OpportunityCard: An Example
(Created by David Reinstein, Owen Southam, Harry Masters, and Rasif Alakbarov. Linked in “Should we help companies tailor prices to your wage packet?” in The Conversation)
A tale of two prices (Example 1)
A tale of two prices (example 2)
To fix ideas we offer a hypothetical scenario, comparing before and after the introduction of an OpportunityCard.
Four people are waiting at a bus stop (this is not the opening line of a joke): a student, a pensioner, a dishwasher (who earns minimum wage), a maid, a lawyer, and a banker.
The standard fare is £4. Do all passengers pay this? No, the pensioner can ride the bus for free for most of the day, even if he retired from an investment bank with a gold-plated annuity, because his fare is subsidised by the government. The student gets a discount bus pass for a different reason: the bus company price discriminates: they know that students will tend not to ride the bus unless it is cheap, so they can make more money by offering them discounts. The dishwasher and lawyer are required to pay full price.
When governments consider taxes, spending, and regulation a key concern is efficiency: which policies will ‘increase the size of the pie’, and which will be ‘Pareto dominated’?[1]
Suppose the dishwasher ‘Dave’ found the £4 fare too dear, and decided to walk instead. The bus company now has lost income and Dave has lost time. As long as the bus was not overcrowded and the dishwasher was boarding and departing at required stops, this is a pure loss. Offering lower prices to students made them want to take the bus. Similarly, the company could offer discounts to low income consumers like the dishwasher -- if they can be identified. If Dave was willing to pay £2.50, then (assuming no ‘marginal costs’ for picking up passengers) if they charged any fare in between 0 and £2.50, Dave and the bus company would both be better off.[2]
In general, when a firm has ‘market power’ and can only charge a single price, there is a loss of efficiency: the firm reduces the quantity and keeps prices high. The bus company could reduce the fare to £2.50 (or even to 25p) but it makes more money charging £4. Although it loses Dave’s fare, the £4 it gets from the other passengers makes up for this.
On the other hand, if the firm could perfectly price-discriminate -- charging everyone his or her maximum willingness-to-pay -- there is no efficiency loss. If Dave’s fare were £2 and the lawyer’s was £4, both would ride, and the bus company would profit. (Remember, economists think of efficiency in terms of the total size of the pie, not on how it is divided). However, an intermediate amount of price discrimination may either make things better or worse, from an efficiency standpoint.
What might happen in this example if there was an OpportunityCard?
To flesh out the example, imagine the following ‘valuations’. These represent the most each consumer would be willing to pay to take the bus.
Low-income consumers
Dave the dishwasher: £2.50
Molly the maid: £4
High-income consumers
Larry the lawyer: £5.50
Bob the banker: £10
Suppose that the marginal cost of taking on additional passengers was zero (this assumption is not crucial to the main point). Here, if they can not distinguish between customers, the £4 fare maximized the bus company’s profit. It earned £12: £4 per/passenger from three passengers. Absent price-discrimination, no other fare could earn more.[3] Here the net social value (adding the company’s profits and the surplus of each consumer), is £19.50.[4]
The bus company’s new fares: Now suppose that the OpportunityCard allows the bus company to perfectly distinguish between the low and high-income consumers. The low-income consumers will present the OC while the high-income consumers will be charged the base fare. The bus company could always ignore the new information provided by the OC -- thus, the OC should never make it worse off. However, it would do better by using this information to price discriminate.
It can now segment consumers and offer two distinct prices. Considering the low-income customers only, a fare of £2.50 earns the highest profit (£5). Among the high-income customers, a £5.50 (base) fare is most profitable, earning £11. (Although it could charge Bob up to £10, this gain of £4.50 would not be worth losing Larry's £5.50.)
Consumer welfare: Dave now rides the bus, and saves time walking, but he is actually no better off. He is charged his full valuation, £2.50, so the amount he pays balances out the benefit he gets.[5] (However, the full £2.50 is an increase in the ‘size of the pie’, and this entire gain goes to the firm.)
Other low-income consumers such as Molly -- who were willing to pay as much as £4 -- continue to use the bus; Molly gains £1.50 in savings from the OC (an amount lost to the firm).
Larry and Bob are both made worse off. They continue to ride the bus,[6] but each must pay £5.50, or £1.50 more than before.
Bus company profit: The bus company will now earn a total of £16, £4 more than before. This comes from the £2.50 from Dave’s new fare, less the £1.50 lost from Molly, plus £1.50 Larry and £1.50 from Bob.
Overall social value: Adding this up, the low-income consumers gained £1.50, the high-income consumers lost £3, and the firm gained £4. In net, this is a gain of £2.50[7] (and the total social value is £22). Where did this gain in social value come from? Money passed from the consumers to the firms has no impact on social value -- the only thing that matters is the value generated by consumption, less any production costs (here assumed to be zero). Before the OC, only three people rode the bus; now Dave rides as well. His £2.50 in ‘value of riding’ is now added to the ‘size of the pie’ -- the social value.
Now suppose the valuations are as before, except that Larry the lawyer’s is £1 lower. I.e.:
Low-income consumers
Dave the dishwasher: £2.50
Molly the maid: £4
High-income consumers
Larry the lawyer: £4.50
Bob the banker: £10
The bus company’s fares (example 2): The £4 fare is still optimal in the absence of the OpportunityCard. Absent price-discrimination, the firm’s profits are the same as in example 1. The same three customers (Molly, Larry, and Bob) ride, generating a social value of £18.50 (£4 + £4.50 + £10; this is £1 less than in Example 1 because of Larry’s lower valuation).
With the OC, it is still optimal to charge £2.50 to the low-income consumers. However, now that Larry’s valuation has declined, with the OC the most profitable fare for the high-income consumers is £10. The firm now gains more by charging £5.50 more to Bob even if it loses Larry’s fare.
Overall social value (example 2): In contrast to the first example, the OC now reduces welfare. Considering ‘value generated by consumption’, the OC leads Dave to ride the bus (gaining value £2.50), but leads Larry to stop riding the bus (losing value £4.50). The net social value is £16.50, compared to £18.50 without price-discrimination. In this example, while the bus has the same volume as without the OC (three passengers), we have swapped a high-valuing customer (Larry) for a low-valuing customer (Dave), and this ‘misallocation’ has reduced social welfare.
The ‘Wrong consumer’?
It may seem strange that it is considered ‘inefficient’ for the low-income customer (Dave the dishwasher) to purchase the product, here a bus ticket, instead of the high-income consumer (Larry the lawyer). After all, the same amount is being produced and consumed, so where is the inefficiency?
The point is that Larry would get more benefit out of riding the bus than Dave -- perhaps Larry has less leisure time to spare and thus he values the time savings more than Dave. Price discrimination here has shifted both Dave and Larry’s consumption basket here. Dave is now spending more on the bus and less on other things, and Larry spends less on the bus and more on other things. But Larry values the bus ride at £4.50 -- meaning he would be willing to give up £4.50 in other goods to ride the bus. On the other hand, Dave only values his ride at £2.50, meaning he would be willing to give up only £2.50 in other goods to ride the bus. This situation is inefficient: both Larry and Dave could be made better off if Dave gave his bus ticket to Larry and Larry gave Dave (e.g.,) £3.50 in other goods. (But as we assume arbitrage here is impossible, this cannot happen.)
As the above examples show, the overall effect of the OpportunityCard on economic efficiency is ambiguous.
The price discrimination is not perfect -- it classifies people into groups, but even within each group there are different valuations. As a result, there are two effects going in opposite directions. The OC allows the bus company to expand output -- reducing Dave’s fare and getting him to ride -- without having to reduce fares to the wealthier customers. On the other hand, in the second example it led to a misallocation of the output. Dave rode the bus as a result of the discount, even though he valued this ride less than Larry, who stopped riding the bus.
In more general examples and models with a range of consumers, there will be both a misallocation and a (potential) increase in output. For the net effect to be positive, overall output must increase, and it must increase sufficiently to outweigh the misallocation problem.[8]
In our above example, we see lower prices for low-income OpportunityCard users and higher prices for the higher-income consumers. This implies a reduction in inequality in terms of purchasing power. This in turn should lead to a reduction in the inequality of outcomes in terms of what economists call ‘utility’; loosely speaking, a measure of happiness and well-being.
[1]A Pareto-dominated outcome is one in which we could make at least one person better off without making anyone worse off; if such unmixed improvements are possible, the situation is clearly inefficient and sub-optimal.
[2] To keep the example simple, we assume there are no marginal costs to taking on additional passengers. The bus may not stop at every bus stop, and if Dave flags it down, it will have to stop and take his ticket. This slows down the bus for the other passengers, and ultimately raises costs. If it gets too slow, or too crowded, the company will have to run another bus. However, the basic point persists; e.g., even if stopping for Dave brings an bincreased cost of 25p then if they charged any fare in between 25p and £2.50, both would be better off.
[3]Other possible fares
i. £2.50 → 4 passengers, £10 profit
ii. £5.50 → 2 passengers, £11 profit
iii. £10 → 1 passenger, £10 profit
[4] As noted below, as money passed from consumers to the firm generates no social value, we can simply add up the value gained by each consumer who rides the bus: here £4 + £5.50 + £10 = 19.50.
[5] You might ask ‘so then how do you know he will ride the bus’? Basically, we could assume the bus company actually charges the low-income customers £2.49 and the high income customers £5.49, and the results would be nearly the same.
[6] See above footnote.
[7] In this example the consumers lose in net -- ‘consumer surplus’ decreases. This is not a general result. E.g., suppose, instead, there were three dishwashers with a valuation of £2.50, and three maids with a valuation of £4. Here the maids would each gain £1.50 from the OC, and this £4.50 in consumer savings would more than offset the £3 that Bob and Larry lose in net.
[8]E.g., in example 2, if there were two people exactly like Dave, the gain in value from bringing them in (£2.50 + £2.50) would outweigh the value lost from Larry (£4.50). Here both would increase (4 customers instead of 3), and this output gain would outweigh the loss from misallocation.