5 Aug 2010

Subsidies, opportunity cost & deadweight loss

This example is for my book. Does it make sense?

And finally, we get to an important, invisible subsidy – the subsidy for preferential access. Say that you and 5,000 other people want to go to a concert that’s in a hall with a capacity of 800 people. Tickets are only $5, but how do you get a ticket? If there was an open market for tickets, buyers might compete to push the price to $50, but there isn’t. Only some people — the connected, cool folks — are going to get tickets. (I’ll get to reselling tickets in a bit.) Note that the ticket promoter is forgoing $45 per ticket to distribute it to the cool people. We don’t know why he’s willing to pay this opportunity cost, but he is.

Let’s break down this example. Some cool people would have bought the ticket at the full price. Andy, for example, pays $5 for a $50 ticket that he values at $65, so he gets a subsidy ($45 = $50–$5) on top of his benefit ($65 less $50). Other cool people are going to get the $5 tickets that they would not have bought for $50. Bob is cool, but he’s only willing to pay $35 for the ticket. Bob gets a positive value of $30 ($35-$5) from the difference between what he pays and his value, but the remaining $15 of the $45 subsidy is wasted, as a deadweight loss from the difference between the ticket’s value in an open market and Bob’s value. But there’s more, there’s the deadweight loss from Carl not being able to buy that ticket. Carl values the ticket at $75 and would have been happy to pay $50 for it. From a social perspective, this method of distributing tickets creates deadweight losses from tickets ending up in the wrong hands. The $40 deadweight loss is the sum of the foregone benefit when Carl did not get the ticket ($75 less the $50 market price) plus the difference between the market price and Bob’s value ($50 less $35). It also creates subsidies by selling the ticket below the market price ($45 to Adam and $30 to Bob). Although the subsidy is merely a transfer of wealth from the ticket seller (money foregone), it’s valuable to those cool people who get that transfer. The deadweight loss is not valuable to those with preferential access – the cool people – but they are socially costly as a misallocation of resources.

If a secondary market was allowed to function, then we’d expect that Bob would sell his ticket to Carl. If he sold it for $60, then deadweight loss would go to zero.* Although that sale would not reduce the cost of the subsidy ($45 per ticket), it would change its value. The subsidy was only worth $30 to Bob, but now it’s worth $55. So now you have a better understanding of why people like subsidies. First, because they get something for less than cost – and sometimes less than their value. Second, because they can sell subsidized goods to others without preferential access. This ticket example demonstrates how preferential access wastefully misallocates valuable assets. Although it would be better to end such practices, a second-best choice – allowing re-selling – can eliminate most of the waste. Reselling is also more feasible, since winners in the current system would continue to win.

This gets us to water rights and access to infrastructure...
* This is slightly tricky, since deadweight loss is defined as the difference in values when the ticket ends up in the wrong hands ($40), not as the distribution of benefits ($15 to Carl and $25 to Bob) from reallocating that ticket.


  1. It makes sense but I think that there is a simpler, clearer example that you could use.

  2. I loved this example because one of the biggest city government scandals in my city's recent history happened when Elton John came to Sudbury to perform. Ours is a small remote city, and everybody from the city and the surrounding towns wanted to go to the concert, but few tickets were available. Information leaked out that city council members had ticket-buying rights before the tickets went for general sale, while the rest of us stood hopefully, and often unsuccessfully, in line for days. The councillors actually believed they deserved this perk, and even the ones who bought quite a few tickets were astounded by the level of rage felt by the citizenry. Poor Elton John, who just wanted to give a show in a northern community, was caught in the middle. The city council bylaw has been changed to prevent this incident from recurring.

    However, I think you could clarify your examples. You first case should be someone who gets a $50 ticket and values it at $50 but pays only $5. This case defines a straightforward subsidy. Then look at cases where subsidy receivers value it at less or more than $50 to see the deadwight loss of the subsidy itself. Then look at the money foregone within the market because others who were not able to get tickets would have paid more than $5 and maybe more than $50, for the ticket. It's a bit confusing to look at the deadweight loss of the subsidy to the subsidizer, and the deadweight loss to the market of an underpriced ticket, in the same example; it also feels a bit like comparing apples and oranges to an economist novice (me). But it could be your last case, in order to define the total deadweight loss, as per your footnote definition.

  3. Hmm. Perhaps a diagram to accompany this? It's quite a thicket.

  4. David. It is very a nice example, of subsidies and deadweight loss, and you did a good job taking out the economic jargon. However, I second Wainstead opinion, try to include a little graph/diagram to make it easier to digest by the layman audience. It has too much detail and keeping track of it can be tedious. I would use less words and a diagram.

  5. @all -- thanks for the good suggestions. Yes, it's complicated but your simplification ideas are REALLY helpful. Diagram. Yes, I'll do one...

  6. Politicos know the bottom line as well: “So now you have a better understanding of why people like subsidies.”

    However, politicos sell the subsidy as a benefit but attempt to hide the “….subsidy is merely a transfer of wealth”. Politicos also brush aside resource allocation distortion: ‘The deadweight loss is not valuable to those with preferential access – the cool people – but they are socially costly as a misallocation of resources”.

    Is the “subsidy” really a form of picking winners and losers through a wealth transfer scheme which results in a misallocation of resources?

    “Note that the ticket promoter is forgoing $45 per ticket to distribute it to the cool people. We don’t know why he’s willing to pay this opportunity cost, but he is.” If the ticket promoter is a politico, that dishes out the subsidy through the mechanism of government, then is the opportunity cost transferred to the tax payer and the politico pays no opportunity cost?

  7. David,

    This issue is so important that it deserves the clearest example you can possibly provide. In India we are not simply talking about concert tickets but access to housing, telphones and water supplies. These goods and services are all too often provided only to the chosen few or via "lottery" at prices far below market value. Even when a "lottery" is employed, a suspiciously high number of winning tickets always seem to wind up in the hands of the lotteries' organizers.

  8. Your story is getting more complex as I try to figure out how to tell it. I do not yet know the narrative.

    If I take out the classist parts of the story and try to convert it to straight economics, I get a story sort of like yours until I try to understand externalities. Say that I buy a ticket for $50 and give it to you because you have helped me over the years for free, where do the dead weight losses go? Similarly, say that you give a ticket to me because I run a charity that you have interacted with for years. Say that the charity has given out free benefits worth $100 a piece to 10,000 people over the time that you have known us. Is there still a deadweight loss if we consider lifecycle costs for which the concert is a small piece. Say that I give you 10 tickets and you are a landlord who is thinking of converting apartments into industrial space. Say that 6,000 people live in the apartments and because you got the tickets, you do not demolish the apartments. Where does this transaction fit into economic theory?

  9. I am a scientist who is trying to learn some economics. I know the term "subsidies" in terms of payments and tax breaks, both given by legislatures through laws. This example of tickets is confusing to me. It is contrived and complicated. Why don't you explain subsidies in terms of familiar, real examples, such as tax breaks for mortgage deduction or payments to wealthy farmers who grow corn or rice?

  10. On further thought, I would not use concert tickets as an example.

    Concert tickets are a one time event in which the concert producer has to guess the correct market value of an individual ticket. If the producer guesses too high a value, then lots of tickets are left unsold. If the producer guesses a ticket value that is too low, then, on paper, there is a nominal deadweight loss but the producer cannot take advantage of this deadweight loss because she or he can't reprice the tickets to this concert especially the tickets that have already been sold. The only repricing that can occur is for the next concert but the repricing has the same risks in income that exist in this concert and the performing group is different so that 'correct price' may not be knowable in advance. Also in the concert example, concert goers who know the producer may decide that the guessed at price is low and may choose to buy more tickets so that the available tickets are sold more quickly.
    I would like an example in which the price of an item has a stable, known, long term value and for which selling this item below the stable, known, long term value can be better considered as a subsidy and deadweight loss. Opportunity costs seems to be a more complex topic.

  11. Your example is wonderful. However, I agree with Wainstead and JMA. A diagram would surely be helpful. In addition, I feel the argument is too long, and one may get to lose track after some time, because of the complications that wind up successively. And I feel the deadweight is not appropriate in this case, as you have marked in the footnote.

  12. Rent control might be a good example. Certainly the people like Charlie Rangel enjoy a good deal, but both the property owner and other, market rate, tenants are disadvantaged. Depending on how the rent control regeime is managed, it may well discourage improvement of existing stock and construction of new stock, further damaging the local tax base and all renters. I'm not an economist, but is this an example of deadweight loss?

  13. For this example and some others that you use, like MWD, the example appears to be off target.
    What if the named product of the entity is not the real product of the entity?
    So what if the seller of tickets for the concert is not focused on the income from the tickets but on raising money to put on the next concert. Then the ticket price is not the guiding factor of the economics.
    Similarly, if Los Angeles' MWD is actually selling re-election success not water, then economics change.
    So, the question is 'In the economic analysis of an entity, has the actual product been identified and how is the entity doing in selling that product?'

  14. I think, on the whole, the example works. It's clear and understandable to the uninformed reader. Applied to water rights in general, I would agree that preferential access is an evil, but one you're never going to get rid of in the West, so you're right to recommend the "second-best choice" of re-selling.

    One caveat: I understand the use of "cool people" as shorthand for rights holders, but it does short shrift for the historical circumstances that led to the allocation of rights. It wasn't just a popularity contest...

    Also, if this is being applied to MWD and access to its infrastructure--as some of the above comments suggest--there are further complications, as MWD is using access to its infrastructure as a lever to develop control over existing local groundwater rights regimes and markets.

  15. David, I think may have the economics wrong. If there's a secondary market, then there's no economic loss in your example. In fact, I wouldn't call this a subsidy.

    Subsidy is harmful when it creates a misalignment between supply and demand. If the government were to subsidize concert tickets, say, giving the venue $10 for every ticket they sell, then venues will sell tickets beyond the point at which marginal benefit and marginal cost meet (maybe they'll install bleachers or something). The deadweight loss would be from the last several tickets sold for which the cost to produce them is higher than their benefit to concert-goers. In an efficient market these tickets would not exist, but the subsidy has induced the venue to produce them, since the net cost to the venue is lower than the benefit to the concert-goers.

  16. @WEH -- yes, the politicos are shifting cost to taxpayers (as usual)

    @Eric -- all of your questions and examples are too far from my point, which is to highlight the TWO types of cost to these preferential access programs.

    @FC -- there are TWO types..

    @J David and Debal -- thanks!

    @Kurtz -- no, MY DWL is not related to "dynamics" - LT impacts.

    @Justin -- yes (on cool) and no (NOT about MWD and "side effects" except as political CYA).

    @Outsider -- you're right BUT there are transactions costs, and the market MAY NOT develop (or be allowed...

  17. To me, your example does not work because it does not really highlight the two types of costs. It pretends to, but on inspection it highlights other things, is not really about the stated costs, and so invalidates your argument and the logic of this section of the book.

    Another example, without the holes, might be better.


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