Problem Set 4, 2009

Do the following problems from Berck and Helfand.

Chapter 5.  Q1

1.         While price is a very effective way of allocating goods, governments sometimes like to keep the price of a good low for political reasons.  Suppose, using Figure 5.3, that the Tunisian government decided to provide 36 cubic meters of water, but only charge 0.18 dinars per cubic meter.

(a)  What is total willingness to pay?

(b)  What is consumer surplus in this case?  Remember that consumer surplus is the area under the demand curve, but above the price paid, between the vertical axis and the quantity consumed.

(c)  If the government sells the water at the market-clearing price of 0.28 dinars per cubic meter, what is the consumer surplus?

(d)  What happens to the difference in consumer surplus between these cases?  Does it vanish?

Chapter 6 Q2

2.  The following table gives information on visitors to Jellybear Park

 City of Origin Population Distance Alabaster 1000 1 Beautiful 3000 3 Cornucopia 5000 5 Delight 7000 7

A researcher keeps careful track of visitors to Jellybear and learns that there is a total of 3,750 visits to the park.  The only cost of traveling to the park is is mileage, at \$1/mile.  The researcher estimates the relationship between costs and number of visits per capita (per person) to be Visits/Capita= 1 – 0.15 * Cost.

(a)  Add columns to this table identifying total costs of a visit from each place, visits per capita from each town, and the total number of visits from each town (that is, the visits/capita multiplied by the population).

(b)  Why doesn’t the researcher observe anyone coming from Delight to Jellybear?

(c)  If getting to the park is the only cost associated with a visit (that is, there is no admission price), how many people in total visit Jellybear?  Start a table with one column of admission price (in this case, \$0) and total visits.

(d)  Because of management costs, park managers are considering charging for admission to Jellybear.  They are considering prices ranging from \$1/visit to \$5/visit.  For each whole dollar value between \$1 and \$5 per visit, figure out (i) the new cost of visiting for each town, (ii) the new number of visits/capita from each town, (iii) the new number of visits from each town, and (iv) the total visits (remember that negative visits do not exist; they count as zero).

(e)  Put the information on admission price and total visits in the table from (c).  This table shows the relationship between admission price and total number of visits.  What is it?

(f)  Estimate the consumer surplus associated with visiting Jellybear Park when the admission fee is \$0.  (It will be an approximate value, since the relationship in (e) is not a straight line.)

(g)  What method have you used to estimate the value of visits t

Chapter 7 Q3

3.  In the Argo Dam study, about 62% of the survey population preferred to take down the dam, while 31% preferred to keep it, and 7% expressed no preference.  For those who preferred keeping the dam, the estimated willingness to pay to keep it was \$161/adult; those who wanted the dam removed would pay an estimated \$135/adult to have it taken down.  Ann Arbor has about 96,000 people.

(a)  Democracy is based on each person having one vote.  If there were a vote in Ann Arbor on dam removal, what is the likely outcome, if a representative fraction of the population votes?

(b)  If willingness to pay is a measure of how strongly people care about an issue, which group felt more strongly about whether to remove Argo Dam, those who wanted to keep the dam or those who wanted to remove it?  Who would be more likely to show up to vote?

(c)  Use the above values to estimate whether the aggregate willingness to pay for keeping the dam was larger or smaller than the aggregate willingness to pay for removing the dam.  Would this calculation produce a recommendation different than the outcomes in (a) or (b)?  If so, what are some advantages and disadvantages of a decision based on (i) seeking high voter turnout from a representative share of the population, (ii) those who feel most passionate encouraging those who think like them to vote, or (iii) having the city council decide based on an analysis of whether net benefits are larger for keeping or removing the dam?

Chapter 8 Q2

2.  Automakers can produce cars using machinery and labor.  In particular, 50 cars can be produced using the following combinations of machinery and labor:

 Machinery Labor 5 2 4 3 3 5

(a)  If you were to graph these points on a figure with Machinery on the horizontal axis and Labor on the vertical axis, what would you be graphing?  In other words, what do these different combinations of inputs represent?

(b)  Suppose machinery costs \$30/machine, while labor costs \$40/worker.  How much would each of these combinations cost?  Perform a similar calculation if machinery costs \$50 and labor \$40; and if machinery costs \$70 and labor \$40.

(c)  What is the lowest-cost combination of machinery and labor when the price of machinery is \$30 and the price of labor is \$40?  When machinery costs \$50 and labor costs \$40?  When machinery costs \$70 and labor costs \$40?

(d)  As the price of machinery rises relative to the price of labor, what happens to the relative amounts of machinery and labor that minimize cost?

(e)  As the price of machinery increases, while the price of labor stays constant, what happens to the minimum possible total cost of producing 50 cars?

Suppose that the use of machinery causes pollution, while the use of labor does not.  Machinery costs \$30/machine if environmental costs are not considered, but each machine causes \$20/machine of environmental damage.

(f)  If the environmental damage from machinery use is not included in the cost of production-in other words, if the damage is an externality from the automakers’ point of view- -, what input combination would they use, and what would be their costs?

(g)  If automakers had to pay for the damages associated with machine use, what input combination would they use, and what would be their costs?

(h)  If the government instead used a standard to limit machine use to 4 machines, what input combination would automakers use, and what would be their costs?