3. A monopolist demand curve and MR curve are separate. There are two different

Question

3.   A monopolist demand curve and MR curve are separate. There are two different customers with two different elasticities but you still want to maximize profit (with MR=MC for each customer separately). A price discriminating defense monopolist manufacturer has a marginal cost of MC = $200. The monopolist can segment the market into two different groups: Customer A has a demand for guns
P = 400 -.5Q and MR=400-Q. Customer B demand is P = 300 – Q and MR=300-2Q. How many guns and at what price should the producer sell to each customer? Quantify why is price discrimination – two different prices - better for the producer than a one standard price? Pick any reasonable one standard price and examine if the revenue would be higher or lower? Make a conclusion about price discrimination as a strategy.

Explanation / Answer

FOR CUSTOMER A =>

We know that to maximise price, we need to equate MR & MC .

MR = 400-Q & MC =200

400-Q = 200

Q = 200

Now P=400-0.5Q and Q=200,

Substituting, P = $300.

TR (total revenue) = P*Q

TR = 300*200

TR = $60,000.

FOR CUSTOMER B =>

MR= MC

MR = 300-2Q & MC = 200

300-2Q = 200

Q = 50.

Now P = 300-Q & Q=50

P = $250.

TR = P*Q

TR = 250*50

TR = $12,500

Lets assume the monopolist doesn't discriminate any prices, and charges one single price to all its customers at $300.

Then all the calculations for customer A will remain the same. But for customer B it'll change.

Now we know P = $300. So Q would be P = 300-Q

300 = 300-Q

Q = 0.

TR = P*Q

TR = 0.

As we can see that without price discrimination the total revenue fell altogether to 0 from customer B which the producer was able to generate $12,500 earlier. Its better to charge different prices to different customers in order to earn more profit. This strategy basically applies with customers having different price elasticities and then charging accordingly as per their willingness to pay. This is a way to extract all of the consumer surplus.

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