The town of Smallsville is considering building a museum. The interest on the money Smallsville will have to borrow to build the museum will be $1,000 per year. Each citizen's marginal benefit from the museum is shown in the following table, and this marginal benefit schedule is public information. Citizen Marginal benefit from museum ($/year)
Anita…………………………. 340
Brandon…………………………. 290
Carlena…………………………. 240
Dallas…………………………. 190
Eloise…………………………. 140
a. Assuming each citizen voted his or her private interests, would a referendum to build the museum and raise each citizen's annual taxes by $200 pass?
b. A citizen proposes that the city let a private company build the museum and charge the citizens a lump-sum fee each year to view it as much as they like. Only citizens who paid the fee would be allowed to view the museum. If the private company were allowed to set a single fee, would any company offer to build the museum?
c. A second citizen proposes allowing the private company to charge different prices to different citizens and auctioning the right to build the museum to the highest bidding company. Again, only the citizens who pay the fee may view the museum. What is the highest bid a private company would make to supply the museum to Smallsville?

a. Assuming that each citizen voted their private interests, a referendum to build the museum and raise each citizen's annual taxes by $200 would pass because 3/5 (60%) of the citizens would vote in favor.  They derive more marginal benefit than the head tax increase from the museum project.

b. No company would likely offer to build the museum based on a single lump-sum fee because the marginal benefits derived by the five citizens are not equal nor more than $200 each.  If the private company charges above $140, not all the citizens would be willing to pay.

c. The highest bid a private company would make to supply the museum to Smallsville is $100,000.  This cost is based on a 10% annual interest ($1,000/10% x 10 years) for ten years.

Thus, given the facts of the case, it would be more beneficial for the town of Smallsville to borrow $100,000 to build the museum and raise the annual tax by $200 to enable the citizens to enjoy the services of the museum while the town recovers the investment costs plus interests on the borrowed funds over time.

Data and Calculations:

Cost of Annual Interest Expense = $1,000

Citizens     Marginal        Net                           Accumulated

                   Benefit     Benefit                         Net Benefit

Anita           $340       $140 ($340 - $200)      $140 ($0 + $140)

Brandon     $290        $90 ($290 - $200)     $230 ($140 + $90)

Carlena      $240        $40 ($240 - $200)      $270 ($230 + $40)

Dallas         $190        ($10) ($190 - $200)      $260 ($270 - $10)

Eloise         $140       ($60) ($140 - $200)      $200 ($260 - $60)

Total       $1,200

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See explanation

Explanation:

a. This has been solved and attached.

Note that the net benefits was calculated as:

= Marginal benefit - $200

b. Looking at the table and information provided in the attachment, we would see that no company offer to build the museum because since their cost of $1000 can't be covered by the revenue generated. The highest revenue gotten for the single price monopolist is $760 and this can't even cover their cost.

c. Based on the scenario given in (c), the highest revenue the price discriminating monopolist would make is $1200 and coupled with the fact that the cost is $1000, the maximum bid that a private company would make to supply the museum to Smallsville is $200 ($1200 - $1000)

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