Question

1. You are asked to 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

Answer 1

Equation of Solow model is: (1+n)k(t+1)= sy+(1-d)k(t), where n= population growth rate, k(t+1)= per capita Capital required in next period; s= savings rate; d= depeciation rate, y= per capita output

At steady state, the change in capital is 0. So, it means k(t+1)=k (t). Therefore, equation becomes: K/Y= s/(n+d).

a) investment rate rises in Tanzania: If we assume that Tanzania is a closed economy, then I= sY. Which means an increase in interest rate increases the sY component of equation. So, there is shift as shown below:

Steady state capital and output per capita, both increases. growth rate is equal to the increase in rate of investment at time 0, but as GDP per capita reaches steady state, growth rate becomes 0. Due to more investment, there is rise in capital stock and output.

b) immigration increases population of france by 10%. there is increase in n. So, graph will change as below:

Steady state capital and output per capita falls. Since there is a larger population, per capita value declines. Growth rate is also declined in short run but it soon returns to 0.

c) Earthquake destroys 10% of per capita stock of chile. So, there is 10% decline in k. Sice k appears in both graphs, both the curves shift as below:

So, there is no change in per capita capital. But, per capita GDP falls down. this is because of loss of capital, GDP falls. But per capita level of capital does not change because low k also means lower depreciation. Growth rate of per capita GDP falls until it reaches new steady stae level.

d) Malaysia realises 10% increse in TFP. It not only affects the level of per capita value of GDP but also affect growth rate of GDP. Hence, growth rate of GDP per capita will be 10% at time 0. There will an increase in both per capita capital and per capita GDP: