Mary Goret
2 days ago
Why is it that in harrod-domar model a change in savings rate has a permanent effect on the growth rate on GDP per capita while in the solow model a change in savings rate has a temporary effect.
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Google Gemini AI
2 days ago
Harrod-Domar Model
In the Harrod-Domar model, a change in the savings rate (s) has a permanent effect on the growth rate of GDP per capita (y) because the model assumes:
- A fixed capital-output ratio (k): The amount of capital required to produce one unit of output is constant.
- A constant population growth rate (n): The population grows at a constant rate, leading to an increase in the labor force.
With these assumptions, the model states that:
```
Δy/y = s/k - n
```
Where:
- Δy/y is the growth rate of GDP per capita
- s is the savings rate
- k is the capital-output ratio
- n is the population growth rate
Therefore, an increase in the savings rate (s) will directly increase the growth rate of GDP per capita indefinitely.
Solow Model
On the other hand, in the Solow model, a change in the savings rate (s) has a temporary effect on the growth rate of GDP per capita because the model incorporates:
- Diminishing returns to capital: As capital increases, the marginal productivity of capital decreases.
- Technological progress: The model assumes a constant rate of technological progress, which shifts the production function upward over time.
With these factors, the Solow model states that:
```
Δy/y = α(k - k-) + ηg
```
Where:
- α is the elasticity of output with respect to capital
- k is the current capital stock
- k- is the steady-state capital stock
- η is the weight on technological progress
- g is the rate of technological progress
When the savings rate increases, it initially leads to an increase in the capital stock. However, as capital accumulates, diminishing returns set in, and the marginal productivity of capital falls. This eventually slows down the growth rate of GDP per capita.
Furthermore, technological progress shifts the production function upward, which also contributes to the decline in the growth rate. Over time, the economy reaches a steady state where the capital stock stabilizes at k- and the growth rate of GDP per capita converges to the rate of technological progress (g).
Thus, in the Solow model, the effect of a change in the savings rate on the growth rate is temporary, as the economy eventually converges to its steady state.
In the Harrod-Domar model, a change in the savings rate (s) has a permanent effect on the growth rate of GDP per capita (y) because the model assumes:
- A fixed capital-output ratio (k): The amount of capital required to produce one unit of output is constant.
- A constant population growth rate (n): The population grows at a constant rate, leading to an increase in the labor force.
With these assumptions, the model states that:
```
Δy/y = s/k - n
```
Where:
- Δy/y is the growth rate of GDP per capita
- s is the savings rate
- k is the capital-output ratio
- n is the population growth rate
Therefore, an increase in the savings rate (s) will directly increase the growth rate of GDP per capita indefinitely.
Solow Model
On the other hand, in the Solow model, a change in the savings rate (s) has a temporary effect on the growth rate of GDP per capita because the model incorporates:
- Diminishing returns to capital: As capital increases, the marginal productivity of capital decreases.
- Technological progress: The model assumes a constant rate of technological progress, which shifts the production function upward over time.
With these factors, the Solow model states that:
```
Δy/y = α(k - k-) + ηg
```
Where:
- α is the elasticity of output with respect to capital
- k is the current capital stock
- k- is the steady-state capital stock
- η is the weight on technological progress
- g is the rate of technological progress
When the savings rate increases, it initially leads to an increase in the capital stock. However, as capital accumulates, diminishing returns set in, and the marginal productivity of capital falls. This eventually slows down the growth rate of GDP per capita.
Furthermore, technological progress shifts the production function upward, which also contributes to the decline in the growth rate. Over time, the economy reaches a steady state where the capital stock stabilizes at k- and the growth rate of GDP per capita converges to the rate of technological progress (g).
Thus, in the Solow model, the effect of a change in the savings rate on the growth rate is temporary, as the economy eventually converges to its steady state.
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