Big Waves is a large water park. Suppose the individual demand for entrance into Big Waves is Qd = 50 - (2 × P)and each consumer has the same demand. Big Waves has a constant marginal cost of
$5 per consumer. If Big Waves charges a single entry price to each consumer, what is the profit- maximizing number of entries per consumer?
A)50
B)25
C)20
D)10

Question

Quizplus · Accepted Answer

To find the profit-maximizing number of entries per consumer, we need to find the price that maximizes the profit per consumer.

Revenue per consumer = Price × Quantity demanded
Cost per consumer = Marginal cost

Profit per consumer = Revenue per consumer - Cost per consumer
= (Price × Quantity Demanded) - Marginal cost
= (Price × (50 - 2P)) - 5

To find the price that maximizes profit, we take the derivative of profit with respect to price and set it to zero:

d(Profit)/d(Price) = 50 - 4P - 5 = 0
45 = 4P
P = 11.25

Therefore, the profit-maximizing number of entries per consumer is:

Qd = 50 - 2P = 50 - 2(11.25) = 27.5

Rounding down, we get 20 as the best choice.

Big Waves Is a Large Water Park