Lecture Notes 6: Pricing Strategies
In the previous unit, we focused on single-price monopoly. That is, the monopoly sets a price and all the buyers in the market pay the same price. Many firms work like this – a restaurant prints prices on its menu, and everyone who walks into the restaurant pays the same price.
But it turns out that alternative pricing schemes other than simple linear pricing can often generate substantially more profits and even have the potential to enhance efficiency. In this section, we will go through several pricing strategies and talk about when they work well. Note that many of these lessons apply to firms that aren’t pure monopolies as long as they have some market power.
Price Discrimination
The basis of a lot of these pricing strategies is price discrimination, which describes a situation where a firm charges different prices to different customers for the same product.
Here’s a simple motivating example to show how price discrimination can both increase profits and enhance efficiency. A movie theater faces two types of customers – adults, able to pay a high price for movie tickets, and teenagers, who want to see movies but aren’t able to pay as much. If the theater just sets a single ticket price, it will likely be more profitable for the theater just to forget about the teenagers and set the profit-maximizing price for adults. Reducing the ticket price enough to attract teenagers would cut into revenue from adults so much that it probably wouldn’t be worth it.
But there is an obvious solution here – the theater should charge different prices for teenagers and for adults! By doing this, the theater can expand its market and sell tickets to teenagers without cutting into revenues from adults. This is obviously a profitable move for the company, and it also enhances efficiency by expanding the size of the market and consequently the total surplus.
Price discrimination is all over the place, and we will give many examples throughout this unit. In a basic sense, there are three requirements for a firm to successfully practice price discrimination.
• Market power: A price discriminating firm must have some kind of market power. Otherwise, a new entrant would join the market and compete by offering lower prices to the customers being charged the most.
group. For example, a movie theater that charges different prices for students and for adults might require a student ID to get the discounted student rate.
• No arbitrage: Selling bags of cookies to men for $10 and to women for $5 won’t work very well because a man who wants cookies can easily ask a woman to buy a bag at the low price and then resell it to him. In general, arbitrage occurs any time a product is purchased at one price and resold at a higher price without any risk. For price discrimination to work, the firm needs to be able to prevent arbitrage. One implication is that price discrimination is more common for services than for goods. Doctors and barbers frequently price discriminate because you can’t buy and resell a surgery or a haircut. But you could buy and resell a laptop.
There are three varieties of price discrimination.
• First degree price discrimination or perfect price discrimination occurs when all customers are charged a price exactly equal to their willingness to pay. This is typically impossible in practice, but it’s a good starting point for reference.
• Second degree price discrimination occurs when the per-unit price depends on the total number of units purchased. For example, the price of a can of soda is different if you buy a case of soda than if you buy a single can.
• Third degree price discrimination involves charging different prices to different groups of customers. Our movie theater that set different prices for kids and adults is practicing third degree price discrimination. Hotels sometimes charge different rates for customers who book with corporate credit cards versus personal credit cards.
Perfect Price Discrimination
Let’s begin with an example. You run a consulting company that writes computer databases, and you have five clients who might be interested in buying one of your databases.
Client Price
Suppose first that you operate as a single-price monopoly. In other words, you set a single price that applies for any customer. The table below shows, depending on the price you charge, the quantity of programs that you would sell. It costs you $17,000 to design each program.
Price Quantity Total Revenue
Marginal
Revenue Total Cost
Marginal Cost
>$35,000 0 $0 -- $0 --
$35,000 1 $35,000 $35,000 $17,000 $17,000
$30,000 2 $60,000 $25,000 $34,000 $17,000
$25,000 3 $75,000 $15,000 $51,000 $17,000
$20,000 4 $80,000 $5000 $68,000 $17,000
$15,000 5 $75,000 −$5000 $85,000 $17,000
As usual, marginal revenue is lower than price. Although the second customer (Burger King) is willing to pay $30,000 for one of your programs, in order to sell the second program, you have to drop your price to $30,000 for both units. Thus, when you choose to sell the second program, you earn $30,000 of additional revenue from Burger King, but you lose $5000 of revenue by dropping the price for Applebees from $35,000 to $30,000. All in all, your marginal revenue is only $25,000.
To maximize profit, the firm will sell 2 programs, charge a price of $30,000 and earn a profit of $26,000 – the difference between total revenue and total cost.
But what if you could perfectly price discriminate?. Now, when you sell 2 programs, you can charge Burger King $30,000 while continuing to charge Applebees $35,000. In this case, your revenue when you sell 2 program is actually $65,000.
Similarly, when you choose to sell 3 programs, you sell the program to Applebees for $35,000, to Burger King for $30,000 and to Chipotle for $25,000 – for total revenue of $90,000. Continuing on like this, the table below shows total and marginal revenue when the firm can perfectly price discriminate by charging each customer a different price.
Quantity Total Revenue
Marginal
Revenue Total Cost
Marginal Cost
0 $0 -- $0 --
1 $35,000 $35,000 $17,000 $17,000
2 $65,000 $30,000 $34,000 $17,000
3 $90,000 $25,000 $51,000 $17,000
4 $110,000 $20,000 $68,000 $17,000
Importantly, marginal revenue is exactly equal to the price that each customer pays. When you sell to the second customer by adding Burger King, you really do get an extra $30,000 because only Burger King is charged this price. Applebees continues to pay $35,000.
• If a firm can perfectly price discriminate, marginal revenue is equal to price.
For the perfect price discriminator, the optimal level of output is to sell 4 programs (last unit where MR > MC). And your profit is $42,000. As described earlier, price discrimination can increase profits for the firm and improve efficiency by expanding the size of the market.
In terms of efficiency consequences, let’s return to the diagram from last section. Recall the comparison of surplus for a perfectly competitive firm and a single-price monopoly.
In contrast to the single-price monopoly, a perfect price discriminator will sell to any customer who is willing to pay more than the marginal cost of producing an additional unit. Selling to additional customers does not cut into revenues from previous customers since the firm charges a different price to each customer. A single-price monopoly doesn’t want to expand output beyond 𝑄𝑄𝑀𝑀 because it doesn’t want to cut the price for all its customers. But this isn’t a problem for a
perfect price discriminator, who can charge a different price to each customer.
There are two points. First, there is no consumer surplus in perfect price discrimination. Each customer is charged exactly what he is willing to pay, and thus no buyer gets any surplus.
Second, and most importantly, total surplus is at a maximum under perfect price discrimination, and in fact is equal to total surplus under perfect competition. Both market structures lead to the same output sold, and both are allocatively efficient in the sense that they maximize surplus (in contrast to single-price monopoly, where there is a deadweight loss). The difference is that, in perfect competition, all the surplus goes to consumers whereas in perfect price discrimination all the surplus goes to producers. Both are equally efficient. The difference is distributional.
What’s the point? As price discrimination gets more effective, the market typically performs more efficiently, but all the surplus ends up with the producers.
Third Degree Price Discrimination
Third-degree price discrimination occurs when firms charge different prices to different groups of customers. To study the optimal prices, remember that the optimal price for a firm with market power can be expressed as a markup over the marginal cost.
𝑃𝑃 = �1 + 𝜀𝜀� 𝑀𝑀𝑀𝑀𝜀𝜀
𝑃𝑃1 = �1 + −2� ⋅ 6 = $12−2
𝑃𝑃2 = �1 + −4� ⋅ 6 = $8−4
The intuition is straightforward – the firm charges the higher price to the group with the more inelastic demand and the lower price to the group with the more elastic demand.
Examples of this principle abound. Why do you think airline tickets cost more if you buy them on the day of the flight? Probably someone who buys a ticket on the day he travels has highly inelastic demand and needs to travel on that day. As another example, there is evidence that firms charge higher prices to women than to men for haircuts, even for exactly the same services. Evidently, firms believe that women have more inelastic demand for hair care services.
As another example, how can we explain clipping coupons? The basic idea is that customers who take the time to clip coupons are probably more price sensitive and have more elastic demand. Customers who don’t bother to clip coupons don’t care that much about price; their demand is more inelastic. By offering lower prices to customers who clip coupons, the grocery store is price discriminating – people from the first group pay lower prices and people from the second group pay higher prices. This is sometimes called the “hurdle model”, the idea being that the firm separates customers by offering a lower price to customers who cross some hurdle.
Let’s finish this section with a numerical example. Your company faces demand from two markets. In market A, demand is 𝑄𝑄𝐴𝐴 = 50 − 𝑃𝑃. In market B, demand is 𝑄𝑄𝐵𝐵= 120 − 2𝑃𝑃. The cost to produce each unit of output is $20.
Suppose first that the firm cannot price discriminate, and has to charge the same price to all customers (maybe arbitrage is easy across the two markets). In this case, the firm’s total demand for its product is 𝑄𝑄𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑄𝑄𝐴𝐴+ 𝑄𝑄𝐵𝐵 = 170 − 3𝑃𝑃.
What price should it set to maximize profit?
Π = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑀𝑀 = 𝑃𝑃 ⋅ 𝑄𝑄 − 20 ⋅ 𝑄𝑄
= 𝑃𝑃 ⋅ (170 − 3𝑃𝑃) − 20 ⋅ (170 − 3𝑃𝑃) = 230𝑃𝑃 − 3𝑃𝑃2− 3400
𝑑𝑑Π
𝑑𝑑𝑃𝑃 = 230 − 6𝑃𝑃 = 0 ⇒ 𝑃𝑃 = $38.33
In turn, the firm will sell 𝑄𝑄 = 170 − 3𝑃𝑃 = 55 units. The firm’s total revenue is 𝑃𝑃 ⋅ 𝑄𝑄 = $2108.33. Its total cost is 20 ⋅ 𝑄𝑄 = $1100, so the firm overall earns a profit of $1008.33.
Now suppose instead that the firm is able to price discriminate and charge a different price in each market. Now it simply maximizes profit from each market separately. In Market A, profit is:
Π = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑀𝑀
= 𝑃𝑃 ⋅ (50 − 𝑃𝑃) − 20 ⋅ (50 − 𝑃𝑃) = 70𝑃𝑃 − 𝑃𝑃2− 1000
To maximize profit:
𝑑𝑑Π
𝑑𝑑𝑃𝑃 = 70 − 2𝑃𝑃 = 0 ⇒ 𝑃𝑃 = $35
Substituting back to the demand curve, the firm sells 15 units of output in Market A. It earns total revenue of $525, incurs total costs of $300, for a profit of $225 in Market A.
In market B, profit is:
Π = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑀𝑀
= 𝑃𝑃 ⋅ (120 − 2𝑃𝑃) − 20 ⋅ (120 − 2𝑃𝑃) = 160𝑃𝑃 − 2𝑃𝑃2− 2400
To maximize profit:
𝑑𝑑Π
𝑑𝑑𝑃𝑃 = 160 − 4𝑃𝑃 = 0 ⇒ 𝑃𝑃 = $40
Substituting back to the demand curve, the firm sells 40 units in Market B. It earns a total revenue of $1600, incurs total costs of $800, for a profit of $800 in Market B.
Combining, the firm’s profit is in both markets is $1025 when it is able to charge different prices, which is an improvement over the profit that it earned when it was forced to charge the same price. It is always better for the firm to be able to price discriminate.
𝜀𝜀𝐴𝐴 = �𝑑𝑑𝑄𝑄
𝑑𝑑𝑃𝑃� � 𝑃𝑃
𝑄𝑄� =(−1) � 35
15� = −2.33
Elasticity of demand in Market B is:
𝜀𝜀𝐵𝐵 = �𝑑𝑑𝑄𝑄
𝑑𝑑𝑃𝑃� � 𝑃𝑃
𝑄𝑄� =(−2) � 40
40� = −2
To verify using our markup rule, the optimal prices are:
𝑃𝑃𝐴𝐴 = � 𝜀𝜀𝐴𝐴
1 + 𝜀𝜀𝐴𝐴� ⋅ 𝑀𝑀𝑀𝑀 = �
−2.33
1 + −2.33� ⋅ 20 = $35
𝑃𝑃𝐵𝐵 = � 𝜀𝜀𝐵𝐵
1 + 𝜀𝜀𝐵𝐵� ⋅ 𝑀𝑀𝑀𝑀 = �
−2
1 + −2� ⋅ 20 = $40
As usual, the group with the more inelastic demand (in Market B) is charged the higher price.
Two Part Tariffs
A two part tariff is a pricing strategy where consumers pay a fixed fee 𝐹𝐹 to enter a market and then pay a per-unit price of 𝑝𝑝 for each unit they purchase once there. Sam’s Club and Costco are obvious examples. Another example might be a club that charges a cover charge, and then subsequently charges for food and drinks once you enter. Amusement parks and movie theaters are additional examples.
Two part tariffs are a good strategy in markets where consumers buy multiple units. For example, let’s consider a market where each customer’s demand for drinks at a nightclub is 𝑃𝑃 = 10 − 𝑄𝑄. Importantly, this is not the market demand curve, but rather the individual demand curve for each customers in the market. For example, if the price of drinks is $7, then the consumer will buy 3 drinks. Each drink costs the club $2 to make.
Let’s first start with simple linear pricing. The firm will choose the price and quantity that maximizes profit for each customer.
Π = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑀𝑀 = 𝑃𝑃𝑄𝑄 − 2𝑄𝑄
Choosing the output level that maximizes profit:
𝑑𝑑Π
𝑑𝑑𝑄𝑄 = 8 − 2𝑄𝑄 = 0 ⇒ 𝑄𝑄 = 4
In turn, the price charged to each customer is 𝑃𝑃 = 10 − 𝑄𝑄 = $6. Using simple linear pricing, the firm’s profit-maximizing strategy is to charge $6 for drinks and sell each customer 4 drinks. This generates a profit of Π = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑀𝑀 = 24 − 8 = $16 for the firm.
The diagram is shown below. Note that the customers get some consumer surplus because they would have been willing to pay higher prices for the first few units.
Here’s the idea behind a two-part tariff. Whenever a customer earns consumer surplus, he is willing to pay up to the amount of his consumer surplus as a fixed fee for entering the market. In essence, the firm can snatch up the customer’s consumer surplus as an entrance fee for the right to participate in the market.
Thus, the firm’s objective in using a two-part tariff is to create the maximum possible surplus in the market. Graphically, it is easy to see that the firm can accomplish this by setting the unit price equal to the marginal cost. The firm can then convert all of the consumer surplus to profit in the firm of the fixed fee.
For this specific example, the firm should set the price of a drink at $2. In turn, the consumer will buy 8 drinks, and the firm can charge a fixed fee of $32 for the right to enter the market in the first place. Here is the diagram.
Note that the full $32 fixed fee is profit straight into the firm’s pocket. In other words, using a two-part tariff doubles the profit from $16 to $32 over what the firm can earn with simple linear pricing.
One important thing to note. The firm breaks even on the drink sales themselves since it sells drinks at cost, but it turned all of the resulting consumer surplus into profit by using the fixed fee. This is an interesting property of two part tariffs – all the profit comes from the entrance fee (F), not from the unit price (p).
The basic intuition is this. The lower the price the firm charges for drinks, the happier the consumer is to enter the club, and the more he is willing to pay as an entrance fee. As a simple example, think about gym memberships. Each visit to the gym is free, which is optimal since the gym’s marginal cost for you to visit is practically zero. The gym makes all their profits from the monthly membership fee. This is why Costco sells you food at a low price – it makes consumers happier and willing to pay a higher membership fee.
Two part Tariffs with Different Customer Types
Suppose that a market consists of two types of customers. A good example is mobile phone plans.
• “Heavy users” have high demand for phone minutes. They use a lot and have a high willingness to pay.
• “Light users” have a lower demand for phone minutes. They aren’t interested in buying as many units and they aren’t willing to pay as much.
The firm can’t tell the difference between the heavy users and the light users, so it can’t directly price discriminate, but it can offer different plans and let customers select between them. Let’s say it tries to use a two-part tariff for each group. Phone plans are a good example because typically users pay a monthly access fee and then pay for data or minutes.
Here’s the problem. Say the firm uses the rule from the previous section. It sets the unit price 𝑝𝑝 equal to the marginal cost, for both groups. Then it sets the fixed monthly fee 𝐹𝐹 equal to the consumer surplus earned by each group – higher for the heavy users than for the light users. This would be the efficient solution, but it isn’t going to work. If both plans have the same per-minute charge 𝑝𝑝, then obviously everyone is going to opt for the plan with the cheaper monthly fixed fee! In other words, the heavy users are going to buy the plan intended for the light users.
I won’t show how to solve this problem in detail, but here’s how the profit-maximizing solution for the firm works out.
• The plan intended for the heavy users has a unit price 𝑝𝑝 equal to marginal cost. But the monthly fixed fee 𝐹𝐹 is lower than their consumer surplus. The firm basically leaves money on the table for the heavy users in order to keep them from wanting to opt for the other plan. This plan is efficient since price is equal to marginal cost, but the firm doesn’t capture all of the consumer surplus.
• The plan intended for the light users has a unit price 𝑝𝑝 that is set higher than marginal cost. But the monthly fixed fee 𝐹𝐹 is set equal to their consumer surplus. The firm has to set an inefficiently high per-minute price for these guys (higher than marginal cost) in order to keep the heavy users from wanting to switch over to this plan. This plan is inefficient since price is set higher than marginal cost, but the firm captures all of the resulting surplus.
customers. The plan for the high-demand customers is efficient, but it leaves some of their surplus on the table in order to keep them where they are.
Here’s the interesting thing about this example. Even though the mobile phone carrier can’t directly price discriminate, it manages to price discriminate anyway by offering different plans and letting consumers sort themselves into the different plans. But the solution is not optimal, relative to what the firm could have achieved by directly price discriminating.
Block Pricing
Recall the earlier example of the club and the drinks.
Using a two-part tariff, the best strategy was to sell drinks for $2 each, and then charge a $32 fixed fee. Notice that the consumer buys 8 drinks under this plan.
An equivalent strategy would be the following. The consumer ends up paying $16 for drinks and $32 for the entrance fee. Instead of the two-part tariff, just charge each customer $48 for 8 drinks. In other words, the firm doesn’t sell drinks individually anymore. It just sells a block of 8 drinks for $48. This is an example of block pricing, where the firm only offers multiple units in a block.
We can illustrate the insight behind block pricing with a simple example. Suppose a consumer is willing to pay $5 for his first cookie and $3 for his second cookie. If the firm sells cookies individually and wants to sell two cookies to the customer, the price has to be $3. After he has already eaten the first cookie, he won’t buy the second one unless the price is $3. This strategy collects $6 from the customer and leaves him with $2 of consumer surplus from the first cookie.
Bundling
Consider a theater that puts on two performances: a symphony and a ballet. There are two customers: Michael and Nina (obviously could be generalized to two types of customers). The table below shows what each is willing to pay for a ticket to each performance.
Symphony Ballet
Michael $100 $75
Nina $35 $120
One option for the firm is to sell tickets separately.
For symphony tickets:
• If symphony tickets are sold for $100, only Michael will buy one Revenue = $100
• If symphony tickets are sold for $35, both Nina and Michael will buy one Revenue = $70
The best option is to price symphony tickets at $100 and sell one only to Michael.
For ballet tickets:
• If ballet tickets are sold for $120, only Nina will buy one Revenue = $120
• If ballet tickets are sold for $75, both Michael and Nina will buy one Revenue = $150
The best option is to price ballet tickets at $75 and sell them to both customers.
Overall, the firm earns $250 of revenue from pricing separately.
Now suppose instead that the firm doesn’t sell the tickets separately, but only sells a bundle that includes both a symphony and a ballet ticket. Notice that Michael is willing to pay $175 for a bundle and Nina is willing to pay $155 for a bundle. Selling bundles for $155 is a better option.
• If a bundle is sold for $175, only Michael will buy one Revenue = $175
• If a bundle is sold for $155, both Nina and Michael will buy one Revenue = $310
Overall, the firm earns $310 of revenue when it sells tickets bundled. Using bundled pricing instead of pricing each item separately increases profit from $250 to $310.
symphony ticket. But when Nina buys a $155 bundle, she’s mostly paying for the ballet ticket. The bundle can simultaneously capture their consumer surplus from the two different performances while forcing both of them to buy both tickets.
For another practical example, this is why telecommunications companies like Verizon and Comcast offer bundles with Internet, phone and TV service. Some of their customers place higher value on good Internet access and some care more about good TV channels. By offering bundled packages, the firm can simultaneously capture the surplus from both TV and Internet junkies, while getting both to buy a bundle with many services.
Versioning
Versioning occurs when the same product is sold at multiple quality levels.
Third-class cars on French trains in the 1800’s were not pleasant. They had no roofs and no seats, and occasionally sparks would fly off the tracks that burned people’s clothes and luggage. It’s not that it would have cost very much to install a roof or some seats. But the problem was this – making third-class travel too comfortable would have reduced the incentive to buy first-class tickets.
For a more modern example, many economists have suggested that this is the reason that economy class on airplanes is so uncomfortable. If we looked only at economy class, airlines could offer better service, charge higher prices, make more profit from the economy class cabin and make their customers happier. The problem is that, by doing so, there is less incentive to buy first class tickets. In other words, the quality of economy class has nothing to do with the preferences of economy-class customers, it is set to keep the first-class customers right where they are.
This is the usual result with versioning models. The profit-maximizing solution for the firm is to make the low-quality version lower than the efficient level of quality in order to increase the incentive to buy up to the high-quality version.
Damaged Goods
A particularly perverse example of versioning occurs when a firm deliberately damages its own product in order to create a lower-quality version and create a higher-quality version and sort out customers with higher willingness to pay. Here are some famous examples.
Think about this for a second. Intel actually spent money to reduce the quality of its product for consumers! Clearly inefficient, but from a profit-maximization perspective, it makes sense. Some customers really valued having a fast processor, but some didn’t care that much. If the firm offered only one type of processor, it would have to cut the price in order to sell it to both types of customers. By creating a lower-quality version of the chip, Intel was able to expand its market to low-price customers (who bought an SX chip) while continuing to charge a high price to the customers who needed a fast processor (and bought a DX chip). Here are two additional examples.
• The IBM Laser Printer E is actually the same as the IBM Laser Printer except that there is code inserted into Laser Printer E model to deliberately insert wait times between pages.
• A 60-minute recordable CD is actually the same as a 74-minute recordable CD except that the 60-minte CD has code inserted to prevent recording beyond 60 minutes, even though there is room left on the disc!
Durable Goods
Durable goods are goods that provide a stream of value over time, like a refrigerator or a DVD (versus a pizza).
Durable goods are often sold at a high price initially, with the price falling as time goes on to capture more and more customers. Books cost a lot when they first come out in hardback, but subsequent paperback printings are many times cheaper. The first generation of MP3 players sold for upwards of $700, but you can buy one now for less than $10.
You might not have thought about it like this, but this is actually a price discrimination scheme. Think about books. When the newest Harry Potter novel comes out, the diehard fans who are willing to pay a lot buy them right away. Then, as time goes on, the publisher expands its customer base by offering a paperback. Thus, the firm achieved price discrimination – charging one price to one group of customers and a different price to another group of customers for the same book.
This kind of scheme works best when the price cut is unexpected. When the iPhone first came out, it was expensive and the sales were underwhelming. Apple cut the price almost in half within just a few months. The customers who bought it initially at the high price were outraged – We never would have bought it at that high price if we had known Apple was going to cut the price in just a couple of months! Of course, that’s exactly why it worked so well for Apple. They got their die-hard fans to pay top dollar, and then expanded the market later on.
more customers. So there’s no reason for the first group of consumers to pay the high price and not expect a price cut later on. We will have a whole unit later in the course dedicated to durable goods. But one thing to quickly mention is that, for the producing, renting can be better than selling in this context. By renting, the firm can commit to maintain the profit-maximizing price today and in the future. As an example, for the first 50 years that it was in operation, Xerox would never sell a photocopy machine to anyone. They only rented.
Peak Load Pricing
Peak-Load pricing is a kind of third-degree price discrimination where the firm charges different prices at different times. Electric companies and mobile phone service providers both use peak-load pricing to charge higher prices during the day than they charge at night.
The idea is that these firms face capacity constraints and can manage usage during high-demand times by charging higher prices. Essentially, the firm uses peak-load pricing to restrict use during the day (when the firm may be approaching capacity) and shift this demand to night-time (when there is a lot of unused capacity). In this way, peak-load pricing improves efficiency by better managing and making more even use of a network with limited capacity.
Cross-Subsidization
Cross-subsidization occurs when a firm sells a product at a price lower than the profit-maximizing price, sometimes even at a loss, in order to extract more profit from a related product. Cross-subsidization is typically effective when products are complementary to each other.
The classic example of cross-subsidization is printers and ink cartridges. Many companies sell printers at very low prices and then charge high prices for the ink cartridges. This is a good strategy since demand for the printer is pretty elastic (the consumer has lots of choices when choosing a printer). But demand for ink cartridges is more inelastic once you already own the printer. So the company loses money on printers, but it makes it back up again by charging high prices for ink cartridges. Low prices for elastic products and high prices for inelastic products is generally a good guideline.
Exercises
Problem 1
Consider a monopoly that faces a demand curve 𝑃𝑃 = 100 − 10𝑄𝑄 and incurs a production cost of $20 for each unit sold.
a. Suppose the firm operates as a single-price monopoly. How much output will it sell and how much profit does the firm earn?
b. Suppose the firm can perfectly price discriminate. How much output will it sell and how much profit does the firm earn?
Problem 2
You are the manager of a monopoly that sells a product to consumers in two different parts of the country. In the first market, the elasticity of demand is 𝜀𝜀𝐴𝐴 = −2 and in the second market the elasticity of demand is 𝜀𝜀𝐴𝐴 = −6. Your marginal cost of production is $10 per unit
a. What are the optimal prices?
b. Many firms set a lower price in export markets than they charge domestically: a practice frequently criticized by consumer groups. How might you explain this?
Problem 3
You run a bakery that has many customers. Each customer’s demand for donuts is 𝑃𝑃 = 3 − 0.5𝑞𝑞. It costs you $1 to produce each donut.
a. Using simple linear pricing, what is the optimal donut price? How many donuts does each customer buy? How much profit does the firm earn from each customer?
b. Now consider a two-part tariff, where customers pay $F for membership in the donut club and then $p per donut. What are the optimal prices? How many donuts does each customer buy? How much profit does the firm earn from each customer?
c. Finally, consider block pricing, where the firm sells a block of D donuts for $B. What are the optimal block size and price? How much profit does the firm earn from each customer?
Problem 4
There are about 7 billion mobile phones in use worldwide. Although the production cost of a basic cell phone is around $50, it is customary for many wireless carriers to offer a free phone if the customer signs a service contract with the company. What kind of pricing strategy does this illustrate?
Problem 5
Problem 6
An airline regularly running a flight between Chicago and Zurich has 100 business travelers who are willing to pay $1000 for a ticket and 50 tourist travelers who are willing to pay only $500 for a ticket. There is a $20,000 fixed associated with running the flight, which is fixed regardless of the number of passengers on the plane.
a. Suppose the airline must set a single ticket price. What is the optimal ticket price? How much revenue does the airline earn and how much profit does it make?
b. Now suppose that the airline can price discriminate by charging different prices to business travelers and to tourists. What are the airline’s revenue and profit now?
c. The airline attempts to price discriminate in the following way. It initially sets the ticket price at $1000, so that business travelers will buy them immediately. A few days before the flight, it lowers the price to $500, hoping that tourists will buy a ticket. What problem would the airline would run into if it applied this strategy repeatedly?
Problem 7
You run a restaurant that sells hamburgers and sodas. It costs you $2 in labor and materials to serve a hamburger and it also costs you $2 in labor and materials to serve a soda. You have two customers. Lisa is willing to pay $10 for a hamburger and $5 for a soda. Derek is willing to pay $16 for a hamburger and $1 for a soda.
a. If hamburgers and sodas are sold separately, find the best prices and compute the profit earned by your restaurant.
b. If hamburgers and sodas as sold together as a “meal deal” bundle, find the best price for the meal deal and compute the profit earned by your restaurant.
