(a) Suppose that both Ghana and Nigeria have the following production_function Y = f(K,L) = K©5L05 (1) What is the per-worker production function? (i) Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that Ghana saves 10 percent of output cach year and Nigeria saves 15 percent of output cach year. Using your answer from (1) and the steady-state condition that investment equals depreciation, find the steady-state levels of income (output) per worker and consumption per worker for each country.
(a) Suppose that both Ghana and Nigeria have the following production_function Y = f(K,L) = K©5L05 (1) What is the per-worker production function? (i) Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that Ghana saves 10 percent of output cach year and Nigeria saves 15 percent of output cach year. Using your answer from (1) and the steady-state condition that investment equals depreciation, find the steady-state levels of income (output) per worker and consumption per worker for each country.
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![### Educational Content on Production Function and Economic Analysis
#### Production Function Analysis for Ghana and Nigeria
### (a) Production Function
Both Ghana and Nigeria are assumed to have the following production function:
\[ Y = f(K, L) = K^{0.5} L^{0.5} \]
1. **Per-Worker Production Function:**
- The per-worker production function is derived by expressing output \(Y\) as a function of per-worker quantities. Let \( y = \frac{Y}{L} \) and \( k = \frac{K}{L} \). Thus, the per-worker production function becomes:
\[ y = k^{0.5} \]
2. **Steady-State Analysis:**
- Assume:
- No population growth or technological progress.
- 5% of capital depreciates each year.
- Ghana saves 10% of output each year.
- Nigeria saves 15% of output each year.
- **Objective:** Find the steady-state levels of income (output) per worker and consumption per worker for each country.
- Conditions:
\[ s \cdot y = \delta \cdot k \]
where \( s \) is the savings rate and \( \delta \) is the depreciation rate.
### (b) Variation in Saving and Investment Rates
Discuss four reasons why the rates of saving and investment vary significantly from country to country. Possible factors may include:
1. **Cultural Preferences:** Cultural attitudes towards saving versus consumption.
2. **Economic Policy:** Government policies on taxation, interest rates, and incentives for saving and investment.
3. **Income Levels:** Higher income levels generally lead to higher savings rates as basic consumption needs are met.
4. **Financial Systems:** The development and accessibility of financial markets and institutions that facilitate saving and investment.
### (c) Fiscal Expansion and Macroeconomic Effects
Using a diagram, explain the effect on exchange rate, income, output, and employment in Ghana if there is a fiscal expansion under conditions of a steeply sloped BP curve and a flatter LM curve.
1. **Diagram Explanation:**
- **BP Curve:** Represents the balance of payments equilibrium. A steeply sloped BP curve implies a low sensitivity of the capital account to the interest rate.
- **LM Curve:** Represents the equilibrium in the money market. A flatter LM curve suggests high sensitivity of money demand to income.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65e73232-57a7-48a2-9fe1-7eeb67aea2e1%2F07bfa0a5-7fdd-4366-b738-3723b9061c43%2F7yp4rsd.png&w=3840&q=75)
Transcribed Image Text:### Educational Content on Production Function and Economic Analysis
#### Production Function Analysis for Ghana and Nigeria
### (a) Production Function
Both Ghana and Nigeria are assumed to have the following production function:
\[ Y = f(K, L) = K^{0.5} L^{0.5} \]
1. **Per-Worker Production Function:**
- The per-worker production function is derived by expressing output \(Y\) as a function of per-worker quantities. Let \( y = \frac{Y}{L} \) and \( k = \frac{K}{L} \). Thus, the per-worker production function becomes:
\[ y = k^{0.5} \]
2. **Steady-State Analysis:**
- Assume:
- No population growth or technological progress.
- 5% of capital depreciates each year.
- Ghana saves 10% of output each year.
- Nigeria saves 15% of output each year.
- **Objective:** Find the steady-state levels of income (output) per worker and consumption per worker for each country.
- Conditions:
\[ s \cdot y = \delta \cdot k \]
where \( s \) is the savings rate and \( \delta \) is the depreciation rate.
### (b) Variation in Saving and Investment Rates
Discuss four reasons why the rates of saving and investment vary significantly from country to country. Possible factors may include:
1. **Cultural Preferences:** Cultural attitudes towards saving versus consumption.
2. **Economic Policy:** Government policies on taxation, interest rates, and incentives for saving and investment.
3. **Income Levels:** Higher income levels generally lead to higher savings rates as basic consumption needs are met.
4. **Financial Systems:** The development and accessibility of financial markets and institutions that facilitate saving and investment.
### (c) Fiscal Expansion and Macroeconomic Effects
Using a diagram, explain the effect on exchange rate, income, output, and employment in Ghana if there is a fiscal expansion under conditions of a steeply sloped BP curve and a flatter LM curve.
1. **Diagram Explanation:**
- **BP Curve:** Represents the balance of payments equilibrium. A steeply sloped BP curve implies a low sensitivity of the capital account to the interest rate.
- **LM Curve:** Represents the equilibrium in the money market. A flatter LM curve suggests high sensitivity of money demand to income.
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