Assume that households’ consumption function is given by C(Y − T) = 50 + 0.75(Y − T), that firms’ investment function is I(r) = 150 − 10r, government spending is G = 150, and the tax bill T = 200. a. Solve for the equation of the IS Curve ("Investment-Savings") from the original consumption, investment and government spending functions. That is, for different levels of interest rate, what will be the GDP?
b. How will the IS equation change if government spending increases to 200?
c. Suppose the money supply is MS = 3000 and the price level is P = 4. Money/liquidity demand is given by Md/P = L(r, Y ) = Y − 50r. Solve for the equation of the LM Curve ("Liquidity-Money").
d. Based on your answers to the previous two questions, what are the equilibrium levels of the real interest rate and real GDP? (G is back to 150.)
e. Allow the price level to be a variable now and solve for the aggregate demand induced by the IS-LM intersection. This is to say, solve for r in either the IS curve or LM and plug it into the other. This should leave an equation in Y and P.
f. Show the derivation of the AD curve graphically: Plot the IS and & LM curve and demonstrate how, when price-level moves this induces a new GDP level