1. Suppose we introduce government purchases into the Solow Growth model. Assuming a constant popu- lation...

 

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1. Suppose we introduce government purchases into the Solow Growth model. Assuming a constant popu- lation N, output per worker, y, is given by the production function 3/₁ = Akt where A is a measure of total factor productivity and k, is the level of capital per worker. Output per worker is split between consumption per worker, c, investment per worker, it, and Government purchases per worker, 9₁, according to Y₁ =4₂+4+9₁- Assume that government purchases are always a constant fraction of total output so 9₁ = 94₁ for some constant g. Investment is used to create new capital and replace depreciated capital. i₁ = k₁+k₁ + dk₁. Rather than assuming the savings is a constant fraction of output we'll assume that consumption is a constant fraction of output (a) Given a, d, g, c, and A, solve for the steady state level of capital per worker and consumption per worker. (b) How will an increase in g affect steady state capital per worker? (c) How will an increase in g affect steady state consumption per worker? (d) Download the SolowModelAssignment5.xlsx file from canvas. Use it to simulate the model. Verify that when d = 0.1, g = 0.1, 0.3,A = 1, and c = 0.5 your model converges to the steady state found in (b). (e) [Bonus] What choice of e maximizes steady state consumption per worker? (Hint: You may use the fact that steady state consumption per worker is maximized when capital per worker is kg = ((1-g)a4) T-a 1. Suppose we introduce government purchases into the Solow Growth model. Assuming a constant popu- lation N, output per worker, y, is given by the production function 3/₁ = Akt where A is a measure of total factor productivity and k, is the level of capital per worker. Output per worker is split between consumption per worker, c, investment per worker, it, and Government purchases per worker, 9₁, according to Y₁ =4₂+4+9₁- Assume that government purchases are always a constant fraction of total output so 9₁ = 94₁ for some constant g. Investment is used to create new capital and replace depreciated capital. i₁ = k₁+k₁ + dk₁. Rather than assuming the savings is a constant fraction of output we'll assume that consumption is a constant fraction of output (a) Given a, d, g, c, and A, solve for the steady state level of capital per worker and consumption per worker. (b) How will an increase in g affect steady state capital per worker? (c) How will an increase in g affect steady state consumption per worker? (d) Download the SolowModelAssignment5.xlsx file from canvas. Use it to simulate the model. Verify that when d = 0.1, g = 0.1, 0.3,A = 1, and c = 0.5 your model converges to the steady state found in (b). (e) [Bonus] What choice of e maximizes steady state consumption per worker? (Hint: You may use the fact that steady state consumption per worker is maximized when capital per worker is kg = ((1-g)a4) T-a