The residents of the town Ectenia all love economics, and...

The residents of the town Ectenia all love economics, and the mayor proposes building an economics museum. The museum has a fixed cost of \$2,400,000 and no variable costs. There are 100,000 town residents, and each has the same demand for museum visits: $QD = 10 - P$, where $P$ is the price of admission. a. Graph the museum's average-total-cost curve and its marginal-cost curve. What kind of market would describe the museum? b. The mayor proposes financing the museum with a lump-sum tax of \$24 and then opening the museum to the public for free. How many times would each person visit? Calculate the benefit each person would get from the museum, measured as consumer surplus minus the new tax. c. The mayor's anti-tax opponent says the museum should finance itself by charging an admission fee. What is the lowest price the museum can charge without incurring losses? ($Hint$: Find the number of visits and museum profits for prices of \$2, $3, $4, and $5.) d. For the break-even price you found in part (c), calculate each resident's consumer surplus. Compared with the mayor's plan, who is better off with this admission fee, and who is worse off? Explain. e. What real-world considerations absent in the problem above might provide reasons to favor an admission fee?

The residents of the town Ectenia all love economics, and the mayor proposes building an economics museum. The museum has a fixed cost of \$2,400,000 and no variable costs. There are 100,000 town residents, and each has the same demand for museum visits: $QD = 10 - P$, where $P$ is the price of admission.
a. Graph the museum's average-total-cost curve and its marginal-cost curve. What kind of market
would describe the museum?
b. The mayor proposes financing the museum with a lump-sum tax of \$24 and then opening the
museum to the public for free. How many times would each person visit? Calculate the benefit each person would get from the museum, measured as consumer surplus minus the new tax.
c. The mayor's anti-tax opponent says the museum should finance itself by charging an admission fee. What is the lowest price the museum can charge without incurring losses? ($Hint$: Find the number of visits and museum profits for prices of \$2, $3,
$4, and $5.)
d. For the break-even price you found in part (c), calculate each resident's consumer surplus. Compared with the mayor's plan, who is better off with this admission fee, and who is worse off?
Explain.
e. What real-world considerations absent in the problem above might provide reasons to favor an
admission fee?

Transcript

00:01 Okay, guys, this is chapter 15, problem seven.

00:05 So we're given that a city wants to make an economics museum, which is always a great idea.

00:11 The museum is going to cost $2 .4 million to build and then have no variable costs after it's built.

00:18 The town is 100 ,000 residents, and each has the following demand curve where the number of visits equals 10 minus the price.

00:26 So the first part, we're told to graph the museum's marginal cost and average cost curves.

00:34 So the marginal cost, we're told, right, there's no variable cost associated.

00:38 So the marginal cost is going to be down here.

00:40 It's going to equal zero.

00:42 So let's do, so here's price, here's quantity, or here is also marginal cost equals zero.

00:49 And so the average cost is then going to be 2 .4 million divided by the number of people that go to the museum.

00:56 And so that is going to be constantly decreasing, but it's going to start decreasing less and less with each person is never going to quite get to zero.

01:05 And so this shape of a graph is characteristic of a natural monopoly.

01:14 Natural monopoly.

01:16 And so that's the kind of market that this is.

01:20 The second part of the question is saying, if the museum was paid for by a lump sum of $24 on 100 ,000 people, which would exactly equal the cost of the museum, and then admission were free to the museum, how many times would each person go? remember that the demand curve was, remember the quantity demanded equals 10 minus the price, and if the price is zero, that means everybody would go 10 times.

01:47 And so then what would be the consumer surplus? remember that consumer surplus is the difference between a person's willingness to pay and how much they actually have to pay.

01:58 So here's the demand curve for each individual person, here's price and quantity, and remember the price is, so people are going to be consuming out here.

02:07 And so we have, you know, 10 and 10.

02:10 And so it's going to be one half of 10 times 10.

02:16 And that's going to equal 50.

02:17 So the consumer surplus with a lump sum, sorry.

02:20 No, yeah, the consumer surplus, a lump sum tax is going to be 50 minus the cost, which is 24, which is going to equal 26.

02:29 So the total consumer surplus will be 26.

02:34 The third part is saying, if the museum now charged a fee, what's the lowest fee that it could charge without losing any money.

02:42 And so to do this, we're going to do a quick chart.

02:45 So we're going to have price, we have quantity, and then we have total revenue...

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