Suppose a country has a production function that exhibits constant returns to scale. Starting from an initial steady state with population growth rate n and a rate of capital depreciation Delta, the country is devastated by an epidemic that quickly kills half of its population without affecting its capital stock.
1. According to the Solow growth model, what would be the immediate impact of this epidemic on total output? Explain.
2. Explain what the Solow model implies would be the immediate impact of this epidemic on output per worker.
3. If the saving rate is unchanged and the population regains its pre-epidemic growth rate, the economy will eventually return to its initial steady-state level of k*. Draw three graphs with time on the horizontal axis to illustrate the time paths of capital per worker k, consumption per worker consumption, and output per worker y in the initial steady state (to the left of line A), after the epidemic strikes but before the new steady state is reached (between lines A and B), and after the final steady state is reached (to the right of line B).