Consider a monopolist selling to a demand curve given by p = 310 - Q. The monopo

Question

Consider a monopolist selling to a demand curve given by p = 310 - Q. The monopolist faces constant average and marginal cost equal to $10. If the monopolist had perfect information on consumers' willingness to pay and implements first degree price discrimination, compute the maximum amount of profit that the monopolist can extract from this market. If the monopolist decides to implement non-linear pricing via a quantity discount, what is the optimal quantity discount to offer if the discount is in the form of, "...buy q at a price of p and get the remainder for x% off..."? (You need to specify an initial price, p, a quantity threshold, q, and a discounted percentage, x% off of p).

Explanation / Answer

a.

P = 310 – Q

TR = PQ

      = (310 - Q) × Q

      = 310Q – Q^2

MR = Derivative of TR

       = 310 – 2Q

Profit maximizing condition: MR = MC

310 – 2Q = 10

Q = 150

Putting the value of Q = 150 in the demand function, P = 310 - 150 = 160

Therefore, the price is $160 and the quantity is 150 units.

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