1 st degree price discrimination. A form of Monopoly Power. Our story of monopoly is incomplete. We have seen the case where the monopolist charges all customers the same amount. This is the single price monopoly case.
A form of Monopoly Power
Our story of monopoly is incomplete. We have seen the case where the monopolist charges all customers the same amount. This is the single price monopoly case.
Do not get me wrong, monopolies can change their price. But once they do, the single price monopolies will charge all consumers the same price. But, some monopolies charge different consumers different prices. This type of monopoly is a price discriminating monopoly.
Some folks tell us that Microsoft discriminates when it sells Windows to the various computer makers. Some pay less than others.
You have probably heard of cases where senior citizens pay less, or maybe college students get to pay less. These are other examples of discrimination.
Why discriminate? The answer is that it may be more profitable than charging a single price.
Can every firm with monopoly power discriminate? Discrimination can only occur when both of the following hold.
1) The monopolist must have knowledge of how consumers differ in their demand for the good or service. Then the difference can be exploited.
2) Arbitrage must not be possible. Customers in the low price market segment must not be able to sell to the customers in the relatively high price segment.
We typically distinguish between three types of discrimination. I will finish this section by considering price discrimination of the 1st degree.
Say we have consumer demand of the form in the first two columns of the table on the last screen. You can see the quantity demanded rises as the price falls. TRs and MRs refer to the total revenue and marginal revenue when we have a single price monopoly. For example, when the price is 9, 2 units are demanded and the total revenue is 18. At a price of 10 the TRs was 10, so the additional revenue of the second unit – what we call the marginal revenue – is 8.
Remember that when we have a single price monopoly and the demand has the general form P = A – BQ, then the MRs = A – 2BQ.
TRd1 and MRd1 refer to the total revenue and marginal revenue when we have a price discriminating monopoly using the first degree method.
In 1st degree price discrimination the monopoly knows what the individual is willing to pay for each unit and is able to extract that amount. In the example we know the individual will pay 10 for the first unit. Since two units are demanded at a price of 9, we know the individual is willing to pay 9 for the second unit. So on the two units the monopoly can charge 10 for the first one and 9 for the second one.
Think about a quantity discount idea. Pay 10 for one or get 2 for 19. The TRd1 for two units is thus 19 and the MRd1 for the second unit is 9. We follow the same idea the rest of the way down the columns
Note that the MRd1 and the P are the same. This is an example that shows that the price and marginal revenue are equal for a 1st degree price discriminator. Now if demand is
P = A – BQ, then MR = A – BQ.
The MRd1 curve is the demand curve for the 1st degree discriminator.
Now, all businesses make the output where MR = MC, as long as they are not losing more that the variable costs of production.
When you look at the table in the single price case if MC is 4 all the time the monopoly will make Q = 4 and charge $7 to each. If the MC is 4 always for a 1st degree discriminator, then the firm will sell 7 units, one for $10, one for $9 and so on down to one for $4.
Demand of consumer and MRd1
MC = 4 and special case of competitive supply
1 2 3 4 5 6 7
On the previous screen we see the demand in the market. If the market was competitive we know the MR = MC output level is 7 because MR = P and P = MC cost at Q = 7. Consumer surplus would be the large triangle formed by the vertical axis, then horizontal line a $4 and the demand line.
If the market was single price monopoly we would use the MRs line and the Q where MR = MC would be at 4 and the price on the demand curve is 7. The consumer surplus falls to a smaller triangle than the one before, here we have the horizontal line at 7 as the base of the triangle. The monopoly takes the consumer surplus that would have existed had the market been competitive.
Now, if the monopoly can discriminate in the first degree in this example, then it will charge 10 for the first unit, 9 for the second unit, on down to 4 for the 7th unit. It would not want to sell 8 or more units because the MRd1 on those units is less that the MC and thus take away from profit.
NOTE 1st degree discriminator
1) sells same output as in competition,
2) charges a different price on each unit and the last unit has P = MC,
3) takes all the consumer surplus away from the consumer. Remember consumer surplus is what consumers are willing to pay minus what they have to pay and the 1st degree discriminator has the ability to get them to pay their willing amount on each unit.
A two part tariff is a special way to get the consumer to pay all they are willing to pay for units they buy. If you think back to the graph, the discriminator extracts all the surplus from consumers. It can do the same thing in two steps.
1) charge a single price for all units - the competitive price - or when P = MC,
2) charge a fee to be able to buy any units at all and make the fee the consumer surplus that would result in competition.
We see this type of pricing in buyer clubs, country clubs and other situations.
The 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.
MKT 1 MKT2 firm level
In 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 market
2) Sell the total output where the firm MR = MC
3) 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
The 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.
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?
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.
The task we just completed could be bipassed 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
Say 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
Let’s review the economic story about price discrimination.
1st degree – we can get the maximum each is willing to pay on each unit
2nd degree – (I didn’t cover) 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.