Question

2. Suppose a war destroys part of a nation’s population but not its capital stock, (say on account of a neutron bomb being deployed). Use the Solow model without technological change to show the effect of this event on the country’s total output and per capita output over time. Assume prior to this event the economy was on its steady state path.

Answer 1

The graph below depicts the Solow model.In vertical axis output/worker ( Y/L) is measured and in horizontal axis Capital/worker ( K/L) is measured. Here the curve y= f(k) shows the relationship between Marginal product of worker and capital available per worker. Further the straight line from the orgin shows the constant population and Depreciation rate. The curve sy shows the investment curve. The steady state is at the point where sy= (n+d)k and capital output ratio is constant ( k^*).

Now, when war takes places and there is no affect on capital stock. Only population declines due to casualties. Due to less workers total output falls. However it increases capital available per worker to k_{​​​​​1}. Due to greater capital availability per worker , marginal product increases from y^* to y₁ ( As shown in graph in orange line)

Therefore it can be concluded that in this situation total output falls but output per worker increases from steady state.

Overtime at k₁ we find investment < Depreciation. So capital stock will decline overtime assuming all other things constant. This will decline until it reaches the old steady state at k^*.