Consider an IS-LM model described by the following equations: Y = C + G + I (Aggregate Demand) C = 120 + 0.6(Y − T) I = 160 − 8r T = 120 G = 180
Md /P = 2Y − 80r (Money Demand)
Ms = 1280, (Money Supply Targeting) where r is the interest rate expressed in percentage points. Here Y denotes output (GDP), C is consumption, I is investment, T is taxes raised by the government, G is government spending, P is the price level and Md and Ms are money demand and supply, respectively. Here, the central bank follows money supply targeting (Ms given). Consequently, r will be determined in equilibrium. Exercise 1 Equilibrium in the IS-LM Model In the short run, we assume that prices are fixed at P = 1.
1. Derive the equations for the IS curve and the LM curve in this economy. Express both as output as a function of the interest rate. Illustrate graphically.
2. Derive the equilibrium values for output and the interest rate in this IS-LM model.