There was a recent Planet Money Podcast episode that includes a fun exercise. An NPR employee produces a dozen chicken eggs and wants to sell them at cost to another employee for $5. That’s the setup. How does the employee decide who should receive the eggs? Clearly, the price mechanism won’t work since the price is fixed. A lottery is also not allowed. The egg recipient could engage in arbitrage, reselling the eggs for a higher price. But that’s not very likely and would be socially awkward. The egg producer wants to make someone happy. Who would he make the happiest?
That’s the challenge that the Planet Money team tries to solve.
First, they started with a survey. Rather than asking coworkers to rank a long list of things that includes eggs, the survey adopts a more robust method of pairwise comparisons. Do you prefer toast vs eggs? Eggs vs oatmeal? Toast vs oatmeal? and so on. One problem that they encounter, however, is that there is a lot of diversity among preparations methods. My oatmeal is better than my eggs. But my brother’s oatmeal is not. As it turns out, there is not a standard quality of prepared oatmeal and prepared eggs. So the survey is a flop.
Then they consult an economist. They decide to try to measure “willingness to pay”, which is an economic concept that identifies the maximum that a person could pay for something without becoming worse off. They couldn’t really ask the coworkers what their WTP is. People are social creatures and have many reasons to lie, mislead, signal, and to simply not know. Since someone’s WTP reflects preferences and values, we need a way to solicit the true preference while avoiding lies and most mistakes. Here’s how the economist suggested that they reveal the coworker preferences.
- Step 1: Tell the coworker these rules.
- Step 2: Coworker reports their WTP for a single egg in dollars
- Step 3: A random price will be chosen by a machine. If the price is above the self-reported WTP, the coworker is not allowed to buy the egg. If the price is below the WTP, then the coworker must buy the egg at the random price.
The idea is as follows.
If the self-reported WTP is correct, then the coworker is happy no matter what the price is. They wouldn’t want to buy at the higher price, and they are eager to buy at the lower price. If the reported WTP is below the true WTP, then the random price could fall between them and the coworker will have lost the ability to buy at a price that would have made them better off. If the reported WTP is above the true WTP, then the coworker might find themselves paying a higher price than reflects their value of the egg. So, the dominant strategy is to tell the truth and to be right about it.
The hosts of planet money celebrate their conclusion and the power of economics to identify the best coworker to buy the $5 dozen of eggs. The episode ends and we all had fun and learned something along the way.
But, a subtlety lurks in the method.
The problem is that people consider their opportunity cost. In this case, the opportunity cost includes purchasing comparable eggs at the market price. We can be more liberal and add the saved transaction cost of going down an extra aisle during their next grocery store visit. So, the method above yields the coworker’s expected market price plus saved transaction costs and *not* the willingness to pay in isolation of the prevailing market prices.
Is there trickery afoot? Not necessarily. WTP is calculated when all related prices are given. If one of those goods is a perfect substitute (which we’re pretty close to in this circumstance), then we should expect people to desire a corner solution: they want to spend their ‘egg money’ entirely on the coworker eggs or entirely on the market eggs. If the marginal rate of substitution is one-to-one, then the incentive for coworkers is to report the market price for the perfect substitute and *not* the maximum that one would be willing to pay for eggs in some intrinsic sense. The game works if a coworker’s WTP is below the market price. But there is no incentive to report a WTP that is above the market price, since being forced to pay a randomly generated price higher than the market price would make the coworker worse off.
In other words, our WTP is fundamentally related to our preference AND to the other prices that characterize the market. WTP is not intrinsic only to preferences, but also depends on our other opportunities to purchase. This insight is somewhat muddled by simple supply and demand in partial equilibrium analysis since we just take the other prices as ‘given’. We often forget those givens. The relevance of other prices is clear as day if we consider general equilibrium.
Go listen to the podcast yourself. It’s fun!
https://podcasts.apple.com/us/podcast/planet-money/id290783428?i=1000704052517
Economist Writing Every Day 