Need help.. Consider a Solow economy where the technology is Cobb-Douglas and takes the form1-1of Y; = AțK?-° Nº , the saving rate is constant at s, the population growth rate is constantat n, and assume that the technology coefficient At = A for all t. The aggregate capitallaw of motion is Kį = I – 8Kt.(a)Write down the fundamental growth equation of the Solow model in terms of thecapital evolution per person.Use the fundamental equation to solve for the steady state capital per person.(b)And compute the marginal product of capital.(c)Consider the following three cases. Describe how the changes affect the break-even curve and the actual investment curve in the baseline diagram for the Solowmodel (corresponding to the fundamental growth equation)1) The population growth rate falls2) The depreciation rate rises3) The capital share in the production function, 1– 0, rises(d) Solve for the optimal capital and consumption per person under the golden-rule.What saving rate is needed to yield the golden-rule capital stock?

Given,In the Solow economy, the CD production function is:Where,

Consider a Solow economy where the technology is Cobb-Douglas and takes the form of Y₁ = A₁K¹²¯º Nê, the saving rate is constant at s, the population growth rate is constant 1-0 at n, and assume that the technology coefficient A₁ = A for all t. The aggregate capital law of motion is K₁ = It - 8Kt. (a) (b) (c) Write down the fundamental growth equation of the Solow model in terms of the capital evolution per person. Use the fundamental equation to solve for the steady state capital per person. And compute the marginal product of capital. Consider the following three cases. Describe how the changes affect the break- even curve and the actual investment curve in the baseline diagram for the Solow model (corresponding to the fundamental growth equation) 1) The population growth rate falls 2) The depreciation rate rises 3) The capital share in the production function, 1 – 0, rises (d) Solve for the optimal capital and consumption per person under the golden-rule. What saving rate is needed to yield the golden-rule capital stock?

Consider a Solow economy where the technology is Cobb-Douglas and takes the form of Y₁ = A₁K¹²¯º Nê, the saving rate is constant at s, the population growth rate is constant 1-0 at n, and assume that the technology coefficient A₁ = A for all t. The aggregate capital law of motion is K₁ = It - 8Kt. (a) (b) (c) Write down the fundamental growth equation of the Solow model in terms of the capital evolution per person. Use the fundamental equation to solve for the steady state capital per person. And compute the marginal product of capital. Consider the following three cases. Describe how the changes affect the break- even curve and the actual investment curve in the baseline diagram for the Solow model (corresponding to the fundamental growth equation) 1) The population growth rate falls 2) The depreciation rate rises 3) The capital share in the production function, 1 – 0, rises (d) Solve for the optimal capital and consumption per person under the golden-rule. What saving rate is needed to yield the golden-rule capital stock?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Question

Need help..

Consider a Solow economy where the technology is Cobb-Douglas and takes the form
1-1
of Y; = AțK?-° Nº , the saving rate is constant at s, the population growth rate is constant
at n, and assume that the technology coefficient At = A for all t. The aggregate capital
law of motion is Kį = I – 8Kt.
(a)
Write down the fundamental growth equation of the Solow model in terms of the
capital evolution per person.
Use the fundamental equation to solve for the steady state capital per person.
(b)
And compute the marginal product of capital.
(c)
Consider the following three cases. Describe how the changes affect the break-
even curve and the actual investment curve in the baseline diagram for the Solow
model (corresponding to the fundamental growth equation)
1) The population growth rate falls
2) The depreciation rate rises
3) The capital share in the production function, 1– 0, rises
(d) Solve for the optimal capital and consumption per person under the golden-rule.
What saving rate is needed to yield the golden-rule capital stock?

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Step 1: State the given information

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Step 2: Write down the per capita form of the fundamental growth equation

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Step 3: Find steady state capital person and MPC

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Step 4: Analyze the effects of the following factors on the breakeven and actual investment curves

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Step 5: Find the optimal capital and consumption per person under the golden-rule

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