find the IS equation and graph the IS curve.
(b) Find the LM equation and add the LM curve to your graph from part (a).
(c) Find the equilibrium interest rate r*, the equilibrium level of income Y*. Depict these values on the graph above. Show graphically how an increase in the price level will change the IS‐LM model.
(d) Find the Keynesian-cross government spending multiplier. Find the effective (actual) government spending multiplier. (Hint: consider how output changes in the full IS‐LM model if G increases by 100 for instance). Explain why the two multipliers are different.
(e) Find the Keynesian‐cross tax multiplier. Find the effective tax multiplier. Explain why they are different.
(f) Now suppose that the government moves from a lump‐sum tax system to a tax system with a marginal tax rate equal to 0.1. Find the new equilibrium and show how it changes the IS‐LM curves.