Af(k)

1. Homework: Suppose that δ falls from δ1 to δ2 in our model (δ1>δ2 ). Hold all other parameters as exogenous. Explain what happens to y and k over time. Do y and k grow forever or will they eventually arrive at a steady state? How does the new steady state compare to the initial steady state? How would δ have to change in order for y to grow forever? Is it reasonable to think that the depreciation rate can continue to change like this over time?

2. y Af(k) δ1k δ2k Af(k) k

3. When the depreciation rate increases both y and k begin to rise. • However, y and k do not grow forever as they settle down to new steady states • In the new steady state both y and k are greater compared with the original steady state • For y to grow forever, δ would have to keep falling. • But the depreciation rate can not get smaller than zero so this can not cause persistent growth in output per capita

4. Homework: Suppose that A rises from A1 to A2 in our model (A1<A2 ). Explain what happens to y and k over time. Do y and k grow forever or will they eventually arrive at a steady state? How does the new steady state compare to the initial steady state? How would A have to change in order for y to grow forever? Is it reasonable to think that productivity will continue to change like this over time?

5. y A2f(k) A1f(k) δk A2f(k) A1f(k) k

6. When productivity increases, k and y begin to rise. • But k and y do not rise forever since they arrive at a new steady state eventually • The new steady state has higher levels of y and k • For y to grow forever, productivity must continue to rise over time • It is reasonable to think productivity can continue to grow for a very long time. New technologies continue to be developed and there is no sign of this stopping