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Diminishing Marginal Returns September 9, 2015

Posted by tomflesher in Micro, Models, Teaching.
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Close your eyes.

Well, finish reading the next paragraph first, and then close your eyes.

I am going to offer you unlimited access to something good, something useful, something tasty. That’s right – I’m going to let you have as big a bottle as you’d like of Sriracha. As long as you can carry it away, you can put as much Sriracha as you’d like on your plate of pad thai and I won’t look askance at you. No, I might even respect you. How much are you going to take?

Open your eyes.

The funny thing about that thought experiment is that everyone can picture how much they’d put on a plate of noodles. Some people might put none at all;1 others might put a little dab on the side, while still others, possibly economics professors who operate multiple blogs with self-deprecating titles, might put a truly ridiculous amount and allow the streets to run red with the blood of the non-rooster-sauces. Almost no one would ever take an unlimited amount of sauce.

That’s because, like most goods, Sriracha demonstrates diminishing marginal returns. That means that if Sriracha is meant to create tastiness, then for every extra drop of Sriracha, the tastiness increases, but the increase gets smaller. Mathematically, that means the slope is positive, but decreasing; that’s the same as saying the function has a positive first derivative and a negative second derivative. One common function used to model diminishing marginal returns is the natural log function, y = ln(x). If we assume that tastiness is logarithmic in grams of Sriracha, the graph might look like this:

SrirachaJust about any good demonstrates diminishing marginal returns, and at some point you’ll have enough of a good that its marginal benefit no longer exceeds its marginal cost.


1 Those people are called wimps.


When is a filibuster not a filibuster? December 7, 2012

Posted by tomflesher in Micro, Models, Teaching.
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A filibuster is a legislative technique where a lawmaker who is in the minority will block passage of the bill. Historically, that required talking continuously on the legislature floor, as that would prevent anyone else from doing anything. In the US Senate, a bill can be filibustered simply by declaring it so – the filibustering Senator doesn’t actually need to talk. The Senate is considering a rule change to move back to historical, “talking” filibusters. In either case, a filibuster can be broken by a 60-vote supermajority (called cloture), but a talking filibuster can also be broken by the filibustering Senator getting tired and quitting. What’s the economic difference between these two rules?

The fact is that talking imposes an extra cost on the filibustering party. When people are

The model:1

First, like all good economists, let’s make some simplifying assumptions. Say there are two parties, the Bears and the Bulls, and that there are 59 Bears and 41 Bulls. Assume that everyone votes strictly along party lines, so every vote comes out in favor of the Bears 59-41. That’s not enough for a 60% majority, so under the current system, the Bulls can filibuster every bill without stopping other legislation.

Parties aim to maximize their political capital, which is generated in two ways:

  • Passing bills. The more partisan a bill is, the more capital is generated. A bill that the entire country would agree to pass has zero partisanship; a bill only Bears would vote for has a very high partisanship. The minority party generates goodwill based on voting for bills, but it decreases when the bills are more partisan.
  • Public perception (goodwill). Filibustering leads to a negative public perception. This is directly related to how partisan a bill is – filibustering a totally nonpartisan bill (discount bus fares for war widows) would lead to a highly negative perception, but filibustering a very contentious bill would be offset. Similarly, a filibuster stops all business, so the longer it goes on, the angrier people get.

The Bulls’ capital generation would look like this, with the “talking filibuster” term last, P=Partisanship and D = Days spent filibustering:

C = - P^2+ 41*P - \frac{1}{P}*D^2

Under the current system, days spent filibustering is 0, since nobody actually has to filibuster. That is, the marginal cost of filibustering a bill is 0. If a bill passes, the Bulls generate 41 political capital per unit of partisanship for voting, but lose some capital for losing the vote. If a bill has Partisanship of 20.5, then the Bulls are indifferent between filibustering and allowing the vote; anything more partisan will definitely be filibustered, and anything less partisan will be voted on.

If talking filibusters are required, though, the whole thing gets much more complicated. Adding a marginal cost for being on TV filibustering makes the minority party far less likely to filibuster. The marginal political capital generated for filibustering for one day is

MCapital = -2*P + 41 + \frac{1}{P^2}

The Bulls are indifferent between filibustering and allowing the vote when Partisanship is about 20.5012. That’s just what we’d expect – that it takes a more contentious bill to justify a talking filibuster than a silent filibuster. Then, let’s take a look at a two-day filibuster:

MCapital = -2*P + 41 + \frac{4}{P^2}

A slightly longer filibuster requires a slightly more controversial bill, requiring Partisanship to be 20.5048. Finally, let’s take a look at a 90-day (3-month) filibuster:

MCapital = -2*P + 41 + \frac{8100}{P^2}

That would require a bill of partisanship 26.338. The model displays the expected features: that it takes a more contentious bill to merit a filibuster at all, and longer filibusters require much more contentious bills. If we raise the costs of doing something, it becomes used less often.

1 As far as I know, this isn’t stolen from anyone, but if it’s similar to one currently in the literature please let me know so I can do some reading and properly credit the inventor.