5. Consider an economy where the elasticity of output with respect to capital is 0.3 and the elasticity of output with respect to labor input is 0.7. If we assume that the growth rate of output is 3% and the growth rate of both capital and labor input is 2%, what is the implied total factor productivity growth?
5. Consider an economy where the elasticity of output with respect to capital is 0.3 and the elasticity of output with respect to labor input is 0.7. If we assume that the growth rate of output is 3% and the growth rate of both capital and labor input is 2%, what is the implied total factor productivity growth?
Chapter1: Making Economics Decisions
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![**Question 5:**
Consider an economy where the elasticity of output with respect to capital is 0.3 and the elasticity of output with respect to labor input is 0.7. If we assume that the growth rate of output is 3% and the growth rate of both capital and labor input is 2%, what is the implied total factor productivity growth?
**Explanation:**
To find the implied total factor productivity (TFP) growth, we use the following formula based on the Solow residual:
\[ \text{Growth Rate of Output} = (\text{Elasticity of Output with respect to Capital} \times \text{Growth Rate of Capital}) + (\text{Elasticity of Output with respect to Labor} \times \text{Growth Rate of Labor}) + \text{TFP Growth} \]
Given:
- Elasticity of capital = 0.3
- Elasticity of labor = 0.7
- Growth rate of output = 3%
- Growth rate of capital and labor input = 2%
Substitute these values into the formula:
\[ 3\% = (0.3 \times 2\%) + (0.7 \times 2\%) + \text{TFP Growth} \]
\[ 3\% = 0.6\% + 1.4\% + \text{TFP Growth} \]
\[ 3\% = 2\% + \text{TFP Growth} \]
\[ \text{TFP Growth} = 3\% - 2\% \]
\[ \text{TFP Growth} = 1\% \]
Therefore, the implied total factor productivity growth is 1%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92856043-199e-49b6-95ce-27336f8d0cbd%2F53ef5e30-8bee-441e-92fe-1578995c63ac%2F17r55zs_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 5:**
Consider an economy where the elasticity of output with respect to capital is 0.3 and the elasticity of output with respect to labor input is 0.7. If we assume that the growth rate of output is 3% and the growth rate of both capital and labor input is 2%, what is the implied total factor productivity growth?
**Explanation:**
To find the implied total factor productivity (TFP) growth, we use the following formula based on the Solow residual:
\[ \text{Growth Rate of Output} = (\text{Elasticity of Output with respect to Capital} \times \text{Growth Rate of Capital}) + (\text{Elasticity of Output with respect to Labor} \times \text{Growth Rate of Labor}) + \text{TFP Growth} \]
Given:
- Elasticity of capital = 0.3
- Elasticity of labor = 0.7
- Growth rate of output = 3%
- Growth rate of capital and labor input = 2%
Substitute these values into the formula:
\[ 3\% = (0.3 \times 2\%) + (0.7 \times 2\%) + \text{TFP Growth} \]
\[ 3\% = 0.6\% + 1.4\% + \text{TFP Growth} \]
\[ 3\% = 2\% + \text{TFP Growth} \]
\[ \text{TFP Growth} = 3\% - 2\% \]
\[ \text{TFP Growth} = 1\% \]
Therefore, the implied total factor productivity growth is 1%.
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