1Comparative Static AnalysisComparative Static Analysisof the Keynesian Modelof the Keynesian ModelMacroeconomics IECON 309 -- Cunningham2Simple ISSimple IS--LM AnalysisLM Analysis0),(0)()(==−−==−−−−PMrYLGrIYSTwo 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:0==++==−−drLdYLdGdrIdYSrYrY==−−0dGdrdYLLISrYrYWrite in matrix form:3Simple ISSimple IS--LM, ContinuedLM, Continued001001>>++−−==−−==>>++==−−−−==YrrYYrYrYYYYrrYrrYrYrrLILSLLLISLSdGdrLILSLLLISLIdGdYApplying Cramer’s rule for solution:0,00,0<<>>>><<rYYrISLLBecause, by assumption, the following hold:So, in a Keynesian economy, under the conditions given, cet. par. (i.e., prices), an increase in government spending increases GDP and interest rates.4ExtensionExtensionWhat if prices are flexible? To examine this, we must include the labor market and real wage computation.0),(0)()(0)(0−−−−==−−−−==−−==−−PMrYLGrIYSNFYNPwNdDefine the following variable as a convenience:(( ))02>>−−∂∂∂∂==PwPwNXd5Extension (Continued)Extension (Continued)00000010100000100001022>>−−==−−−−−−−−−−−−==JacXFLPMLLISFXPMLIFXdGdYNrrYrYNrrN(Note that the denominator turns out to be
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