PS1 - Economics 102 Introductory Macroeconomics Spring 2005...

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Economics 102 Introductory Macroeconomics - Spring 2005, Professor J. Wissink Problem Set 1 1. The small industrial town of Springfield produces two goods: rafts (produced with labor hours and wood) and girders (produced with metal, machinery and labor hours). The production function (in terms of labor, holding all other inputs constant) for each of these outputs is given in the tables below. Springfield has 80 hours of labor, total, to allocate to these two output sectors. a) What is the Marginal Productivity of Labor (MP L ) in the production of Rafts? What is the Marginal Productivity of Labor (MP L ) in the production of Girders? b) Does the “Law of Diminishing Returns” apply in the production function of Rafts? How about in the production of Girders? If you answer affirmatively, indicate where diminishing returns “set in”. c) Graph the production function for rafts and the production function for girders as labor hours vary in each sector. d) Graph the Production Possibilities Frontier (PPF) between rafts and girders. Put Girders on the horizontal axis and rafts on the vertical axis. Assume that all units of measurement are infinitely divisible, so you can smoothly connect points on your graph. e) What is the Total Opportunity Cost of 4 rafts? What is the Marginal Opportunity Cost of the 4 th raft? f) Time has passed since the first date in which this economic data was collected (the year 2000). During this time there were substantial technological improvements in the production of girders, making its production easier and making labor more productive. The following graph depicts the actual amount of girders produced in Springfield over several years. By looking at this graph, can you conclude that the Law of Diminishing Returns didn’t apply over the 2000-2008 period? Why or why not. Number of Number of Number of Number of Hours Rafts Hours Girders 0 0 0 0 10 1 10 15 20 2 20 28 30 3 30 39 40 4 40 48 50 5 50 56 60 6 60 61 70 7 70 65 80 8 80 67
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Production of Girders over Time 0 50 100 150 200 250 300 350 400 0 20 40 60 80 100 Labor Girders 2000 2002 2008 2006 2004 2. Two friends Claire and Thomas work for a textbook publisher. They have a day to write exercises for the publisher’s new Math and Economics workbooks. Each one can allocate 8 hours that day to writing (and solving) the exercises they dream up. The following table shows how many hours it takes each of one of them to compose one exercise, based on the subject matter. Hours per Math exercise Hours per Econ exercise Claire 0.5 0.5 Thomas 4 1 a) Who has the comparative advantage in writing Math exercises? Who in Econ? Give a brief defense/explanation of why. b) Who has the absolute advantage in writing Math exercises? Who in Econ? Give a brief defense/ explanation of why. c) Draw Claire’s and Thomas’ PPF curves if they compose exercises separately. Put “Econ exercises” on the horizontal axis and “Math exercises” on the vertical axis in each graph.
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