Advanced Pricing Ideas. We have looked at a single price monopoly. But perhaps other ways of pricing can lead to greater profits for the sports team. We will look at two types of situations.
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We have looked at a single price monopoly. But perhaps other ways of pricing can lead to greater profits for the sports team. We will look at two types of situations.
1) In one situation a given consumer looks at perceived quality differences of different games (we will look at variable ticket pricing and bundling).
2) In this other situation for one game there may be many types of consumers in terms of willingness to pay for the game (we will look at various forms of price discrimination).
You may recall that consumers may have some consumer surplus from their purchases. Advanced price techniques are was that maybe the firm can capture some of the surplus and put it in their own pocket.
In this scenario a consumer may look at 2 future games and see the quality of the 2 as different and thus not have the same demand for the 2 games. Under a single price monopoly the team could just charge the same price for every game. But, maybe it can charge different prices to each game. This is the basic idea of variable ticket pricing.
Say the demand for the “big” game is
Dbigone Q = 20 – P
and the demand for the “ho-hum” game is
Dho-hum Q = 12 – P.
On the next slide I have an Excel sheet that I want us to consider.
The context in which we will look at the slides is that the marginal cost of production is zero. As we have said before, this may not be totally realistic, but it makes our work a little easier. In fact, the work is easier because maximizing revenue is the same in this case as maximizing profit. In a more general sense, the 2 are not the same, but that is not the point the authors are trying to make here.
In the first three columns of the Excel I have put in the demand and associated totally revenue at various prices for the big game. Then I have the ho-hum game information, and finally I have a situation where the team would charge the same price for both games.
You can see for the big game the most revenue comes from a price of 10 and the associated output amount of 10 units for a revenue of 100. This could be found by setting MR = MC for that game. Let’s see this next.
Dbigone Q = 20 – P, then if written in inverse for
P = 20 – Q, then please accept the fact that
MR = 20 - 2Q and if MR = MC, 20 – 2Q = 0 or Q = 10. And when Q = 10 P = 10 on the demand curve and TR = 100.
Similarly for the “ho-hum” game Dho-humQ = 12 – P, or
P = 12 – Q, MR = 12 - 2Q and MR = MC means 12 – 2Q = 0, or Q = 6 and thus P = 6 and TR = 36.
So, charging the price of 10 for the big game and 6 for the ho-hum game gives revenue of 136.
If we charge the same price to both games then the total demand across the 2 games would be found by adding the 2 demands horizontally. Thus,
Dbigone Q = 20 – P plus
Dho-humQ = 12 – P, means for the 2 games
Q = 32 – 2P, or P = 16 – 0.5Q and MR = 16 - Q. Setting MR = MC we have 16 – Q = 0 or Q = 16 and thus from the demand curve we see P = 8 and total revenue = 128.
Thus, it is better to charge different prices to the different games in the sense the team can make a greater profit.
A point to consider is that once the relevant demands are considered, make the Q where MR = MC and charge what consumers are willing to pay for that Q.
In a general sense, bundling is when a consumer buys good e they also have to buy good f (or maybe even more). Let’s take an example to consider the idea.
Say Dick is willing to pay $100 to see his team the main rival, but only pay $25 to see the other teams in the league. Say the price to each game separately has a cost of $30. Dick would only go to one game, the rival game and he would have a consumer surplus of $70.
The team could bundle 4 games, only 1 of which is the rival team game, and charge $120 (what is the single game price times 4). Since Dick is willing to pay $175 to see the 4 games, he would now buy tickets and have consumer surplus = $55 (did you see how I calculated this?).
So, with bundling, include the most preferred item in the bundle and also require the purchase of lesser desired items. Admittedly, we have only shown one price scheme (that of charging the same price to each game, just require that more than 1 game be purchased). The more general case here is likely more than you want to digest at this time.
Next, let’s turn to looking at the situation where there is one item, but different consumers see the item differently.
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 have said 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 lesson certain products. 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.
This is also called personalized pricing.
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 S = D output level is 7 and P = 4. Consumer surplus would be the large triangle formed by the vertical axis, the 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 some of 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. For sports economics we see the personal seat license as an example of using the two part tariff form of first degree discrimination.