The Pink Cupcake Loving Economists
If there's one thing everyone knows about economists, it's that they love pink cupcakes. Somewhere, deep in the bowels of Brilliant University, four economists named Smith, Marx, Friedman, and Keynes have formed their own little free market. In this market, Smith and Marx each have 1 pink cupcake, and . On the other hand, Friedman and Keynes have each. The table below shows the value they each place on one cupcake.
| Name | Value of 1 Pink Cupcake |
| Smith | |
| Marx | |
| Friedman | |
| Keynes |
Marx loves cupcakes but believes that they're tools of the proletariat, so values them at on political grounds.
Assuming that they do not value having a second cupcake, that they value a second cupcake at and none want a second one, and that they cannot share or sell portions of the cupcake, which of these options is the Pareto efficient allocation of the cupcakes and dollars? (i.e. Which of these solutions Pareto dominates all the others?)
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There's a couple ways to solve this and a few ways can lead you astray. Again, as with all Pareto Efficient scenarios, it's important to remember that equity and fairness do no matter. And the question posses a hint - which allocation Pareto dominates the others?. It's helpful to lay this out as a chart and add Value (Number of Cupcakes × the value each has for a cupcake + the amount of dollars $ d they possess).
Initially:
Net Value = $ 2 6
One way to solve is to lay out each option in terms of this chart, and calculate net value each time.
But, a smart way to start on that approach is, thinking like an economist, is to ask which two people value cupcakes the most? In all likelihood, they are the ones that should end up with the two cupcakes. In this case that's Smith and Keynes. So let's start with the answer that lets Smith keep his pink cupcake and has Marx sell his to Keynes:
Net Value = $ 3 6
Next, we'd compare every answer to this one. This can be done, formally, by making a chart for each one. Or, more quickly:
- For the choice where Smith sells his cupcake to Keynes for $ 6 , Smith is just as good as he was in the above answer, but Keynes is worse off, he gives up $ 1 and Marx is worse off by $ 5 . So it's Pareto dominated by the above answer. (Net Value = $ 3 0 )
- Similarly, this is true for the choice where Smith sells his cupcake to Keynes for $ 6 AND Marx sells to Friedman for $ 5 , where Keynes is worse off, though Marx is back to being the same. (Net Value = $ 3 5 )
- And for the answer where Smith sells to Friedman for $ 7 AND Marx to Keynes for $ 6 both Smith and Marx are better off than the case above, but Friedman and Keynes are worse off. (Net Value = $ 3 5 .
In every case versus the correct answer, one economist is made worse off and the Net Value is lower than the correct answer, which means the above answer Pareto Dominates the others. Even though it'd be nicer for the two economists with cupcakes to share with the others.