The Pink Cupcake Loving Economists

Quantitative Finance Level pending

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 \(\$0\). On the other hand, Friedman and Keynes have \(\$10\) each. The table below shows the value they each place on one cupcake.

NameValue of 1 Pink Cupcake

Marx loves cupcakes but believes that they're tools of the proletariat, so values them at \(\$0\) on political grounds.

Assuming that they do not value having a second cupcake, that they value a second cupcake at \(\$0\) 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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