Question

The Children’s Theatre Company (CTC) in Minneapolis produces high quality theater for kids. Demand for tickets can be expressed by the following equation P= 40-(Q/50) where Q is the number of tickets sold and P is the price per ticket. The only cost of staging a production is $10,000 per night and is independent of the size of the audience (a fixed cost). Therefore, the marginal cost is $0.

Graph the marginal revenue, marginal cost & demand. What price maximizes their profit?

Answer 1

P = 40 - (Q/50) = 40 - 0.02

When Q = 0, P = 40 (vertical intercept) & when P = 0, Q = 40/0.02 = 2000 (horizontal intercept)

TR = PQ = 40Q - 0.02Q²

MR = dTR/dQ = 40 - 0.04Q

When Q = 0, MR = 40 (vertical intercept) & when MR = 0, Q = 40/0.04 = 1000 (horizontal intercept)

MC being 0, MC is identical to horizontal axis.

Profit is maximized when MR = MC.

40 - 0.04Q = 0

Q = 40/0.04 = 4000

P = 40 - (0.02 x 4000) = 40 - 20 = $20