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Answers to Odd-Numbered Problems
consumer surplus is (.5)($3 ⫺ $1.50)(450) ⫽ $337.50 per hour. At a rate of $1.00, 600 cars will park each hour, generating revenue of $600 per hour. Consumer surplus is (.5)($3 ⫺ $1)(600) ⫽ $600 per hour. The $1 rate generates the greater total benefit, $1,200 per hour. The annual benefit is (2,600)($1,200) ⫽ $3,120,000. Thus, the net benefit of the garage (in present-value terms) is (11.9)(3,120,000 ⫺ 620,000) ⫺ 20,000,000 ⫽ $9,750,000. b. The private developer would use the $1.50/hour rate because it offers the greater revenue. The annual profit is (2,600)($675) ⫺ 620,000 ⫽ $1,135,000. The net present value of the garage is (11.9)(1,135,000) ⫺ 20,000,000 ⫽ ⫺$6,493,000. The garage is not profitable. 13. a. The total benefits (B) for the programs (per $1 million spent) are Program 1. B ⫽ (1.0)($4.8 million) ⫹ $0 ⫽ $4.8 million. Program 2. B ⫽ (.2)($4.8 million) ⫹ $3.2 million ⫽ $4.16 million. Program 3. B ⫽ (.5)($4.8 million) ⫹ $1.5 million ⫽ $3.9 million. Program 4. B ⫽ (.75)($4.8 million) ⫹ $.2 million ⫽ $3.8 million. Thus, program 1 should be funded up to its limit ($14 million), then program 2 (up to $12 million), and next the remaining $6 million on program 3. b. With $7.2 million as the value per life, the program benefits are now Program 1. B = (1.0)($7.2 million) + $0 = $7.2 million. Program 2. B = (.2)($7.2 million) + $3.2 million = $4.64 million. Program 3. B = (.5)($7.2 million) + $1.5 million = $5.1 million. Program 4. B = (.75)($7.2 million ) + $. 2 million = $5.6 million. Again, program 1 should be funded up to its limit ($14 million), then program 4 (up to $16 million), and the remaining $2 million on program 3. With a greater value for each life, the programs saving the most lives are fully funded.
Chapter 12 1. a. The expected values at points E, D, C, B, and A in the decision tree are $15.5, $50, $30, $19.2, and $19.2, respectively. b. The manager is confused. Point D is a point of decision: The manager simply should select the top branch (50 is greater than 37). Thus, the value at point D is $50. Putting probabilities on the branches makes no sense. 3. a. The expected value of continuing with its current software strategy is (.2)(2) ⫹ (.5)(.5) ⫹ (.3)(⫺1) ⫽ $.35 million. The expected value of
