Welfare, Surplus, and Partial Equilibrium

I don’t get welfare analysis. I don’t. If you do, please let me know.

In posts on Stigler, MWG, Rothbard, and Buchanan, I have questioned the use of welfare analysis in economics. I can regurgitate the expressions that welfare economists use, but the supposed benefits of the model confuse me. That’s why I am appealing to the brighter minds online.

The standard picture is below. In any market with a market-clearing price, P, there are certain consumers who would pay more if they had to. How do we know they would pay more? Stop asking stupid questions. We know everything. Well, we assume we know everything about everything that the person wants, that’s how. OK. Let’s ignore that problem for now.

The most willing person is at point A. He would pay A dollars, but only pays P. Lucky him. Therefore, he receives a “surplus” of A minus P dollars.  This approach similarly holds for producers. There is someone who would be willing to sell at price E. Instead, he sells at P and gains P minus E. Big money.

The gap in dollars is some sort of “welfare”.  For this post, I’m not even worried about the comparison between dollars and utility here. I will act like a conversion between dollars and utils exists- we can’t reject all premises at once.

One popular corollary of this is a deadweight lossdepicted below. For example, if governments tax a good, the buyer now has to pay P1 and only Q1 of the good sells. Fewer people benefit from trade, because the tax discourages the marginal traders from trading. The colored area is the deadweight loss, because the potential benefit goes to no one. It is simply lost.

From this, economists derive a crude utilitarian analysis which tries to maximize the colored size, the left triangle, on the first graph. A greater area means people are better off. It is trying to measure benefits minus costs. The consumer surplus is the analog of a producer’s profit. A rational consumer/producer maximizes benefit minus cost.

The problem is that economists are creating a symmetric theory for an asymmetric world. This idea does not work for consumer theory. The cost of buying one of the goods above is not the price P, but the next best thing I could have done with that money, i.e. opportunity cost. Repeat after me, cost means opportunity cost. Economists learn this on day one and forget it on day two.

Therefore, even assuming we can use money as a measure of utility, the benefit is the willingness to pay and the cost is the willingness to pay for the next best option. This difference is then the “profit.” However, this cannot be shown using the started supply and demand graph.  The above graph does not show profit, but benefits minus some constant.  It is like a producer was trying to maximize revenue minus 200 dollars. This does not make sense.

The person on the far left could have a next best option, which is really good, thus making almost no “profit.” A person in the middle might have no other good option, thus making a large “profit.” All that graph shows is revenue.

The confusion reared its head when I was thinking about an extreme example. Suppose there is a market for marijuana. One day the government decides to ban it and the ban actually works. Graphically, the price is forced above the highest consumer’s willingness to pay. Then the whole triangle on the left half is a deadweight loss. There is no consumer surplus.

This does not make sense. I am not left with zero surplus. Instead, I choose to spend my P dollars on something else, where I gain a surplus. I move to a new market, with a new supply and demand, and earn a surplus there.

The problem, on top of comparing utilities, stems from the partial equilibrium analysis used in standard welfare analysis. While it makes sense to talk about a company’s profit in one market, it does not make sense to talk about a person’s profit in one market. Profits can be separated across markets. People’s welfare is necessarily a general equilibrium concept. My welfare from work cannot be separated from my welfare from home.

This is the classic partial versus general equilibrium debate. The common reason for doing partial equilibrium analysis is that it is more manageable. It is easier to focus on one market. This makes sense when the goal is making predictions.

However, when economists try to do pseudo-philosophy through welfare analysis, the prediction benefit disappears and we are left without the general part of general equilibrium. Looking at someone’s welfare in one market will clearly obscure the picture. The profit of this approach is negative.

Again, the method that economists use falls short before the point where they want to use it. Let’s stick to using partial equilibrium because it allows for predictions. If we want to do more, say provide a cost/benefit analysis, we need to use general equilibrium and incorporate opportunity cost.

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    5 thoughts on “Welfare, Surplus, and Partial Equilibrium

    1. “Repeat after me, cost means opportunity cost. Economists learn this on day one and forget it on day two.”

      I laughed at this, because it’s so true.

      You’ve inspired me to blog about this topic, because it is really important, and you are right that we economists in general can conveniently drop crucial concepts, then invoke them again, when it suits. I’ll keep you posted.

      • I’m glad you liked it. It is so true.

        People use opportunity cost when they want to and accounting cost at other times. The problem is that we change without being explicit, because we just say cost.

        Similarly, it is so easy for me to invoke welfare analysis as “proving” that markets maximize happiness and I’m sure I’ve used it in a weak moment. It is also easy to reject welfare analysis for externality problems.

        The real challenge is to consistently apply our economic reasoning when it fits and doesn’t fit my priors. For me, opportunity cost is a central economic idea that we should always use in our reasoning. I am definitely not the only one who struggles with this.

    2. 1) The business about translating between dollars and utils is a red herring. Even assuming that we know exactly what a util is, it’s crucial in welfare analysis to IGNORE utils in favor of dollars. That’s because a dollar is transferable at a fixed rate of exchange (take one dollar from me and you can give exactly one dollar to someone else) while a util is not.

      Here’s why that matters: Suppose I live next door to Bill Gates. His Christmas tree keeps me up at night. I’d pay $10 (the equivalent of 1000 utils) to take the tree down. Bill would pay $50,000 (the equivalent of 10 utils, because money has quite a low marginal value to Bill) to keep it up. Should Bill keep his tree?

      If you calculate with utils, you’ll say that the tree comes down, but the right answer, according to welfare analysis is that the tree should stand. And here’s why: It’s crazy to impose a $50,000 cost on Bill in order to create a $10 benefit for me, when you could instead impose a $40,000 cost on Bill and create a $40,000 benefit for me, simply by transferring some cash. The whole point of welfare analysis is that whenever you decrease the total surplus, you’ve missed an opportunity to do something else that *everyone* prefers.

      You can’t make that argument with utils, because there’ s no way in general to take utils away from one of us and transfer exactly the same number of utils to the other.

      So the *whole point* of welfare analysis is that utils don’t matter — only dollars do. There are, of course, other points of view, but it’s important to understand each pont of view on its own terms.

      2) The much more important issue is partial versus general equilibrium. I’ve already typed enough and it’s late here, and it takes longer to address this one — but the quick answer is that you should read the complete works of Arnold Harberger, where you’ll find thoughtful responses to these concerns.

      • 1) As is usually the case, you explain an argument better in one short post than others (myself included) can make in a whole book. Your point makes complete sense.

        However, (there’s always a however) that is not the way welfare economics has been explained to me. Extrapolating from my experience, I assume many students have not had it explained your way either.

        For example, in MWG on page 81, if you have it nearby, the authors derive a money metric indirect utility function and use it as a means to measure welfare changes in dollars. The link always goes back to the utility function. In the next chapter on aggregating demand, the structure is the same. I read it and my professors teach it under the pretense that money measures utility.

        I’m not saying you agree with this and my interpretation of MWG might be wrong, but students do learn from MWG and interpret it the same way.

        If you have poked around here, you will see I’m doing a little journey through different approaches to price theory. One of my common complaints about “modern” price theory or micro, via MWG and it’s derivatives, is that they forget the assumptions, reasoning, or interpretation that underlie their analysis. You clearly have not forgotten the reason for welfare analysis.

        2) My other point of this post, which wasn’t clear, was to explain that general equilibrium could allow for a better connection between welfare analysis and the idea of opportunity cost. I may be completely wrong, but that’s my impression.

        Thanks for the recommendation. I’ve started to read Harberger. I’ll respond when I’ve gone through more thoroughly. In the article I read this morning from the JEL, he compares welfare analysis to national accounting. He seems to be setting a low bar for the quality of welfare analysis. Of course, his point is that welfare analysis, as he understands it, is the best available. It may be, but that doesn’t mean we shouldn’t search for better understandings of welfare. That is my goal, although I don’t think a grad student will move beyond Harberger, but I need to start somewhere.

    3. “If you calculate with utils, you’ll say that the tree comes down, but the right answer, according to welfare analysis is that the tree should stand. And here’s why: It’s crazy to impose a $50,000 cost on Bill in order to create a $10 benefit for me, when you could instead impose a $40,000 cost on Bill and create a $40,000 benefit for me, simply by transferring some cash. The whole point of welfare analysis is that whenever you decrease the total surplus, you’ve missed an opportunity to do something else that *everyone* prefers.”

      Aren’t there a couple of sneaky assumptions here.

      1. Even after the $40,000 transfer, we will still be in a position to increase overall welfare by getting Bill to know his tree down.

      2. Following on from this, if I recall my MWG, there is an assumption that all welfare enhancing transfers have already taken place. Thus in the world of economic theory there is no option to transfer cash anyway, since if there was, it would already be done.

      This is one of the sneakiest parts of economics which often leads to analysis that assumes away distributional concerns. In MWG go to p117 and you find this comment when describing the idea of the social welfare function.

      “Let us now hypothesise that there is a process, a benevolent central authority perhaps, that, for any given prices p and aggregate wealth w, redistributes wealth in order to maximise social welfare.”

      They then present the maximisation equation and continue on to show that under that condition they can invoke the representative consumer and aggregate utils 1:1 with dollars.

      If you have an objective read of MWG you would come away thinking the most obvious welfare enhancing policy is redistribution of wealth from the richest to poorest, and that this should deb the priority policy for an economist to support.

      3. If Bill and his neighbours income are the same, then their util:$ ratio would be more approximately equal and then Bill should bring down his tree.

      Our faith in our welfare analysis is thus restored.

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