Endogenous Growth Model

Notes on Macroeconomics – 3Revised on September 21, 2007than at the socially optimum as the following:( 1 βθ ) > ⎡1β ( θ γ )CEθ+ γ θ+γc = − Ak Ak0 0 ⎣ − + ⎤⎦ =0 0SOc .Thus, we can have the time path of the consumptionc tas the following figure.ctConsumption path in the socially optimal equilibriumConsumption path in the competitive equilibriumcCEocPOotFigure 1. The time path of consumption in the equilibriumsSuppose that there exists the government in the economy, then we can consider thegovernment’s interventions, tax and subsidy, which may guarantee the social optimum. Letτ andsbe the income tax rate and the rate of subsidy per unit of capital accumulation,respectively, then the resource constraint (3.29) can be written as( )c + k = − Ak K + sk . (3.38)θ γ1 τt t+ 1 t t t+1To obtain the policy functions, we have the following first order conditions:sk = θ + γτ Ak (3.39)t+ 1t( τ )c + k = − Ak + sk(3.40)θ+γ1t t+ 1 t t+110/16