Question

Q:

Suppose an individual’s inverse demand function for gym visits per year is P = 36 – 0.06Q. If the marginal cost of gym visit is 15 AZN for the gym, what would be the extra profit the gym earns by using two-part pricing relative to uniform pricing?

Show the solution steps please

Answer 1

With uniform pricing, profit is maximized when marginal revenue (MR) equals marginal cost (MC).

Total revenue (TR) = P x Q = 36Q - 0.06Q²

MR = dTR/dQ = 36 - 0.12Q

Equating with MC,

36 - 0.12Q = 15

0.12Q = 21

Q = 175

P = 36 - (0.06 x 175) = 36 - 10.5 = AZN 25.5

Profit (AZN) = Q x (P - MC) = 175 x (25.5 - 15) = 175 x 10.5 = 1,837.5

With two-part pricing, profit is maximized when Price equals MC, and profit equals consumer surplus (CS).

36 - 0.06Q = 15

0.06Q = 21

Q = 350

P = MC = AZN 15

From demand function, when Q = 0, P = AZN 36 (Maximum willingness to pay)

Profit = CS (AZN) = Area between demand curve & price = (1/2) x (36 - 15) x 350 = 175 x 21 = 3,675

Extra profit = AZN 3,675 - AZN 1,837.5 = AZN 1,837.5