Econ 156 Second Midterm Exam

Transcription

1 Professor David N. Weil 11/6/07 Econ 156 Second Midterm Exam Instructions: Please answer all questions in the blue books. You may not use notes, books, or calculators. Please show your work. There are six questions, for 100 points. Overall, the test is a bit hard, and will be curved accordingly. Partial credit will be given for partially correct answers. Good luck! 1) [10 points] If a country s physical and human capital both double over the course of 100 years, and output increases by a factor of eight, by what factor does productivity increase during this time? Assume that, the exponent on capital in the production function, is equal to ) [10 points] The following text is from the web site CNET reviews Two rival next-generation formats--blu-ray and HD DVD--are now vying to become the successor to DVD's throne. Both display movies in full high-definition resolution, addressing one shortfall of the current DVD format, which is only standard-def. The video and audio quality of both formats can be truly spectacular when shown on an HDTV with a quality home theater audio system, surpassing even high-def television itself in fidelity and impact. The bad news? To get that improved fidelity, you have to decide between either a Blu-ray player or an HD DVD player, and you won't be able to play certain studios' movies on either one. For example, if you're a sci-fi fan and want to watch The Fifth Element (Sony Pictures), you'll need a Blu-ray player, but if you want to watch Serenity (Universal) you'll need an HD DVD player. Yes, combo players that can handle both formats are available, but they currently cost more than actually purchasing two players, one for each format! How does the example of Blu-ray and HD DVD relate to the discussion of the technology production function in Chapter 9 of the textbook? 3) [10 points] A student reading the case study in the textbook about the textile industry in 1900 makes the following statement: It is true that in the US each worker was taking care of 10 looms while in India each worker was taking care of only one loom. However, in India at the time there was significant unemployment. Thus, if each worker had taken care of ten looms, only one tenth as many workers would have been employed in the textile industry, while the other nine-tenths of workers would have been unemployed. Thus output would have been no higher in India if textile workers had worked just as hard as US workers. Therefore, the source of India s low output at that time was not inefficiency. Comment on this statement. Is the conclusion correct? Why or why not? Your answer should be four or five sentences long.

2 4) [25 points] Consider a country in which output is produced with a standard constant returns to scale production function, where the only factors of production are capital and labor. Factors earn their marginal products. Let L be the quantity of labor and K D be the quantity of capital (D is for domestic). Let k D be the quantity of domestic capital per worker. Initially the country is in autarky. A) [5 points] Draw a picture with capital per worker on the horizontal axis and units of output measured on the vertical axis. Show the production function (this is the usual picture of the production function that we draw). Indicate the levels of GDP per worker and GNP per worker. For capital equal to k D show the marginal product of capital. Extend the MPK line to the vertical axis, and indicate on that axis both capital payments per worker and wage payments per worker. B) [5 points] Now suppose that the economy is opened to capital flows. A quantity of k F units of capital per worker enters the country. No domestic capital exits, and labor neither exits nor enters. Draw a diagram like in part (A), showing the new level of GDP per worker. On the horizontal axis, you should mark the points k D, the quantity of capital per worker in autarky, and (k D + k F ), the quantity of capital per worker when the capital market is open. C) [5 points] Using the diagram for part B, show the new level of wage payments per worker. How do wage payments per worker compare in the open economy vs. under autarky? D) [5 points] Using the same diagram (or a copy), show per-worker payments to domestic capital. How do total payments to domestic capital compare in the open economy vs. under autarky? E) [5 points] Finally, use this diagram to show how GNP per worker compares in the open economy vs. under autarky.

3 5) [20 points] Consider the one-country model of technology and growth. The equation for technological progress is ˆ L A A And the production function (in per worker terms) is y A(1 A ) Suppose that L=1, 10, and A = Now suppose that A is raised to How many years will it take before output per worker returns to the level it would have reached if A had remained constant? To answer this question, you will have to use the table of natural logarithms that I have conveniently included below. Note that these logarithms are rounded to two decimal places to make your calculations easier. Note also that you are welcome to solve this problem in either discrete or continuous time. In discrete time, ˆ / A ( At 1 At)/ At, while in continuous time ˆ da dt A. You will get the A same answer either way. For those not familiar with calculus, discrete time is easier. X ln(x) X ln(x)

4 6) [25 points] A country produces two good: corn and beans. These are also the two goods that are consumed in the country. Specifically, corn and beans are always consumed in the same proportion of one to one (that is, equal quantities of corn and beans). Corn and beans are both produced using land and labor. For peculiar agricultural reasons, some land can only be used for growing corn and other land can only be used for growing beans. In the country, there are 800 acres of corn-only land and 800 acres of bean-only land. There is no land that can be used for either crop. Labor, however, can move from crop to crop. The total labor force in the economy is 1,000 workers (which is the same as the total population). The production function for corn is 1/2 1/2 c C C X L, Where X c is land devoted to corn and L C is labor devoted to corn. The production function for beans is 1/2 1/2 B 2X B L B Notice that in both production functions, the variable on the left is a physical quantity (kilograms of corn or beans) and not the value of the output. Both the corn and bean sectors are perfectly competitive, so that workers and land earn their marginal products. A) [5 points] Suppose that the country is in autarky. Solve for the quantities of labor that will be used in the corn and bean sectors. [Hint #1: to solve this part of the question, you don t need to know anything about the relative prices of corn and beans. Indeed, you can approach this problem like a social planner who simply seeks to maximize output, subject to the relevant constraints. Hint #2: this should only take about 5 lines of algebra] B) [5 points] Solve for total production of corn and beans in autarky. C) [5 points] This part is hard, and not necessary for what comes next. Solve for the relative price of beans in terms of corn in autarky. That is, how many kilograms of corn are required to buy one kilogram of beans. [Hint: remember that labor can move freely between the sectors.] D) [5 points] Now suppose that the country opens to trade with the rest of the world. The world price of beans in terms of corn is one. In other words, one kilogram of corn can be traded for one kilogram of beans, and vice versa. Solve for the allocation of labor to corn and bean production in the country.

5 E) [5 points] Solve for total consumption of corn and of beans when there is free trade.