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EC 390 Hoemwork Assignment

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Question;Answer all 6 questions. In order to get full credit you must show all of your work. If questionshave 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 beasked to solve for growth rates using the formulas given in class and specic values for individualparameters.(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 rateincreases from s to s does the growth rate go up, down, or stay the same? Show how youarrived at your answer.3.(15 points) The Solow ModelComparative Statics: Show graphically how thesteady-state level of capital changes in response to changes in the following parameters.(a) s increases(b) d falls(c) n falls4.(10 points) Increasing Returns and Imperfect Competition: Suppose a new pieceof computer softwaresay a word processor with perfect speech recognitioncan be created fora onetime cost of $100 million. Suppose that once its created copies of the software can bedistributed at accost of $1 each.(a) If Y denotes the number of copies of the computer program produced and X denotes theamount spent on production, what is the production functionthat is, the relation betweenY and X?(b) Make a graph of this production function. Does it exhibit increasing returns? Why or whynot?(c) Suppose the rm charges a price equal to marginal cost ($1) and sells a million copies of thesoftware. What are its prots?(d) Suppose the rm charges a price of $20. How many copies does it have to sell in order tobreak 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 growingat a constant rate in the Romer model, and then in the year 2030, research productivity, z risesimmediately and permanently to the new level z.(a) Solve for the new growth rate of knowledge and yt.(b) Make a graph of yt over time.(c) Give two reasons why research productivity may increase in an actual society.6.(5 points) An increase in the initial stock of knowledge: Suppose we have twoeconomieslets call them Earth and Marsthat are identical, except that one begins with astock of ideas that is twice as large as the other: AEART H = 2AM ARS. The two economies are00so far apart that they dont share ideas, and each evolves as a separate Romer economy. On asingle graph, plot the behavior of per capita GDP on Earth and Mars over time. What is theeect of starting out with more knowledge?

 

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