Lecture 9More on Dynamic General EquilibriumGrowth AccountingNoah WilliamsUniversity of Wisconsin - MadisonEconomics 312Spring 2010Williams Economics 312Competitive EquilibriumAdd government with PV Budget Constraint:G +G01 + r= T +T01 + rIn a competitive equilibrium, households chooseconsumption and leisure (c, c0, l and l0) to maximize utilitygiven wages and interest rates (w, w0, and r).Firms choose employment and investment (N , N0, and I )to maximize value given wages and interest rates (w, w0, r).The labor market clears in both periods,N + l = N0+ l0= h.The goods market clears in both periods,zF(K , N ) = C+I +G and z0F(K0, N0)+(1−d)K0= C0+G0Note that the credit market clears by Walras law.Williams Economics 312Labor Market EquilibriumLabor supply: increasing in the real wage.Substitution effect dominates income effect.Labor demand: decreasing in real wage.Equate marginal product of labor to the real wage.An increase in the interest rate directly and indirectlyreduces future wages, raising current labor supply.Direct effect: PDV of wages isw01+r.Indirect effect:r = z0FK(K0, N0) − d, decreasing in K0/N0.So higher r reduces K0/N0.w0= z0FN(K0, N0), increasing in K0/N0.So lower K0/N0reduces future wages w0.Both work through intertemporal substitution of leisure.Williams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.9-13Figure 9.11 Determination of Equilibrium in the Labor Market Given the Real Interest Rate rWilliams Economics 312Output Supply and Output DemandWe focus on determining current period equilibrium valuesof (N , Y , C , r, w). These depend on exogenous factors,(z, G, T ) in particular), as well as expectations of future(z0, G0, T0).Output supply curve: summarizes equilibrium in labormarket, as it is translated into production. Ys(r)increasing in r since labor supply is increasing in r.An increase in the interest rate raises current labor supply.This increases employment, raising output.Output demand curve: summarizes equilibrium in goodsand capital markets. Yd(r) is decreasing in r becauseCd(r) is and Id(r) is.Higher real interest rates reduce investment.Higher real interest rates reduce consumption.Williams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.9-14Figure 9.12 Construction of the Output Supply CurveWilliams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.9-16Figure 9.14 An Increase in Current Total Factor Productivity Shifts the Ys CurveWilliams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.9-18Figure 9.16 Construction of the Output Demand CurveWilliams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.9-20Figure 9.18 The Complete Real Intertemporal ModelWilliams Economics 312Effect of an increase in G on Equilibrium.Increase in G raises current output demand.Increase in current or future taxes reduces householdwealth.Leisure falls and so labor supply increasesConsumption demand falls, but by less than G increased.Future labor supply increases, raising investment demand.In net, both output demand and supply increase.Wages unambiguously fall.Do interest rates rise or fall?Wealth effects are small for a temporary change.G + C increases sharply.N increases only slightly.So it is likely that interest rates rise.Williams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.9-19Figure 9.17 The Output Demand Curve Shifts to the Right if Current Government Spending IncreasesWilliams Economics 312Copyright © 2005 Pearson Addison-Wesley. All rights reserved.9-21Figure 9.19 A Temporary Increase in Government PurchasesWilliams Economics 312The effect of an anticipated increase in G0Increase in current or future taxes reduces householdwealth.Leisure falls and so labor supply increasesConsumption demand falls.Future labor supply increases, raising investment demand.In net, output supply increases but output demand mayfall.Interest rates fall and output probably rises.Wages fall due to the increase in labor supply.The effect is partially offset by declining interest rates.The book discusses an increase in both G and G0.Williams Economics 312Copyright © 2008 Pearson Addison-Wesley. All rights reserved.9-50Figure 9.18 A Permanent Increase in Government ExpendituresWilliams Economics 312Increase in current TFP zLabor is more productive, increasing Nd. Output supplycurve Ys(r) shifts out due to direct effect of z and due toincrease in labor input.No effect on output demand, since TFP unchanged infuture, hence no change in Id(r)In equilibrium, real interest rate falls, consumption andinvestment rise, employment rises, real wage rises.Productivity shocks are a potential explanation forbusiness cycles, as we’ll discuss later.Ongoing productivity improvements are the mainexplanation for long run growth, as we’ll discuss shortly.Williams Economics 312Copyright © 2008 Pearson Addison-Wesley. All rights reserved.9-54Figure 9.21 The Equilibrium Effects of an Increase in Current Total Factor ProductivityWilliams Economics 312Increase in future TFP z0No (direct) effect on labor market (only through change inr), no effect on current production. Hence no effect onYs(r).Investment demand Id(r) increases for any r, sincez0FK(K, N ) increases. Output demand curve shifts right.In equilibrium, real interest rate rises, investment increases,consumption may rise or fall, employment rises, real wagefalls, output rises.That is, news of future productivity causes boom today.Important in explaining investment boom in the 1990s.Williams Economics 312Copyright © 2008 Pearson Addison-Wesley. All rights reserved.9-56Figure 9.22 The Equilibrium Effects of an Increase in Future Total Factor ProductivityWilliams Economics 312Copyright © 2008 Pearson Addison-Wesley. All rights reserved.9-57Figure 9.23 Percentage Deviations From Trend in GDP and Investment, 1990–2006Williams Economics 312Economic Growth: MotivationNow will turn to analysis of the process of economicgrowth. A main determinant of living standards.Differences across countries:- Out of 6.4 billion people, 0.8 do not have access to enoughfood, 1 to safe drinking water, and 2.4 to sanitation.- Life expectancy in rich countries is 77 years, 67 years inmiddle income countries, and 53 years in poor countries.Differences across time:- Japanese boy born in 1880 had a life expectancy of 35years, today 81 years.-An American worked 61 hours per week in 1870, today