Question

NH 2015 is the only amusement park in Goleta (it has monopoly power). The owners have decided to enact a two-part tariff: a fixed fee to enter and a per-photo price to get a photo taken with local celebrity Serena. Suppose that the demand for photos is q = 17 - p, and that NH 2015's cost function is C(q) = 11q. If the owners choose the fixed fee and per-photo price to maximize profits, what will the profits be?

Answer 1

Maximum Profit = $9

Step-by-step explanation:

We know that maximum profit occurs when,

Marginal Revenue = Marginal Cost

We are given that

q = 17 - p

or

p = 17 - q

Total revenue is given by

TR = p*q

TR = (17 - q)*q

TR = 17q - q²

The marginal revenue is given by

MR = d/dq(TR)

MR = d/dq(17q - q²)

MR = 17 - 2q

The total cost is given by,

TC = 11q

The marginal cost is given by

MC = d/dq(TC)

MC = d/dq(11q)

MC = 11

For maximum profit,

Marginal Revenue = Marginal Cost

MR = MC

17 - 2q = 11

-2q = 11 - 17

-2q = -6

q = 6/2

q = 3

So the total revenue is

TR = 17q - q²

TR = 17*3 - (3)²

TR = 51 - 9

TR = $42

So the total cost is

TC = 11q

TC = 11(3)

TC = $33

Maximum profit is given by

Maximum Profit = TR - TC

Maximum Profit = $42 - $33

Maximum Profit = $9

Therefore, a maximum profit of $9 will be obtained.