Discounting is examined. Suppose that individual demand for a product is given b

Question

Discounting is examined.

Suppose that individual demand for a product is given by QD=1000-5P. Marginal revenue is MR=200-0.4Q, and marginal cost is constant at $20. There are no fixed costs.

a) The firm is considering a quantity discount. The first 400 units can be purchased at a price of $120, and further units can be purchased at a price of $80. How many units will the consumer buy in total?

b) Show that this second-degree price-discrimination scheme is more profitable than a single monopoly price.

Please show work so I can fully understand. Thank you!

Explanation / Answer

First we must find optimal Q and P Set MC=MR and solve 20=200-0.4Q 0.4Q=180 Q=450 Now plug 450 into MR 200-0.4(450)=20=P A. In this case, we use the QD=1000-5(P) We must now look at the given prices. If P=120 then 1000-5(120)=400 If P=80 then 1000-5(80)=600 Therefore, our total units sold is 1000 B. If they just charged 120, they would sell 600 goods for a total revenue of 600*120=72,000 However, if we price discriminate to facilitate different demand total revenue will be 120*600+400*80=104,000 Hope this helps

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