Question

Individuals in the market consist of two types A and B. The individual demands for each type are $x_{A}=24-p$ and $x_{B}=24-2p$ . (Note: they look similar to the ones in the earlier questions, but these are individual demands and those were market demands). The firm's cost function is C(x)=6x. A consultant proposes a two-part tariff. Consumers have to pay a fixed fee F and a per-unit fee of 6. The fixed fee is equal to the consumer surplus the lower demand type would have had if it just paid the per-unit fee. What is the firm's profit under this pricing scheme assuming there is one 1 consumer of each type. Enter a number only.

Answer 1

Ans:

Demand for type A:

x = 24 - p

Inverse demand: p = 24 - x

Demand for type B:

x = 24 - 2p

p = 12 - 0.5x

Optimal conditions:

• Fixed fee = Consumer surplus of lower willing consumer. This keeps both consumers in the market.
• Price = MC as it maximizes consumer surplus.

Less willing consumer = B.

Reason: Maximum willingness to pay is 12 only.

MC = dC / dx = 6.

Price = 6.

Efficient quantity for type B consumer:

P = MC

12 - 0.5x = 6

x = 12.

Fixed fee (F) = Consumer surplus of B

= 0.5(12 - 6)(12) = 36.

Firm's profit: Profit from A + Profit from B

= 2 X F + (P - MC)xa + (P - MC)xb = 2 X 36 + 0 + 0= 72.

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