Question:
Consider the following model combining the Solow model and the Romer model:
?? = ???? ????1−?
Δ??+1 = ?̅?????
??? + ??? = ?̅
??? = ? ̅?̅̅
a) Assume initially that ? = 0, ?0 = 1 , ? ̅= 0.02, ?̅= 0.00001, ?̅ = 10,000, the depreciation rate ?̅= 0.1 , ?̅=0, ?0 = 500,000.
What type of model is that?
Find the growth rate of knowledge in the economy.
Find the growth rate of output per person.
Find the growth rate of consumption per person.
b) Now assume that ? = 0.3, ?0 = 1 , ? ̅= 0.02, ?̅= 0.00001, ?̅ = 10,000, the depreciation rate ?̅= 0.1 , ?̅=0.3, ?0 = 500,000.
Using Excel or the similar software find the values of ?? , ?? , output per person ?? and consumption per person in periods 1, 5, 10, 20, 50, 100 and 200.
What are the growth rates of these variables from period 0 to period 1, from period 4 to period 5, from period 9 to period 10, from period 19 to period 20, from period 49 to period 50, from period 99 to period 100 and from period 199 to period 200?
Plot output per person from period 0 to period 200 on a graph.
c) Now assume that parameter values are the same as in b) except for the investment rate which is now ?̅=0.4.
Based on the model what would be your predictions about the growth rate of knowledge and growth rate of capital in each period compared to the situation in part b)? Explain.
Now Using Excel or the similar software find the values of ?? , ?? , output per person ?? and consumption per person in periods 1, 5, 10, 20, 50, 100 and 200. What are the growth rates of these variables from period 0 to period 1, from period 4 to period 5, from period 9 to period 10, from period 19 to period 20, from period 49 to period 50, from period 99 to period 100 and from period 199 to period 200?
How these values compare with those in part b)? Are you surprised by any of the results? Explain.
d) Compare two economies: one with parameter values as in b) and the other one with the same parameter values except for the initial set of knowledge ?0 = 5.
Briefly explain what will be the differences in the growth rates of knowledge, capital and output per worker?
e) The government believes that the growth rate of output per worker is low and thinks about the measures that would increase it. There are two options available: (i) increasing the share of workers employed in the research sector and (b) increasing the investment rate. The government can choose only one option. Which option would you recommend and why?
