Question

Solow Growth Model Question:

Consider an economy where output (Y) is produced according to function Y=F(K,L). L is number of workers and Y is the capital stock. Production function F(K,L) has constant returns to scale and diminishing marginal returns to capital and labor individually. Economy works under assumption that technology is constant over time. The economy is in the steady-state capital per worker. Draw graph. In two year time there is a natural disaster which destroys part of economies capital stack. Assume this is a one off event that is not expected to reoccur. Show on a graph what happens to income per worker in the short and long run. Also provide complete explanation of what happens to the graph.

Answer 1

Consider the diagram below, where capital per worker is on X-axis and output per worker, investment per worker and breakeven investment are on Y-axis. The economy is in steady state when the breakeven investment line intersects the investment per worker curve (point E). Hence, k* is the steady state level of capital.

Due to natural disaster, a part of capital stock of the economy gets destroyed. Hence, capital per worker decreases, say to k₁ level. As shown in the diagram, the output per worker also decreases from y* to y₁. This is the short run effect on output per worker. Hoever, the investment is higher than the required (break-even) investment, which subsequently adds to the capital. Hence, the capital as well as capital stock increases till the investment and breakeven investment match each other. This happens at the previous level of steady state equilibrium. Hence, in the long run the capital per worker gets back to its previous level and the output per capita also returns to the steady state level.