An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville, which has a population of 65,000 people and a median household income of $40,000. The analyst identified 24 towns in the region that already had public swimming pools. He conducted a telephone interview with the recreation department in each town to find out what fee it charged per visit (FEE) and how many visits it had during the most recent summer season (VISITS). In addition, he was able to find each towns population (POP) and median household income (INCOME) in the most recent census. Use the data below to answer the following:

DATA:

Town Visits Fee ($) Income ($)Population 1 168,690 $0.00 20,600 36,879 2 179,699 $0.00 33,400 64,520 3 198,695 $0.00 39,700 104,123 4 206,762 $0.00 32,600 103,073 5 170,359 $0.00 24,900 58,386 6 210,995 $0.25 38,000 116,592 7 172,118 $0.25 26,700 49,945 8 190,902 $0.25 20,800 79,789 9 197,119 $0.25 26,300 98,234 10 186,615 $0.50 35,600 71,762 11 152,779 $0.50 38,900 40,178 12 137,513 $0.50 21,700 22,928 13 158,156 $0.50 37,900 39,031 14 157,524 $0.50 35,100 44,685 15 179,590 $0.50 35,700 67,882 16 164,757 $0.75 22,900 69,625 17 184,528 $0.75 38,600 98,408 18 183,922 $0.75 20,500 93,429 19 174,610 $1.00 39,300 98,077 20 187,920 $1.00 25,800 104,068 21 196,418 $1.25 23,800 117,940 22 166,794 $1.50 34,000 59,757 23 161,816 $1.50 29,600 88,305 24 167,605 $2.00 33,800 84,102

1. Regress the number of visits on the other three variables included in the spreadsheet.

2. Using the results of your regression do the following:

a. Clearly present the form of the regression equation, including the beta coefficients you have found from regressing visits on, FEE, VISITS, and INCOME.

b. Present the ordinary demand equation for Dryville.

c. Present the inverse demand equation for Dryville.

d. Calculate and present the consumer surplus assuming a $0 fee entrance to the pool.

e. What would be the total social surplus if the town of Dryville charges a $1.25 entry fee, assuming $0 marginal costs, and an excess tax burden of .25? (In answering this question, assume that the fees are used to reduce taxes that would otherwise have to be collected from the citizens of Dryville to pay for expenses incurred in operating the pool.) Explain and clearly label your answer.

f. Using your response to (e), what would be the total social surplus if the pool cost $150,000 to construct and all of its construction cost were paid for by taxes. Explain and clearly label your answer.