03 Jun Question Answer all 6 questions. In order to get full credit
Question
Answer all 6 questions. In order to get full credit you must show all of your work. If questions
have multiple parts please clearly label which part of the question you are answering.
1.
(6 points ) The Harrod-Domar Model with numbers: In this question you will be
asked to solve for growth rates using the formulas given in class and specic values for individual
parameters.
(a) s = 15%, c = 3, d = 2%
(b) s = 20%, c = 4, d = 5%
(c) s = 4%, c = 2, d = 6%
2. (4 points ) The Harrod-Domar ModelComparative Statics: If the savings rate
increases from s to s does the growth rate go up, down, or stay the same? Show how you
arrived at your answer.
3.
(15 points ) The Solow ModelComparative Statics: Show graphically how the
steady-state level of capital changes in response to changes in the following parameters.
(a) s increases
(b) d falls
(c) n falls
4.
(10 points ) Increasing Returns and Imperfect Competition: Suppose a new piece
of computer softwaresay a word processor with perfect speech recognitioncan be created for
a onetime cost of $100 million. Suppose that once its created copies of the software can be
distributed at accost of $1 each.
(a) If Y denotes the number of copies of the computer program produced and X denotes the
amount spent on production, what is the production functionthat is, the relation between
Y and X ?
(b) Make a graph of this production function. Does it exhibit increasing returns? Why or why
not?
(c) Suppose the rm charges a price equal to marginal cost ($1) and sells a million copies of the
software. What are its prots?
(d) Suppose the rm charges a price of $20. How many copies does it have to sell in order to
break even? What if the price is $100 per copy?
(e) Why does the scale of the marketthe number of copies the rm could sell matter?
5.
(10 points ) An increase in research productivity: Suppose the economy is growing
at a constant rate in the Romer model, and then in the year 2030, research productivity, z rises
immediately and permanently to the new level z .
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