Question: let y10 sqrtk sqrtl suppose households save 10...
Let Y=10 * sqrt(K) * sqrt(L)
Suppose households save 10% of all output. This savings is added to the capital stock for the next period. On the other hand, depreciation destroys 3% of capital in each period.
- Draw a graph depicting the steady state equilibrium. (You should have per capita capital on the x axis and per capita investment on the y axis.)
- Solve for the equilibrium, giving values for y*, k*, i*, and c*.
- Suppose the savings rate were to increase to 15%.
- Show the effect of this change on a graph like that you drew for part a.
ii. Draw a graph showing income across time. Start the graph a little before the change in savings, assuming the economy was in the steady state in part a. Then show how incomes change over time after the one-time change in the savings rate.
- Go back to the original problem. Now suppose the shift to computer technology means that the depreciation rate increases to 5%. Repeat parts i and ii of part c.