Intermediate Macroeconomics

#3
This homework is due at the start of class on September 23, 2014. Please complete all problems and show
work for full

credit.
1. Suppose that the economy is on a balanced growth path in the Romer model, and then, in the
year 2020, research

productivity, 2, increases immediately and permanently to a new higher level
2’ > Z.
a. Solve for the new growth rate of

knowledge and per capita output, yt.
b. Make a graph of yt over time using a ratio or log scale.
c. Why might research

productivity increase in an economy?
2. Suppose the parameters of the Romer model take the following values: /To =

100, l: 0.06, 2
1/3,000, and Z = 1,000.
a. What is the growth rate of output per person in the economy?
b. What is the initial

level of output per person? What is the level of output per person in
100 years?
c. Now consider the following changes,

one at a time: a doubling of the initial stock of
knowledge Ao, a doubling of the research share l_, a doubling of research

productivity 2,
and a doubling of the population Z. How would your answer to parts (a) and (b) change
in each case?
d. If

you could advocate one of the changes considered in part ( c), which would you choose
and why?
3. Consider a version of

the Romer model with the following production function:
Y, = A-EL“
In this version of the model the exponent on ideas in

the output production function has been
reduced so that ideas have diminishing returns in the production of output.
a.

Provide an economic interpretation of this re-formulation of the problem.
b. What is the growth rate of knowledge in this

economy?
c. What is the growth rate ofoutput per person in this economy?
d. Solve for the level of output per person at

each point in time.

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