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Comparative Static Analysis of the Keynesian Model Macroeconomics I ECON 309 -- Cunningham Simple IS-LM Analysis S(Y ) I (r ) G 0 M L(Y , r ) 0 P Two equations, two endogenous variables (Y and r), and one exogenous variable G. Real money supply (M/ P) is taken as constant since nominal money (M) and (P) are exogenous as well. Take total differentials: SY dY I r dr dG LY dY Lr dr 0 Write in matrix form: SY L Y I r dY dG Lr dr 0 2 Simple IS-LM, Continued Applying Cramer’s rule for solution: 1 0 dY SY dG LY SY L dr Y dG SY LY Ir Lr Lr 0 I r SY Lr I r LY Lr 1 0 LY 0 I r SY Lr I r LY Lr So, in a Keynesian economy, under the conditions given, cet. par. (i.e., prices), an increase in government spending increases GDP and interest rates. Because, by assumption, the following hold: Lr 0, LY 0 SY 0, I r 0 3 Extension What if prices are flexible? To examine this, we must include the labor market and real wage computation. w Nd N 0 P Y F (N ) 0 S (Y ) I (r ) G 0 M L(Y , r ) 0 P Define the following variable as a convenience: N d w X 0 w P P 2 4 Extension (Continued) 0 1 0 FN 0 0 1 0 Ir 0 dY 0 dG 1 0 Lr 1 0 FN 0 SY 0 Ir LY 0 Lr X 0 0 M P 2 Lr FN X 0 X Jac 0 0 M P2 Similarly: dN LX r 0 dG Jac dr 0 dG dP 0 dG w d P 0 dG (Note that the denominator turns out to be positive.) 5