Economics 100b Professor K. Kletzer Ucsc

Economics 100b Professor K Kletzer Ucsc

Analyze each of the following events using the Solow growth model (the events all happen at time 0): a) The investment rate rises in Tanzania. b) Immigration increases the population of France by 10%. c) An earthquake destroys 10% of the capital stock of Chile. (Hint: does steady state GDP per capita change in Chile?) d) Malaysia realizes a 10% rise in TFP due to technology transfer. For each of these: Draw a Solow diagram to show what happens when the economy is initially in steady state. Explain how steady-state GDP per capita changes. Use algebra to help in your explanation. Does steady-state capital per capita change? Explain how the growth rate of GDP per capita changes at time 0. Explain how the economy adjusts from the short run to the long run after the change.

Paper For Above instruction

The application of the Solow growth model to various economic events provides crucial insights into how economies respond to shocks and policy changes. In this paper, I analyze four distinct scenarios—changes in investment rates, immigration levels, capital destruction, and technological progress—employing both graphical and algebraic tools to understand their effects on steady-state output and growth trajectories.

1. The Effect of a Rise in the Investment Rate in Tanzania

When Tanzania experiences an increase in its investment rate, holding all else constant, the impact is spatially depicted through a shift of the savings function upward on the Solow diagram. The savings rate directly influences the steady-state capital per worker (k*), as the per capita capital accumulation depends on the amount of investment relative to depreciation and population growth. Algebraically, the steady-state capital per worker is defined as:

k* = (s / (n + δ))^{3}

where s is the savings rate, n is the population growth rate, and δ is depreciation. An increase in s elevates k, subsequently raising steady-state per capita output (y). The economy smoothly transitions from the initial to the new higher steady state, with the short-term growth rate of GDP per capita exceeding zero due to increased investment, then tending to zero in the long run as the new steady state is reached.

2. The Effect of a 10% Immigration Increase in France

Increased immigration effectively raises the population growth rate (n). Graphically, the steady-state shifts are represented by a move along the savings and investment curves, with higher n increasing the denominator in the steady-state formula, thereby reducing k*. Algebraically, an increased n decreases the steady-state capital per capita, but total output per worker may still increase, depending on initial conditions. The growth rate of GDP per capita approaches zero in the long run, but short-term dynamics might involve transitional growth as capital per worker adjusts downward.

3. Impact of a 10% Capital Destruction in Chile

A sudden destruction of capital reduces the current capital stock, shifting the economy below its steady state. According to the Solow model, the economy will experience a period of accelerated capital accumulation to return to the original steady state, assuming no changes in s, n, or δ. Since the destruction affects the total capital stock but not the steady state directly, the per capita GDP does not change in the long run, although the short-term growth rate increases temporarily as capital rebuilds. Algebraically, the steady state remains unchanged, but the transient dynamics involve a faster growth rate of capital and output until the steady state re-establishes.

4. The Effect of a 10% TFP Increase in Malaysia

Technological progress, represented by an increase in TFP, shifts the production function upward. Graphically, this corresponds to a higher level of output per worker at every level of capital per worker, shifting the steady-state line upwards. Algebraically, the new steady state per worker is higher, with the long-run growth rate of output per capita equal to the rate of productivity growth. Short-term, TFP increases lead to immediate higher growth of output per capita, and the economy transitions smoothly to a higher steady state characterized by elevated income levels and growth rates equal to TFP growth.

Conclusion

The detailed analysis reveals that changes in investment, demographics, capital stock, and technology have profound, yet predictable, effects within the Solow framework. Investment and technological improvements directly raise the steady-state output, while demographic shocks primarily influence growth rates. Capital destruction temporarily reduces capital per worker, prompting a recovery phase. Each case demonstrates the importance of both short-term dynamics and long-term steady states in understanding economic growth.

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