Macroeconomics
Problem set 2
Due date: Tuesday, November 3. Your group must submit the problem set by the beginning of
the class.
You must provide explanation for your answers. Please write clearly. If your answer is not
clear, I cannot give you the credits for the questions.
Simplified Romer Model (Answer the questions 1 and 2 below based on the model we
discussed in the class);
1. An economy is on a balanced growth path in the Romer model. Suppose that, a country is
trying to encourage knowledge/idea production sector. To represent this policy in a simple way,
let’s assume that, in the year 2020, ̅ rises immediately and permanently to the new level ̅ . (4
points)
(a) What are the new growth rates of knowledge and output per person? Explain in words as
well.
(b) Make a graph of output per person over time using a ratio scale. Do we observe the economy
grow at a higher rate? Explain.
̅
2. Now suppose that the parameters of the model take the following values: ̅̅̅ =80, =0.08,
̅
, and ̅ =2000. (4 points)
(a) What is the growth rate of output per person in this economy?
(b) What is the initial level of output per person? What is the level of output per person after 200
years?
3. Consider the following variation of simplified Romer model:̅

̅

̅̅
There is a simple change. Don’t be intimidated by the change. Just solve the model in steps and
see what you observe.

(A) Solve this variant Romer model in detail. You need to show all the necessary steps to derive
the solutions (5 points). After that, answer the following questions:
a. What is the growth rate of knowledge in this economy? (2 points)
b. What is the solution for the level of output per person? What is the growth rate of output per
person in this economy? (3 points)
c. Suppose we have two economies — let’s call them country 1 and country 2. The economy of
country 2 is described by the variant Romer model above.
Country 1 is identical with the country 2 except that the production process of output in this
country 1 is described by the following production function (as we discussed in the class):

These two economies are so far apart that they don’t share ideas, and each evolves as a separate
economy. On a single graph (with a ratio scale), plot the path of per capita GDP of country 1 and
country 2 over time. Explain in words as well. (4 points)