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3rd Price Discrimination

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Review

We saw a monopoly is the only firm that sells a product. Up to this point we worked with a single price monopoly. This meant if the monopoly lowered the price to one consumer it would have to lower the price to all. So we had a single price monopoly.

P

Q

Pm

Qm

MC

D

MR

In the end the monopoly sells the Q where MR = MC and takes this Q and plugs it into the demand curve to get the price.

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We want to spend some time this term exploring monopoly situations where the monopoly is able to charge different customers different prices. This technique is called price discrimination.

In order for price discrimination to work the monopoly must be able to keep the different consumers from trading with each other – so arbitrage must not be allowed to happen.

Example: If you own a small pharmacy say you go buy a bunch of 2 liters of Coke at Wal*Mart and then resell the Coke in your store. The pharmacy presumably buys low at Wal*Mart and then resells at a higher price. This is arbitrage and would make it hard for Wal*Mart to price discriminate. Wal*Mart would likely just sell at a higher price to all and thus the pharmacy has nothing to gain.

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There are 3 types of price discrimination.

1st degree – we (the monopoly) can get the maximum each is willing to pay on each unit

2nd degree – we have two groups and we can get what each is willing to pay on each unit (almost).

3rd degree – we have two groups and in each group we have to charge each the same amount in their group – kind of like a single price monopoly in each group.

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Third degree discriminationThe third degree price discriminator see consumers as being in distinct groups with distinct elasticities. The key to this method working is that buyers in one group can not have the ability to sell to buyers in the other group.Maybe geography keeps this from happening. Big Macs in Nebraska are cheaper, for example, but no one buys a truck load in New York and brings them out by truck. The big Macs would spoil.

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3rd degree

MKT 1 MKT2 firm level analysis

MR1

D1 D2

MR2

MC

MR

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3rd degreeIn this situation the firm is in two markets and would like to maximize profit. It has to decide what to charge in each market and how much to sell in each market. We assume here that the output is made in one location and so there is only one marginal cost to worry about. The way the monopolist proceeds is to 1) Figure marginal revenue at the firm level by horizontally summing the MR in each market2) Sell the total output where the firm MR = MC3) take this MC value back to each market and act like a monopolist in each market- sell where MR = MC and charge the price on the demand curve at those Q’s

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3rd degreeThe firm sells where MC = MR1 = MR2 or in words the firms sells the amount of output where the MC is equal to the marginal revenue in each market.

Mathematically this is similar to a multiplant monopoly, except here we sum across MR’s, not MC’s.

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Let’s do a problem

P = 6 – Q in one group and P = 8 – Q in the other. Marginal revenues in both will be

MR = 6 – 2Q and MR = 8 – 2Q.

To add these two together we need to put them in Q form:

Q = (6/2) – (1/2)MR and Q = (8/2) – (1/2)MR.

So at the firm level we have

Q = 7 – 1MR, or MR = 7 – Q.

Say MC is constant at 4. Then at the firm level sell where MR = MC, or 7 – Q = 4, or sell a total of 3 units. How much to sell in each market?

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Since MC = 4

In P = 6 – Q,

MR = 6 – 2Q = 4 = MC, so Q = 1 and price from the demand is 5.

In P = 8 – Q,

MR = 8 – 2Q = 4 = MC, so Q = 2 and price from the demand is 6.

Note that MC is a constant in this example. We would follow the same pattern if MC was not a constant.

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The task we just completed could be bi-passed if we had information about demand elasticities. Without proof I tell you

MR = P(1 – [1/E]) = P([E – 1]/E), where E is the absolute value of the elasticities.

Since MR = MC for firms, this would mean

MC = P([E – 1]/E) or

P = (E/[E-1])MC

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3rd degreeSay MC is $6 for a firm (constant MC). Say in market 1 the elasticity –4 and in market 2 it is –2. Notice market 1 folks are more responsive to price.

The firm will sell where MR = MC in each market, so in market 1 we have

P = [-4/1 – 4]6 = 8 and in market 2 P = [-2/1-2]6 = 12. Take these prices back to each market, plug into the demand to get the amount to sell and figure profit in each market. Note the market with lower elasticity is charged more. Why? They do not respond as much to price changes