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Wednesday, December 16, 2009

What's the price elasticity of college in Pittsburgh?

Perhaps that is a question that the Mayor of Pittsburgh should ask as they seek to increase tuition by adding a 1% tuition tax on all those who attend college in the city. From this story:
The mayor of Pittsburgh will push for a first-of-its-kind tax on student tuition this week after a special meeting with the city's universities failed to resolve the dispute over the levy.

Pittsburgh Mayor Luke Ravenstahl met Monday with college officials to discuss other ways to remedy the city's pension woes. But the meeting made little progress.

Ravenstahl had set a Monday deadline for universities and other tax-exempt nonprofits to agree to pay $5 million annually to the city.

Without an agreement, Ravenstahl will ask City Council to vote on the 1 percent tuition tax, which would be the first of its kind in the nation. The schools say they are willing to negotiate if the tax is taken off the table.

A vote could come Wednesday.

What are the potential unintended consequences of a tuition tax at the city level?

One of my first papers, published with co-author Trisha Bezmen, estimated the price elasticity of demand for public college (in 1994) to be very low (-0.018). However, our sample was of 226 public schools. If the elasticity of supply for public schools is 0.5 (indicating that a one percent increase in tuition yields a 1/2 percent increase in available student positions on campus) and we make the heroic assumption that all schools are the same, then if the entire country is the market then the individual school's price elasticity of demand can be calculated as

e = NxE - (N-1)u

where e is the individual school's price elasticity of demand, N is the number of firms/schools in the market, E is the market price elasticity of demand, and u is the price elasticity of supply.

Using the values mentioned, the individual school's price elasticity of demand would be e = 226*(-0.018) - 225*.5 = -116.56. In other words, the demand for the individual schools in Pittsburgh is likely much higher than the good Mayor supposes.

On the other hand, perhaps the demands for Pitt and Carnegie-Mellon are actually very insensitive to price changes, in which case the tax will simply be a wealth transfer from students (or those who fund them, which could be you and me if they take Pell grants or other financial aid) to the city.

If the industry elasticity is -0.018 and

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