Wednesday, June 07, 2006

More Gas Pumping

Below in comments and over at Econball, Tony V and Dave essentially make the same argument. That if the market doesn’t provide it, it must not be worth providing. They essentially assume that because producers are better off, the market (and society) are better off.

This is silly. One of the first things we teach undergraduates in economics is that producers following their self-interest do not always produce the efficient market outcome. We talk about how monopolies produce deadweight losses by choosing not to produce goods that consumers are willing to pay more then it costs them to provide.

Something similar is happening with pumping gas. A service which in many (though probably not all) cases could be produced profitably is not being produced. This represents a loss to the economy. Losses to the economy are bad. We want to understand where they come from, and we want to make sure that when we observe them the factors which lead to these losses are more than making up for them by increasing total surplus in some other way.

In brief, what I argued previously is that it is not obvious to me that the marginal gains from not offering full service offset the losses.

Let do this more slowly and try and very clearly identify the marginal benefits and costs to the economy.

Start by examining a single market with one gas station that has a convenience store in an area where self-service is allowed. In order to help clarify the effects on all of the affected parties, assume that the service of pumping gas (and washing windows, etc.) is not directly provided by the station owner, but rather it is provided by independent contractors who pay a fee to owners in exchange for being allowed to work their lot. Finally, assume that these independent contractors and convenience store operators are able to perfectly price discriminate and capture all of consumer’s willingness to pay for these services. (This assumption is not necessary, but it may help make the explanation simpler by concentrating the surplus from the market into fewer agents.)

So we have 3 agents and 4 choices. Owners must decide whether or not to allow the independent servers to work at their stations. Independent servers decide whether or not to provide service or pursue a different job/leisure outcome. Consumers decide whether or not to buy pumping services and whether or not to by convenience store goods/services.

We are focused primarily on the owner’s decision, so let’s start there. Owners allow independent servers if:

Vsscs + Vfscs + bS > V’sscs

Where Vsscs = total value of self-service customers convenience store purchases minus costs; Vfscs = total value of full service customers convenience store purchases minus costs, b is an element of [0, 1] and represents the fraction of the rents from providing full service the owners capture, S is value of full service customers minus the providers reservation wages (e.g., the cost of providing it), and V’ is the surplus from the convenience store when everyone is a self-service customer.

If Vsscs+Vfscs=V’sscs and b>0 and S>0, owners should allow this service to be provided. If it is not being provided it must be either:

1) S=0
2) Vfscs+bS is less than V’fscs (= V’sscs - Vsscs) (What owners can extract from full service customers is less than what they can extract from them when they are forced to be self-service customers)

Case 1 is trivial. In this case, the willingness of those who wish to buy the service does not provide enough compensation for anyone to supply the service.

Case 2 is more interesting (and is essentially what I argued in my previous post). V’fscs-Vfscs represents the maximum potential gain to the economy (this is the marginal gain in value in the convenience item market from forcing people to use self-service). Determining the effect on overall economic welfare requires addressing two questions: (1) does this gain outweigh the losses to the economy of S and (2) how much of this amount represents a gain to the economy (versus a transfer from some other entity)?

First, assume that all of V’fscs-Vfscs represents a gain to the economy. If b is sufficiently small (i.e., owners struggle to extract the rents from providers of the service), owners would choose to prohibit full service even though the whole economy loses as a result of this decision. (b less than (V’fscs-Vfscs)/S) implies V’fscs-Vfscs greater than bS even though S is greater than V’fscs-Vfscs).

Second, even if b=1, V’fscs-Vfscs does not necessarily represent gains to the economy. It represents gains to the owner of the gas station. However, in the full serve state of the world, some (or even all) of this value might have accrued to some other producers (e.g., a different store). Again, if a sufficiently large fraction of these gains do not represent gains to the economy but simply transfers among different agents, then the loss of S outweighs these gains and the economy as a whole is worse off.

I set a time limit on how long I could spend writing this post, and that time is up. However, I think I have made my main point – the decision to eschew providing full service possibly imposes a net loss on the economy. This was the idea in my previous post. Certainly, I have no idea if the net gains and losses of the self-service laws are positive or negative. The point I was making was that the issue is not as simple as my economist friends made it out to me. Later, I might return and discuss what happens if people suffer from self-control problems and what happens when there is competition (e.g., why doesn’t a competitor enter the market to try and capture S), but this will have to suffice for now.

I have to say, I think I'm with Tony on this one. While this is an imperfectly competitive market, it's not clear how Exxon, Chevron, Texaco, etc., are all colluding on this issue. In the absence of a market failure, it may actually not be worth providing.

Just like those burritos that I loved as a kid that had hot dogs in the middle. Those were awesome, but I can't find them anymore. Not enough demand to justify it: or maybe it's collusion!
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