Answer to Question #275361 in Microeconomics for khashayar

Question

3. 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.)

Answer 1

Solution:

a.). Fixed cost, FC=$2,400,000

Number of residents, N=100,000

Average Fixed Cost (AFC) = $\frac{2,400,000}{100,000}$ = $24

As there is no variable cost,

Marginal Cost (MC) =0

The graph is as below:

The museum is a monopoly market since it is constructed and regulated by the government body only.

b.). The price is equal to zero since the mayor charges no price for the entry. The equation gives the demand curve for the firm,

QD=10-P,

So, as the price of the museum visit is zero, the number of visits for each person is 10 visits.

QD = 10 – 0 = 10

As it is a monopoly market, the price equals the average cost, which is $24, then the consumer surplus is:

=$24 $\times$ 10 = $240

The benefit each person would get

Consumer surplus - tax=$240−$24 = $216

Consumer surplus−tax=$240−$24=$216

Thus, each person gets a benefit of $216.

c.). The lowest price the museum can charge to without incurring losses is equal to  $5.