Let’s work out 5 periods of a Solow model with labor augmenting productivity (Z) growth. In your toy economy, the savings rate is 10%, and the depreciation rate is 50% (the high depreciation rate will get us to steady-state faster--think of each period as a decade). The population is fixed (treat it as one worker, N=1 forever). You always start off with 1 unit of capital, and TFP = Z = 1 during the first period. Since TFP and population never change, output each period is created this way: Yt = Kt(1/3)Zt(2/3) Consider two worlds: One where labor augmenting productivity (Z) grows 20% per period, and one where labor augmenting productivity (Z) grows 10% per period Answer the following questions for each of the two worlds What is capital each year, in years 1-5? What is GDP each year, in years 1-5? What is the marginal product of capital each year (MPK) in years 1-5? What is the wage in each period? In a steady state, what will MPK be? In a steady state, what will the market interest rate, MPK - (depreciation rate) be?
Let’s work out 5 periods of a Solow model with labor augmenting productivity (Z) growth. In your toy economy, the savings rate is 10%, and the depreciation rate is 50% (the high depreciation rate will get us to steady-state faster--think of each period as a decade). The population is fixed (treat it as one worker, N=1 forever). You always start off with 1 unit of capital, and TFP = Z = 1 during the first period. Since TFP and population never change, output each period is created this way: Yt = Kt(1/3)Zt(2/3) Consider two worlds: One where labor augmenting productivity (Z) grows 20% per period, and one where labor augmenting productivity (Z) grows 10% per period Answer the following questions for each of the two worlds What is capital each year, in years 1-5? What is GDP each year, in years 1-5? What is the marginal product of capital each year (MPK) in years 1-5? What is the wage in each period? In a steady state, what will MPK be? In a steady state, what will the market interest rate, MPK - (depreciation rate) be?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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I have to change the savings rate, but trying to figure out how to start.
Let’s work out 5 periods of a Solow model with labor augmenting productivity (Z) growth. In your toy economy, the savings rate is 10%, and the
Consider two worlds: One where labor augmenting productivity (Z) grows 20% per period, and one where labor augmenting productivity (Z) grows 10% per period
Answer the following questions for each of the two worlds
- What is capital each year, in years 1-5?
- What is
GDP each year, in years 1-5? - What is the marginal product of capital each year (MPK) in years 1-5?
- What is the wage in each period?
- In a steady state, what will MPK be?
- In a steady state, what will the market interest rate, MPK - (depreciation rate) be?
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Step 1: Define Solow growth model
VIEWStep 2: Calculate capital in years 1-5
VIEWStep 3: Calculate the GDP in years 1-5
VIEWStep 4: Calculate marginal product of capital
VIEWStep 5: Determine the wage in each period
VIEWStep 6: Calculate the steady State MPK
VIEWStep 7: Calculate the Market Interest Rate in Steady State
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