There is a world with just three farmers; one makes wheat, two makes apples. Theirs is a barter economy with no saving – all income (ie, all the apples and bread) are consumed between each harvest. Since there is no money, each farmer’s demand curve is another’s supply curve.

Each farmer produces 10 units, so the market as a whole produces 20 units of apples and 10 units of wheat. Here is each farmer’s demand curve:

Apple Farmer 1 (let’s call him Splitty) wants to consume half his own production and sell the rest at any price. Therefore his demand curve is:

Q = X/2P where X = production, so in this case Q = 10/2P = 5/P.

Apple Farmer 2 (let’s call him Carby) really wants wheat. He will try to get three units; failing that, he will get as many as his apples can by. Therefore his demand curve is:

Q = 3 ↔ (X-3P>0); else Q = X/P, so in this case Q = 3 ↔ (10-3P>0); else Q = 10/P

The Wheat Farmer (let’s call him Hungry), on the other hand, doesn’t want a certain amount of apples or wheat as much as he simply wants as much as possible, subject to certain diminishing marginal utility; therefore, he is willing to part with more wheat in proportion to the number of apples he can get for each unit. His demand curve looks like this:

Q = 1/P

From here forwards, let’s look at the market from an apple-demand/wheat-supply perspective. Therefore, the market demand curve is the sum of the apple farmers, Splitty and Carby, and the market supply curve is P = Q. Some simple algebra tells us the market price is √15, which means Hungry parts with 3.87 units of wheat in exchange for 5 units of apples from Splitty and 10 units of apples from Carby.

Now, a great calamity happens – but to whom? A quantum event happens, splitting our nice universe into parallel universes:

• In World-1, an infestation of apple maggots cuts Splitty’s harvest in half.
• In World-2, an infestation of apple maggots cuts Carby’s harvest in half.

What happens to our apple-wheat market?

• In World-1, Splitty’s demand curve shifts leftward to Q = 5/2P.
• In World-2, Carby’s demand curve shifts leftward to Q = 3 ↔ (5-3P>0); else Q = 5/P.

Hungry the wheat farmer still produces the same amount of wheat, and still wants apples in the same proportion to their price. What happens? Again, some simple algebra, and:

• In World-1, the price is now √12.5, with Hungry parting with 3.54 units of wheat in exchange for 2.5 units of apples from Splitty and 10 apples from Carby.
• In World-2, the price is now √10, with Hungry parting with 3.16 units of wheat in exchange for 5 units of apples each from Hungry and Splitty.

Did you see what happened there? In both World-1 and World-2, the economy as a whole produces 10 units of wheat and 15 units of apples; but in each case the post-trade equilibrium is different because different initial distributions of resources were converted via differing inherent preferences into different market demands which led to different prices.

In evaluating the social costs and benefits of public policy, our standard methodologies are inherently biased towards market prices, and with good reason – they are known, transparent, and based on revealed preferences. Those costs and benefits that are not precisely priced by the market (such as the health costs of air pollution or unhealthy foods) are imputed market prices via a combination of methods to determine “willingness to pay” as a proxy for a market price.

Many people are skeptical of such methods because they believe it is impossible or improper to impute prices onto certain things, such as a human life or or the health of the environment. Beyond this, though, there should be an additional layer of skepticism – willingness to pay, even that willingness as expressed through market prices, is inseperable from ability to pay. The pre-existing distribution of resources determines market prices even in perfectly competitive markets as long as there is no systematic correlation between the distribution of preferences and the distribution of resources. In our example, we showed a transition from an initial state into two seperate worlds struck by random calamity; but what if the two worlds were instead determined by which apple farmer had a productivity-doubling machine? And what if that farmer had that machine not because they invented it, but because they inhereted it? In that case, the difference in pre- and post-trading distribution of resources (and thus the market price) between World-1 and World-2 would be driven solely by which farmer had inhereted the machine.

Obviously, our modern economies, with money, saving, and capital, are vastly more complex than the simple model used above. But the lesson should still hold – and it should make us skeptical (though not entirely averse) of the utility of using market prices to determine social costs and benefits.