Can we compare utility between people? Is it linear?

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Question: 

I'm having trouble understanding something pretty basic about utility: can we compare utility between people? Is it linear? Is it a useful ruler?

Imagine two trades. The first is between a millionaire and a barista at Starbucks. The millionaire pays $4 for a latte. The producer surplus is $4 and the millionaire's consumer surplus is $0, because he's just not that into coffee. Now imagine a second trade between a pauper and the grocery store. The pauper pays the grocery store $3 for some rice which he will use to halt his near-starvation. The grocer's producer surplus is $3, and because the pauper has only exactly $3 (and is therefore only willing and able to make a trade for a maximum of $3), the pauper's consumer surplus is $0. There are no externalities: the hunger isn't going to make the pauper less efficient at work and he is not going to die of starvation, there's nothing wrong with the global supply chain of coffee in this world, and there are no witnesses who might benefit from some weird intangible altruistic benefits or something like that.

If you had to wave a magic wand and make one of these trades impossible (for example, by making either the millionaire or the pauper forget his wallet right before the store closes), which would you choose to preserve to maximize utility in the economy?

My (very limited) understanding of classical economics is that $4>$3, so the latte should be preserved. This strikes me as completely ridiculous. I find it hard to believe that given the choice between a latte you don't want all that much and the extreme disutility of near-starvation, that anybody would choose the latte. I think a rational actor forced to weigh contradictory evidence (between a supply and demand graph that says $4>$3, and any empirical observation of the utility of lattes and disutility of near-starvation) will choose to preserve the rice trade.

Do I have this wrong? Am I mistaken as to what an actual economist would argue here?

If utility isn't exactly equal and linear for everybody, how can we make decisions like "should we tax group A to pay for a service for group B?" If utility is irregular, is it predictably irregular? Do we over-measure the utility of the rich and under-measure the utility of the poor?

I'm fascinated by these problems, and I'm looking for good sources to learn more. Can you point me in a good direction?

Answer: 

The concept of utility was introduced to represent decision makers' ordinal preferences. That is, if I like alternative A better than alternative B, I can represent this ordinal preference by assigning utility values to alternative A and alternative B. This representation is not unique. I can assign infinitely many different pairs of values to alternative A and B to represent my ordinal preference. The important takeaway from this is that numerical values attached to alternatives to rank them by themselves do not contain important information. In this regard, comparing utilities of different people would be meaningless if utility values just reflect how individuals rank alternatives. Note also that utility does not have a unit. 

One reason for the introduction of utility representation is to solve decision makers' optimization problems by using mathematical tools. However, an optimization problem is still solvable if we know every binary comparison a decision maker makes. The use of utility just makes it more convenient to solve. In consumer theory, solving a consumer's optimization problem gives us the optimal commodity bundle(s) she would like to purchase at given prices. When we characterize optimal bundles as a function of prices, we call it demand. If there are multiple individuals in the society, we can obtain aggregate demand as a function of prices. Similarly, solving producers' optimization problems gives us their marginal cost functions, and their supply. Aggregate supply can be found by summing individual firms' supply. Aggregate supply and demand give us an equilibrium from which we can compute consumer and producer surpluses. Both consumer and producer surpluses are dollar amounts (you can think it as price x quantity). 

In the scenario you described, you compare two interactions with respect to total surplus. The pauper's utility from consuming rice can be used to compare rice consumption with her other alternatives. Similarly, the millionaire's utility from latte consumption can be compared to other alternatives she might have had. Therefore, total surplus comparison between the two scenarios cannot be used to make utility comparison across individuals. 

Answered by:
Dr. Bertan Turhan
Assistant Professor
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Last updated on April 5, 2021