QUESTION 1:
Suppose 10 people each have the demand Q = 20 - 4P for streetlights and 5 people have the demand Q = 18 - 2P for streetlights. The cost of building each streetlight is 3. If it is impossible to purchase a fractional number of streetlights, how many streetlights are socially optimal?
QUESTION 2:
The city of Gruberville is considering whether to build a new public swimming pool. This pool would have a capacity of 800 swimmers per day, and the proposed admission fee is $6 per swimmer per day. The estimated cost of the swimming pool, averaged over the life of the pool, is $4 per swimmer per day. Gruberville has hired you to assess this project. Fortunately, the neighboring identical town of Figlionia already has a pool, and the town has randomly varied the price of that pool to find how price affects usage. The results from their study follow:
|
Swimming pool price per day
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Number of swimmers per day
|
|
$8
|
500
|
|
$10
|
200
|
|
$4
|
1,100
|
|
$6
|
800
|
|
$2
|
1,400
|
1. If the swimming pool is built as planned, what would be the net benefit per day from the swimming pool? What is the consumer surplus for swimmers?
2. Given this information, is an 800-swimmer pool the optimally sized pool for Gruberville to build? Explain.
QUESTION 3:
The city of Animaltown plans to build a new bridge across the river separating the two halves of the city for use by its residents. It is considering two plans for financing this bridge. Plan A calls for the bridge to be paid for out of tax revenues, allowing anyone to freely use the bridge. Plan B calls for imposing a toll of $6 for crossing the bridge, with the remainder of the cost to be paid out of tax revenues. City planners estimate a local demand curve for hourly use of the bridge to be Q = 1,800 - 100P. The bridge will be able to accommodate 2000 cars per hour without congestion. Which of the plans is more efficient, and why? How would your answer change if congestion was predicted on the bridge?