Question

You are a monopolist facing inverse demand for your product given by p=40-Q and you have constant marginal cost given MC=10 A) Assume you can charge 2 different prices based on quantity purchased. What are the producer’s surplus-maximizing levels of these prices? B) How much more producer’s surplus do you make by doing this instead of charging a single monopoly price for all your output? (The best answer is a quantitative one.)

Answer 1

Given, P = 40-Q & MC = 10

Thus, In order to find the profit maximizing quantity and price we first need the MR curve for the monopolist,

MR = 40 – 2Q

Then, set MR = MC to solve for Q:

then, we get the equation as- 40 – 2Q = 10 i.e. we get Q= 15units

When Q = 15,

then P = 40 – Q i.e.,40 – 15 = 25

Thus, P= $25

(B) - The value of producer surplus for single monopolist = ($25 per unit - $10 per unit)*(15 units) = $225

And, Total Revenue = ($55 per unit)*(45 units) = $2475

(A) - If we assume the monopolist charges two different prices: $12 and $15. Based on this assumption, :-

Q- If the price is $12 per uni, then how many units of goods will the monopolist sllt?

Ans- If price is equal to $12 then P = 40 – Q tells us that Q = 28 units. If price is equal to $15 then P = 40 – Q tells us that total production by the firm will be 25 units. Since the first 28 units of the good are sold at $12, that implies that the next twenty five units will be sold at $15.

Q. If the price is $15 per unit, the how many goods will the monopolists sell?

Ans - If price is equal to $12 then P = 40 – Q tells us that Q = 28units. If price is equal to $15 then P = 40 – Q tells us that total production by the firm will be 25 units. Since the first 28units of the good are sold at $12, that implies that the next thirty five units will be sold at $15.

Total revenue (TR) for this monopolist when he practices second degree price discrimination = ($12 per unit)*(28 units) + ($15 per unit)*(25 units) = $711

The value of producer surplus (PS) for this monopolist = ($12 per unit - $10 per unit)*(28 units) + ($15 per unit - $10 per unit)*(25 units) = $173