Exercises

1. A number of firms have located in the western portion of a town, after single-family residences took up the eastern portion. Each firm produces the same product and in the process emits noxious fumes that adversely affect the residents of the community.

a. Why is there an externality created by the .firms?

b. Do you think that private bargaining can resolve the problem with the externality? Explain.

c. How might the community determine the efficient level of air quality?

2. A computer programmer lobbies against copyrighting software. He argues that everyone should benefit from innovative programs written for personal computers, and that exposure to a wide variety of computer programs will inspire young programmers to create even more innovative programs. Considering the marginal social benefits possibly gained by his proposal, do you agree with the programmer's position?

3. Four firms located at different points on a river dump various quantities of effluent into it. The effluent adversely affects the quality of swimming for homeowners who live downstream. These people can build Swimming pools to avoid swimming in the river, and the firms can purchase filters that eliminate harmful chemicals in the material that is dumped in the river. As a policy adviser for a regional planning organization, how would you compare and contrast the following options for dealing with the harmful effect of the effluent:

a. An equal rate effluent fee on firms located on the river.

b. An equal standard per firm on the level of effluent each firm can dump.

c. A transferable effluentpermit system, in which the aggregate level of effluent is fixed and all firms receive identical permits.

4. Recent social trends point to growing intolerance of smoking in public areas. Many people point out the negative health effects of "second-hand" smoke. If you are a smoker and you wish to continue smoking despite tougher antismoking laws, describe the effect of the following legislative proposals on your behavior. As a result of these programs, do you, the individual smoker, benefit? Does society benefit as a whole?

a. A bill is proposed that would lower tar and nicotine levels in all cigarettes.

b. A tax is levied on each pack of cigarettes sold.

c. Smokers would be required to carry smoking permits at all times. These permits would be sold by the government.

5. A beekeeper lives adjacent to an apple orchard. The orchard owner benefits from the bees because each hive pollinates about one acre of apple trees. The orchard owner pays nothing for this service, however, because the bees come to the orchard without his having to do anything. There are not enough bees to pollinate the entire orchard, and the orchard owner must complete the pollination by artificial means, at a cost of $10 per acre of trees.

Beekeeping has a marginal cost MC = 10 + 2Q, where Q is the number of beehives. Each hive yields $20 worth of honey.

a. How many beehives will the beekeeper maintain?

b. Is this the economically efficientnumber of hives?

c. What changes would lead to the more efficient operation?

6. There are three groups in a community. Their demand curves for public television in hours of programming, T, are given respectively by

Wi = $150 - T W2 = $200 - IT W3=$250 - T Suppose public television is a pure public good that can be produced at a constant marginal cost of $200 per hour.

a. What is the efficient number of hours of public television?

b. How much public television would a competitive private market provide?

7. Reconsider the common resource problem given in Example 185. Suppose that crawfish popularity continues to increase, and that the demand curve shifts from C= 0.401 - 0.0064F to C = 050 - 0.0064F. How does this -shift in demand affect the actual crawfish catch, the efficient catch,and the social cost of common access? (Hint: Use the Marginal Social'Cost and Private Cost curves given in the example.)

8. The Georges Bank, a highly productive fishing area off New England, can be divided into two zones in terms of fish population. Zone 1 has the higher population per square mile but is subject to severe diminishing returns to fishing effort. The daily fish catch (in tons) in Zone 1 is

Fi = 200(Xi) - 2(Xi)2 where Xi is the number of boats fishing there. Zone 2 has fewer fish per mile but is larger, and diminishing returns are less of a problem. Its daily fish catch is

Fi = 100(X2) - (Xi)2 where Xi is the number of boats fishing in Zone 2. The marginal fish catch MFC in each zone can be represented as

MFC2=100 - 2(Xt) There are 100 boats now licensed by the U.S. government to fish in these two zones. The fish are sold at $100 per ton. The total cost (capital and operating) per boat is constant at $1000 per day.. Answer the following questions about this situation.

a. If the boats are allowed to fish where they want, with no government restriction, how many will fish in each zone? What will be the gross value of the catch?

b. If the U.S. government can restrict the boats, how many should be allocated to each zone? What will the gross value of the catch be? Assume the total number of boats remains at 100.

c. If additional fishermen want to buy boats and join the fishing fleet, should a government wishing to maximize the net value of the fish catch grant them licenses to do so? Why or why not?

APPENDIX

The Basics of Regression

This appendix explains the basics of multiple regression analysis, using an example to illustrate its application in economics.1 Multiple regression is a means of fitting economic relationships to data. It lets us quantify economic relationships and test hypotheses about them.

In a linear regression, the relationships that we fit to the data are of the following form:

Equation (A.I) relates a dependent variable Y to several independent (or explanatory) variables, Xi, X2,____For example, in an equation with two independent variables, Y might be the demand for a good, Xi its price, and Xi income. The equation also includes an error term e that represents the collective influence of any omitted variables that may also affect Y (for example, prices of other goods, the weather, unexplainable shifts in consumers' tastes, etc.). Data are available for Y and the Xs, but the error term is assumed to be unobservable.

Note that Equation (A.I) must be linear in the parameters, but it need not be linear in the variables. For example, if Equation (A.I) represented a demand function, Y might be the logarithm of quantity (log Q), Xi the logarithm of price (log P), and Xi the logarithm of income (log I):

Our objective is to obtain estimates of the parameters bo bi,. . . ,bk that provide a "best fit" to the data. We explain how this is done below.

An Example

Suppose we wish to explain and then forecast quarterly automobile sales in the United States" Let's start with a simplified case in which sales S (in billions of dollars) is the dependent variable that will be explained, and the only explanatory variable is the price of new automobiles P (measured by a new car price index scaled so that 1967 = 100). We could write this simple model as

For a textbook treatment of applied econometrics, see R. S. Pindyck and D. L. Rubinfeld, Econometric Models and Economic Forecasts, 3rd ed. (New York: McGraw-Hill, 1.991).

In Equation (A.3), bo and bi are the parameters to be determined from the data, and e is the random error term. The parameter bo is the intercept, while b\ is the slope-it measures the effect of a change in the new car price index on automobile sales.

Were no error term present, the relationship between S and P would be a straight line that describes the systematic relationship between the two variables. However, not all the actual observations fall on the line, so the error term e is required to account for omitted factors.

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