The town council of Frostbite, Ontario, is trying to decide whether to build an outdoor skating rink which would cost $1 million and last for only one season.Operating costs would be zero.Yearly passes would be sold to anyone who wanted to use the rink.If p is the price of the pass in dollars, the number demanded would be q = 1200 - .6p.The council has asked you to advise them on building the rink.You should tell them that
A)revenues won't cover construction costs at any ticket price.There is no way to increase total consumer surplus by building the rink.
B)if the rink is built and price is set to maximize profits, the town makes a profit and consumers will be better off.
C)if the rink is built and price set to maximize profits, the town makes a profit but consumers are worse off than without a rink.
D)there is no price at which ticket revenues still cover costs but total consumer surplus from the rink exceeds costs.
E)None of the above.

Question

Quizplus · Accepted Answer

We can calculate the revenue from selling passes as follows: Total revenue = price per pass * number of passes Total revenue = p(1200 - 0.6p) To make a profit, the total revenue should be greater than the construction cost of $1 million. p(1200 - 0.6p) > $1,000,000 Simplifying the inequality: 0.6p^2 - 1200p + $1,000,000 < 0 Using the quadratic formula: p < ($1200 ± sqrt(1200^2 - 4(0.6)(1,000,000)))/(2(0.6)) p < $800 or p > $1000 Therefore, there is no price at which the ticket revenues still cover costs but total consumer surplus from the rink exceeds costs. Hence, the correct answer is D.

The Town Council of Frostbite, Ontario, Is Trying to Decide