## Wednesday, March 5, 2008

### The Public Goods Problem and the Sellwood Bridge

One of the examples I often use in my intermediate microeconomics lectures to motivate the idea of public finance and public goods is an example of a bridge over which individuals with very different valuations of the bridge travel. The problem with public finance is this. Suppose only three people use the bridge, A, B and C, and they all cross it exactly twice a day. A gets \$500 benefit from it (and so would be willing to pay up to \$500 to use it), B \$250 and C \$200. Thus the total benefit to this hypothetical society from the existence of the bridge is \$950. Now suppose it costs \$900 to build it. Would it be a good thing for our little economy? Yes. Unequivocally. It would yield a net benefit of \$50.

So now, how do you pay for such a bridge? Suppose we assign the task to government and the government proposed an equal tax of \$300 per person which the citizens could vote on? The vote would fail because both B and C would oppose such a tax given that their benefits are lower than the tax. What about a fee for use. You could charge \$500 and only A would buy access which would not pay for the bridge. You could charge \$250 and both A and B would buy access and \$500 would be raised in revenue, still not enough to pay for it. At \$200 all three would buy access and \$600 would be raised. This is true, by the way, even if you charged it as a per use toll.

What if you asked for voluntary donations? Would A contribute \$500? No, if A knew B and C's valuation, A would know that \$450 is enough if the others contributed their full amounts. B would know that \$200 is enough and C would know that \$150 is enough and a total of \$850 would be raised. This is known in economics as the free rider problem. This seems a bit contrived in a three person example, so think about a large number of citizens and the free rider problem is clearer: no one individual feels as if their single contribution will make or break the project so many do not donate (think OPB).

So you see, it becomes a real challenge to provide a specific public good. This is why we must empower government to make the purchase for us and it is also why I am generally opposed to taxes for specific goods, the more you tie taxes to specific goods the harder it generally becomes to provide the socially optimal level.

This brings us to the Sellwood Bridge, seen above, which is well past its sell-by date and desperately needs replacement (hopefully before the current one falls into the Willamette). Public good problem? Sure, the local government is struggling trying to figure out how to pay for it. Free rider problem? Yes, again, some local governments are not cooperating on a fee plan. Then there is this letter to the Editor from Eric Fox in The Oregonian today:

Collect toll for new bridge

A toll would solve every problem and argument out there concerning the problems of the Sellwood Bridge. A toll would pay for a new bridge, provide money for future maintenance and repairs and reduce traffic through Sellwood. We could even build a beautiful landmark span (like the St. Johns Bridge) instead of am ugly utilitarian cement hulk. If a Clackamas County citizen or truck driver (truck tolls should be higher) does not want to pay, he can find another route. Only the people who use the bridge would pay for the bridge.

I hate to be a naysayer, but I don' t think this will work, partly because of the theoretical example above and partly because it is pretty easy to substitute other bridges for the Sellwood.

Finally, here is an interesting new wrinkle. I guess my dad, whose old condo (not in the building in the story but in the yellow one above) can be seen in the picture above, sold at the right time: a year and a half ago.

jessibeaucoup said...

\$250 plus \$250 equals \$500 not \$750...

Always here to help;).

Patrick Emerson said...

Ooops! Fixed...thanks!

Evan said...

Of course, it's harder to substitute for the Sellwood Bridge if you're a cyclist.

The nearest bike-friendly bridge (Hawthorne) is, I think, 4 to 5 miles away. If you're headed from Sellwood to Lewis and Clark, that's a big detour.

We could ask if cyclists would pay a toll, but that's more an academic question than a feasible plan.

jessibeaucoup said...

I hate the idea of a toll. Sometimes, as part of living in a society, we have to use our tax resouces to pay for things that we don't use but other do. Sometimes, as part of living in a society, other people's tax dollars are uesd for things that benefit us and not them. What's the big dealio?

Xerographica said...

To provide the socially optimal level you would just need to allow tax payers to vote with their taxes. It's all about opportunity cost.

Patrick Emerson said...

X:

Er...no. That is precisely the point of public goods - the free rider problem makes 'voting with your taxes ineffective.'

Xerographica said...

Patrick, how so?