This is a question for the Romer model of innovation.

The East Island and the West Island are the only countries in the world of Oceania. The two islands are so far away that they are not in contact, so ideas do not spread from island to the next and you may consider them in isolation.

a. We have some economic data from the East Island. Population Lbar = 1000; Lyt = 900; Lat = 100. These numbers are constant over time. Suppose that real GDP in 1965 (Y1965) was 5472 and real GDP in 2015 (Y2015) was Y = 9000.

Find the average growth rate of real GDP.

b. Continue using the data from (a). You may also use your answer from (a). We have some economic data from the East Island. Population Lbar = 1000; Lyt = 900; Lat = 100. These numbers are constant over time. Suppose that real GDP in 1965 (Y1965) was 5472 and real GDP in 2015 (Y2015) was Y = 9000.

Find ell (the fraction of population doing research) and the parameter z. (Hint look at the formula for g and g_A. Use this formula to find z.)

c. Continue from parts (a) and (b). You may use your answers from (a) and (b).

Suppose that the West Island has the same z and ell, but Lbar = 2000. Find its growth rate.

d. Suppose that the current level of GDP per capita (in 2015) is the same in both islands. Predict relative GDP in the year 2100. You may need to use your previous answers.