Professor David N. Weil Fall, Econ 1560 Second Midterm Exam

Transcription

1 Professor David N. Weil Fall, 2012 Econ 1560 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 a total of nine questions (some with multiple parts), for 100 points. Questions vary in their level of difficulty. Partial credit will be given for partially correct answers. Good luck! 1) [5 points] According to the Hoetelling model (discussed in Chapter 16) the price of a natural resource should rise at the rate of interest. (write your answer in the blue book). 2) [5 points] Is indoor air pollution an example of the tragedy of the commons? If so, why? If not, why not? You answer should take 3-4 sentences. 3) [10 points] Women in developing countries who watch TV soap operas whose female characters who have low levels of fertility also, on average, have low fertility. This must be because the cultural values exemplified by the characters on the TV shows are being adopted by the viewers. This demonstrates both that culture matters to behavior and that culture can be altered by external factors like television. Briefly discuss and critique this statement. Why might the inference be incorrect? How have social scientists assessed this conjecture using better methods? Why were those methods better? Your answer should be 3-4 short paragraphs.

2 4) [14 points] The table below presents data on physical capital, human capital, and output in two countries. Output per worker Physical capital per Worker Human capital per Worker Sylvania Freedonia The production function (in per worker terms) is 1/2 1/2 y Ak h Of the three possible sources of difference in output per worker that is, physical capital accumulation, human capital accumulation, and productivity which explains the largest part of the income gap between Freedonia and Sylvania? Which explains the second largest part of the gap? Note: you should not try to solve for the value of A for each country. Doing this is impossible without a calculator. Instead, you should find another way to solve the problem that does not require any difficult calculations. 5) [12 points] This question has two related parts. A) [6 points] When Social Security was created in the United States, the normal retirement age at which a worker could start receiving benefits was set at 65. At that time, life expectancy in the United States was 62 years. Thus most workers would have contributed to the system but not received any benefits. Discuss and critique the above statement in terms of what you know about changes in the shape of the survivorship function as countries develop. B) [6 points]the statement above continued: Social Security is mostly a pay-as-you-go system in which those who are working support the benefits received by retirees. Since 1935, life expectancy in the United States has risen to 78 years. This rise in life expectancy has raised the ratio of retirees to workers, and is the only source of the enormous financial strain that Social Security is now facing. Discuss and critique this second statement for reasons that have to do with demography but are not related to those discussed in part (A).

3 6) [8 points] Two economists are talking. One says If you want to study the role of culture in shaping economic outcomes, studying people who are living in a country other than the one they grew up in is a good way to go. The other says, Yes, but it is much better to study refugees than to study other sorts of migrants. Explain in 3-4 sentences why the second economist thinks this. You should not explain the view of the first economist. 7) [15 points] The tables below describe the ethnic and income variations in two countries. In each country, there are three ethnic groups (red, blue, and green) and three income levels (100, 200, and 300). The tables show the fraction of the population that falls into each. Country 1 Ethnicity Income Red Blue Green Total 100 1/ / /3 0 1/ /3 1/3 Total 1/3 1/3 1/3 1 Country 2 Ethnicity Income Red Blue Green Total 100 4/25 2/25 4/25 2/ /25 1/25 2/25 1/ /25 2/25 4/25 2/5 Total 2/5 1/5 2/5 1 A) [5 points] Which country has a higher Gini coefficient? Note, you should not try to actually calculate the Gini coefficient, since that is hard. You should just explain how you know. B) [5 points] Which country has a higher index of ethnic fractionalization? Again, you do not have to calculate the index of ethnic fractionalization, just explain how you know. C) [5 points] The Gini coefficient and the index of ethnic fractionalization are often discussed as factors that influence sociopolitical instability (SPI). However, in the data presented here, there is another factor present that seems likely to have an effect that goes beyond these two factors. Discuss how this third factor varies between Country 1 and Country 2 in the data, and how you might expect it to affect SPI.

4 8) [16 points] Consider the model of the growth and harvesting of a renewable natural resource that was presented in Chapter 16. For this question we will think of the resource as fish. The model was analyzed on a graph with the resource stock (S) on the horizontal axis, and the growth (G) and harvest (H) of the resource on the vertical axis. In that model, there were two components. One was the growth function, which was hump shaped (i.e. an inverted U), starting at the origin, reaching a peak at the maximum sustainable yield, and reaching zero again at the carrying capacity. For the purposes of this question, you should assume that the growth function is exactly has described in Chapter 16. In Chapter 16, we considered what would happen if the harvest was set at some fixed amount. Now, we will instead consider what would happen if the harvest was set by some wise social planner. The social planner reasons as follows: Harvesting more fish is good, because then my people get to eat more. Another thing I care about is how much effort goes into harvesting. For a given size harvest, I would definitely be happier if I could expend less effort on fishing, because then I could devote more resources to other things. Now, my fishermen tell me that, for a given amount of effort, they will catch more fish, the more fish there are in the lake (i.e. the higher the stock). Based on the above reasoning, the social planner plots a set of iso-utility curves in the diagram that we have been using. (An iso-utility curve is the same as an indifference curve it shows combinations of two things that give the same benefit to the social planner.) A) [8 points] Show what these iso-utility curves look like, in the diagram that has S on the horizontal axis and H on the vertical axis. Indicate which curves are associated with higher utility for the social planner. Provide appropriate explanation. B) [8 points] Combining these iso-utility curves with the growth curve from the model, show what the steady state level of harvest and resource stock will be. How does the harvest compare to the maximum sustainable yield? How does the resource stock compare to the optimal stock which is associated with the peak of the growth curve? Give a short explanation as to what is going on.

5 9) [15 points] When we considered the Solow model, we thought about an economy in which capital and labor were combined to produce output. The production function was Y = F(K, L) We then assumed constant returns to scale, so that we could write the production function in perworker terms y = f(k). We summarized this production function in a graph that had capital per worker on the horizontal axis and output per worker on the vertical axis. The graph had a nice curved shape (starting at the origin, positive first derivative, and negative second derivative) and was drawn on the board about 200 times during the semester. When we did this, we were implicitly assuming that there was a single sector of the economy. However, later in the book, for example when we discussed the efficiency of production, we talked about an economy with two sectors. So, suppose that there are indeed two sectors of the economy. One of them has exactly the production function described above, where now the relevant K and L are the amounts of capital and labor used in that sector. Call this the modern sector. Suppose that in the other sector, which we will call the traditional sector, the only input to production is labor. Further, assume that in the traditional sector, the marginal product of labor is constant it does not depend on how many people are working in the sector. Define w T to be the marginal product of labor in the traditional sector. Finally, assume that labor is allocated efficiently (as discussed in Chapter 10) between the modern and the traditional sector. I would like you to draw a diagram relating capital per worker (in the economy as a whole) with output per worker (in the economy as a whole). You should mark any relevant points on the curve. You should also provide some explanation (such as a diagram like the one about labor allocation in Chapter 10) for what is going on. You do not have to provide a formal mathematical proof or anything, and indeed you should be able to answer this question without writing down any equations. Note: I am not asking you to describe how the economy evolves over time, as in the Solow model. You should take the amount of capital and the number of workers as fixed.