You are the manager of a monopoly. a typical consumer’s inverse demand function for your firm’s product is p = 250 – 40q, and your cost function is c(q) = 10q.
a. determine the optimal two-part pricing strategy. per-unit fee: $10 correct fixed fee: $720 correct
b. how much additional profit do you earn using a two-part pricing strategy compared with charging this consumer a per-unit price? $360 correct

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pristina pristina · Answer 1 · 2018-08-02T06:48:06+02:00

Answer: a. Per unit price = $10 , Fixed price = $720

b. Profit= $360

Explanation:

a. The monopoly will charge a a per-unit fee such that it is equal to the marginal cost.

Since, total cost = 10q ,

Marginal cost will be $10

Therefore, per unit price will be $10, which equals marginal cost.

Substituting this into the demand equation we get, q= 6

This means that at $10 per unit price, the monopoly sells 6 units.

The fixed fee then should be [tex] (250 - 10) (6) (0.5) = $720 [/tex]

b. The optimal per-unit price is determined where

[tex] MR = MC [/tex]

[tex] 250 - 80Q = 10 [/tex]

Solving for Q we get,

yields Q = 3 units

Substituting this back into the demand equation we get P = $130.

[tex] Profit = TR - TC = P*Q - MC*Q = ($130*3) - ($10*3) = $390 - 30 = $360 [/tex]

While, the profit from two part pricing was $720. Thus, you earn $360 more by two-part pricing.