Use the Solow model to work out the consequences of a one-time decrease in the total stock of capital (KT ) due to, for example, a natural disaster without loss of life.
i. Start with an economy in steady state, so that kt = k ∗ for all periods t = 0, 1, . . . , T − 1 prior to the disaster.
ii. At time T, a share of the total capital stock is lost. What are the immediate consequences for total output, investment, and consumption, and their per capita counterparts?
iii. What happens to capital per worker over time? What about output and consumption per worker? Plot time paths for K, Y , and C, as well as for k, y, and c. Make sure to include in your plots years both before and after year T.