Lecture 5Applications of StaticGeneral EquilibriumNoah WilliamsUniversity of Wisconsin - MadisonEconomics 312Spring 2010Williams Economics 312Application I: WWII and the Increase in GDuring WWII government spending to finance the wareffort increased to levels unseen previously in the US.What are the predictions of the model for this increase inspending?The assumption that government spending is a pure loss ofoutput arguably makes sense here. Purespending/diversion of resources in short run. Positiveeffects more long-run and harder to measure.Williams Economics 312Figure 1.01 Output of the U.S. economy, 1869-1996Abel/Bernanke, Macroeconomics, © 2001 Addison Wesley Longman, Inc. All rights reservedWilliams Economics 312Abel/Bernanke, Macroeconomics, © 2001 Addison Wesley Longman, Inc. All rights reservedFigure 1.06 U.S. Federal government spending and tax collections, 1869-1999Williams Economics 312Analysis of the Change in GWe’ll work out a parametric example with preferencesu(c, l) = log c + γl and Cobb-Douglas technology.Production possibilities (goods market):c = Y − G = zKα(h − l)1−α− GTo simplify: write g = G/Y . So:c = (1 − g)zKα(h − l)1−α.Firm profit maximization:MPN = zFN(K , h − l) = z(1 − α)Kα(h − l)−α= wWilliams Economics 312Household utility maximization:MRS =ul(c, l)uc(c, l)=γ1/c= wEquate and impose goods market clearing:ul(zF(¯K , h − l) − G, l)uc(zF(¯K , h − l) − G, l)= zFN(¯K , h − l)⇒ γ(1 − g)z¯Kα(h − l)1−α= z(1 − α)¯Kα(h − l)−α⇒ N = h − l =1 − αγ(1 − g).Government spending has a pure income effect here (sincefinanced by lump sum taxes). Increases labor supply.Williams Economics 312Solve for rest of allocation:Y = z¯Kα1 − αγ(1 − g)1−αc = (1 − g)Y = z(1 − g)α¯Kα1 − αγ1−αOutput increases with g, consumption decreases.Solve for wages and interest rates:w = z(1 − α)Kα1 − αγ(1 − g)−αr = zαKα−11 − αγ(1 − g)1−αSo wages decrease with g, interest rates increase.Williams Economics 312Summing Up:Following increase in g = G/Y , the model predicts anincrease in (Y , N , r ), decrease in (c, w).Private consumption spending is “crowded out” byincreased government spending.Output increases but loss of welfare as both c, l fall.These predictions match US experience of WWII.Williams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.5-7Figure 5.6 Equilibrium Effects of an Increase in Government SpendingWilliams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.5-8Figure 5.7 GDP, Consumption, and Government ExpendituresWilliams Economics 312What Does This Analysis Miss?Government debt. A large fraction of the wartimespending was financed by government debt.Deficit/GDP ratio hit 24% by 1944.Debt allows for intertemporal substitution of resources andsmoothing burden of taxation. If needed to increase(distortionary) taxes to finance full war spending,production would have been less.Increased productivity. Wartime mobilization ofproduction increased labor productivity dramatically.Led to larger increase in production than our modelsuggests.Williams Economics 312Abel/Bernanke, Macroeconomics, © 2001 Addison Wesley Longman, Inc. All rights reservedFigure 15.04 Deficits and primary deficits: Federal, state, andlocal, 1940-1998Williams Economics 312Abel/Bernanke, Macroeconomics, © 2001 Addison Wesley Longman, Inc. All rights reservedFigure 1.02 Average labor productivity in the United States,1900-1998Williams Economics 312Output Effects of Fiscal PolicyCan define the multiplier for government spending as thepercentage by which output increases for a given increasein government spending:multiplier =∆Y∆G=Y0− YG0− GIn our model, using G = gY , G0= g0Y0:Y0− Yg0Y0− gY=z¯Kαh1−αγi1−α(1 − g0)α−1− (1 − g)α−1z¯Kαh1−αγi1−α(g0(1 − g0)α−1− g(1 − g)α−1)=(1 − g0)α−1− (1 − g)α−1g0(1 − g0)α−1− g(1 − g)α−1Williams Economics 312Fiscal MultiplierIn current discussions of fiscal stimulus, the size of themultiplier a source of some controversy.Obama administration suggests ≈ 1.5, Barro suggests ≈ 0.In our model with g = 0.2, α = 0.3, g0= 0.25 the multiplieris about 0.75.This isn’t the best framework for current issues, as there’sno unemployment or idle resources. These are the mainrationale for the fiscal stimulus.In the model here, ∆G always bad for welfare.Williams Economics 312Application II: Skill Biased Technical Change andInequalityLarge literature documenting increase in income andwealth inequality in the US. Started in the 1970s andcontinues today.At same time, large increase in the returns to education.Average wages of college graduates from increased by 60%for males and 90% for females from 1963 to 2002.Average wages of high school graduates only increased by20% for males and 50% for females over same period.Main explanation: Skill-biased technical change. Skilledand unskilled labor are effectively different labor markets.Productivity changes have increased the relative demandfor skilled labor.Williams Economics 312Williams Economics 312Williams Economics 312Williams Economics 312Williams Economics 312Analysis of Skill-Biased ChangeExtend the previous to two sectors: skilled and unskilled.Households: Assume both skilled and unskilled workershave same preferences given by:u(c, l) = c −(h − l)22Assume skilled workers own a share β of the capital stock,unskilled a share (1 − β).Wages wsfor skilled wufor unskilled.Williams Economics 312Household ProblemSkilled household problem (unskilled parallel):maxNs{(Nsws+ βrK ) − (Ns)2/2}Optimality conditions:uluc= Ns= wsSo we get:Ns= wsNu= wucs= w2s+ βrKcu= w2u+ (1 − β)rKWilliams Economics 312Firm Decisions with Two Types of LaborFirms: Assume representative firm hires both skilled andunskilled labor. Each has different productivity (zs, zu).Firm substitutes between skilled and unskilled for totallabor input.N = (zsNρs+ zuNρu)1/ρwhere 0 < ρ < 1. Thus production is:Y = KαN1−α= Kα(zsNρs+ zuNρu)1−αρWilliams Economics 312Firms maximize profits:Kα(zsNρs+ zuNρu)1−αρ− rK − wsNs− wuNuFOC’s – each type paid its marginal product:(1 − α)Kα(zsNρs+ zuNρu)1−αρ−1zsNρ−1s= ws(1 − α)Kα(zsNρs+ zuNρu)1−αρ−1zuNρ−1u= wuDivide firm FOC’s:zsNρ−1szuNρ−1u=wswuWilliams Economics 312Characterize