(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 each year and Nigeria saves 15 percent of output each year. Using your answer from (i) and the steady-state condition that investment equas depreciation, find the steady-state kvels of income (output) per worker and consumption per worker for each country. (b) Explain four (4) reasons why the rates of saving and investment vary so much from country to country. (c) With the aid of 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.

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NB: Solve A(ii), B and C

### Problem Set on Production Function and Economic Analysis
---

#### (a) Suppose that both Ghana and Nigeria have the following production function:
\[ Y = f(K, L) = K^{0.5}L^{0.5} \]

1. **What is the per-worker production function?**

2. **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 each year and Nigeria saves 15 percent of output each year. Using your answer from (i) 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.**

#### (b) Explain four (4) reasons why the rates of saving and investment vary so much from country to country.

#### (c) With the aid of a diagram, explain the effects 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.

--- 

### Detailed Explanation for Educational Purposes

**(a)** The given production function \( Y = f(K, L) = K^{0.5}L^{0.5} \) can be written in per-worker terms, where \( y \) represents output per worker ( \( Y/L \) ) and \( k \) represents capital per worker ( \( K/L \) ). 

1. **Per-worker Production Function:**
   \[ y = k^{0.5} \]

2. **Steady-state Analysis:**
   - Depreciation rate \( \delta = 0.05 \)
   - Savings rate for Ghana \( s_G = 0.10 \)
   - Savings rate for Nigeria \( s_N = 0.15 \)

   The steady-state level of capital per worker \( k^* \) is found where savings per worker equals depreciation per worker:
   \[ s \cdot f(k^*) = \delta \cdot k^* \]

   Similarly, the steady-state output per worker \( y^* \) and the consumption per worker \( c^* \) can be derived.

**(b)** Four reasons the rates of saving and investment vary from country to country include:
1. **Cultural Factors:** Cultural attitudes toward savings and consumption can significantly influence national saving rates.
Transcribed Image Text:### Problem Set on Production Function and Economic Analysis --- #### (a) Suppose that both Ghana and Nigeria have the following production function: \[ Y = f(K, L) = K^{0.5}L^{0.5} \] 1. **What is the per-worker production function?** 2. **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 each year and Nigeria saves 15 percent of output each year. Using your answer from (i) 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.** #### (b) Explain four (4) reasons why the rates of saving and investment vary so much from country to country. #### (c) With the aid of a diagram, explain the effects 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. --- ### Detailed Explanation for Educational Purposes **(a)** The given production function \( Y = f(K, L) = K^{0.5}L^{0.5} \) can be written in per-worker terms, where \( y \) represents output per worker ( \( Y/L \) ) and \( k \) represents capital per worker ( \( K/L \) ). 1. **Per-worker Production Function:** \[ y = k^{0.5} \] 2. **Steady-state Analysis:** - Depreciation rate \( \delta = 0.05 \) - Savings rate for Ghana \( s_G = 0.10 \) - Savings rate for Nigeria \( s_N = 0.15 \) The steady-state level of capital per worker \( k^* \) is found where savings per worker equals depreciation per worker: \[ s \cdot f(k^*) = \delta \cdot k^* \] Similarly, the steady-state output per worker \( y^* \) and the consumption per worker \( c^* \) can be derived. **(b)** Four reasons the rates of saving and investment vary from country to country include: 1. **Cultural Factors:** Cultural attitudes toward savings and consumption can significantly influence national saving rates.
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