Question

1. Suppose you are the manager of a Golf Club with monopoly power. A typical consumer’s

inverse demand function for your firm’s product is 𝑃 = 100 − 20𝑄, and your cost function is C(Q) = 20Q.

(a) If you apply a two-part pricing strategy, how much would be the membership fee and the per unit price?

(b) How much additional profit do you earn using a two-part pricing strategy compared with single price strategy?

Answer 1

$𝑃 = 100 − 20𝑄$

$C(Q) = 20Q$

a) Applying two pricing strategies the per-unit price becomes the price at which price equals the marginal cost of production.

P=MC

100−20Q=20=4

P= 20

Membership fees= the area of the triangle above the MC curve, and the per-unit price becomes the price

$Δ = 1 2 ( 100 − 20 ) ( 4 − 0 ) Δ = 160$

b. If there was a single pricing strategy, then equilibrium will occur at MR = MC

MR=MC

100−40Q=20Q=2

P=60

The profit would have been

π$_1$ =TR−TC

π$_1$ =60×2−20×2

π$_1$ =120−40

π$_1$ =80

When there is two pricing strategy, profit is given as:

π$_2$ =(20×4+160)−20×4

π$_2$=80+160−80

π$_2$=160

Additional profit will be:

Δπ=π$_2$−π$_1$ =160−80=80