Class 11 — Financial incentives

Thursday, October 1

This recap comes from a recording of class, transcribed with Whisper and summarized with Claude, with a light edit from me. It’s meant as a convenience rather than a careful document, so the phrasing will sometimes be a little off. If something here looks wrong, please tell me and I’ll fix it.

What we covered

The model behind physician agency. Why we think financial incentives change treatment, then a model where the physician sets both price and quantity, a numerical example, and finally the case where the price is fixed administratively.

Key points

• Agency isn’t special to medicine. It comes up whenever you hand a decision to someone who knows more than you do, which is why contracts and agency problems travel together in economics. The claim here is narrow. If you pay more for some things than others, then on average more of those things get done, and nothing about anyone behaving badly is required.
• We believe that because of a research design rather than a pattern in the data. Medicare redefined its geographic payment regions in the late 1990s, so a physician’s payment formula changed while the physician changed nothing, not their location, not their practice, not their patients. Services shifted toward the ones that became better paid. The credibility comes from the change being in how the regions were drawn rather than in anything about the services themselves.
• The entire result comes from one gap. The physician decides based on their own marginal cost, while you decide based on the price you pay. Since price exceeds cost, the physician pushes care past where you would have stopped. Notice what isn’t needed. Both sides know the same benefit function, so there’s no information problem in this model at all.
• Past your own optimum, each additional unit has marginal benefit below price. Net benefit that would have been yours becomes profit instead, and the only thing that stops the process is your outside option, the point where you’d walk away.
• Fixed prices reverse the intuition, and this is the part worth being careful about. When the price is set administratively, cutting it increases the amount of care. It isn’t that lower prices raise demand. It’s that the constraint now has slack, so the physician can treat more before you’d walk away. Cutting fees to save money changes the quantity of care at the same time, and the savings are smaller than what you’d get by holding quantity fixed.

Worth knowing for the exam

Show your steps. If an answer is right, I don’t care how you got there, but if it’s wrong, I can’t tell a rushed algebra slip from not knowing the method unless the work is there.

This is also why the homework no longer has any theory on it. If I assign a derivation to do at home and ask you not to use AI, I can’t enforce that, and if you do use it you get a perfect answer and learn nothing.

Before Tuesday

Work the in-class problem on the fixed-price case. We set it up but didn’t solve it, and it’s the same steps with the price handed to you.

Be comfortable with the product rule and the chain rule. Tuesday’s model is the same idea with more structure, so the derivative work is a little heavier.

Quiz Tuesday. Expect anything from this section of the course, including Tuesday’s own material, and expect it to be quick. You won’t be asked to solve a model from scratch.