Sunday, November 24, 2013

Assets in Perpetuity

As you know, our primary focus in the Econ 567 course has been understanding prices .  We know that prices are really just rationing devices.  All goods are "scarce" and therefore we need some allocation mechanism to ration these scarce goods.

In this post, lets look at how we price assets in perpetuity.  Imagine you got in your car and drove out into the country into prime Illinois farmland with the goal of buying an acre of corn ground.  Suppose you stop at a farm and ask the farmer how much profit he made on an acre of land.  He truthfully reveals "$200 is about the average".  Now,  if you ask him if you could buy the land from him for, say, $220, would he sell it?  Of course not.  While that appears to be better than the $200 profit, that profit is just one year's net.  The corn ground will turn a profit year after year.

In fact, the way the farmer would look at this is to compute the discounted present value (DPV) of a stream of profits over time.  We use DPV because we know that $100 today is worth less than $100 a year from now.  Indeed, when we compute Present Value we are simply asking "how much would $100 in, say, 1 year be worth today?"  Well, if you put $98.04 in the bank today, at 2% interest, it would be exactly $100 in 365 days.  We compute this by saying "$100 a year from now is equal to $100/(1+r) where r is the interest rate."  Likewise, the DPV of $100 in two years from now would be computed by dividing $100 by (1+r) for the second year and (1+r) again for the first year;  that is we compute this as ($100/(1+r)^2).  At an interest rate of 2%, this would be $96.12.  Said differently, if you put $96.12 in a bank today, earning 2% interest, it would be worth $100 exactly 2 years from now.

So, our farmer would compute the Present Value of keeping his land by estimating his profits in year 1, 2, 3, ... out to N with each year divided by (1+r)^t  where t is the year number.  This would be his estimate of what the long run stream of profits to this acre would be worth in today's values.

Now consider the problem of pricing shares of stock.  These pieces of paper, certificates of ownership of corporations, trade hands more than a billion times a day.  How are the prices of these shares determined? Watch this video.

Friday, February 1, 2013

Common Pool Resource Problems

Economists are fond of pointing out the attractive welfare outcomes of the perfectly competitive model. Of course, economists also concern themselves with analyzing various forms of market failure.  One easy example of a market failure is the monopoly outcome.   However, it is quite possible to find market failure in industries that look like they should be competitive but somehow end up with less than stellar welfare outcomes.

One such outcome is known as the Common Pool Resource problem.  It arises in situations where there is no market mechanism to exclude agents from accessing and utilizing a valuable resource.  To illustrate, consider a 1956 movie called Giant, set around the great oil boom in the East Texas oil fields.  (Giant was nominated for 10 Academy Awards including Best Picture, 2 Best Actor in a Leading Role nominations (James Dean and Rock Hudson), Best Director, etc.  It won just one, the Best Director.)  The James Dean character discovers oil on a small plot of land he owned in an area that was used exclusively as cattle range.  He built a derrick on his land and started making a great deal of money extracting and selling oil.

However, he only owned a small piece of land overtop a large LARGE reservoir of oil.  He went about acquiring more land, but lots of other people owned plots of land overtop other areas of this giant reservoir of oil.  And, they all started constructing their own derricks.  Think of the incentive.  The oil in the reservoir is finite; every gallon of oil your rival pulls out is one less gallon for you to extract.  So, not only do you want your derrick to run 24 by 7, you want to put as many derricks on your physical plot of land that you can;  the more pipes you can stick down into that oil reservoir, the more gallons of the fixed pool of oil will end up belonging to you.  In the case of the East Texas oil fields, it soon looked like this:

      (C) B. Anthony Steward/The National Geographic/Christie's Images

The problem arises because too many derricks are pumping out the oil too fast.  Geologists can show you the models that describe an optimal extraction rate, one that would use the natural pressure from surrounding aquifers to push the oil up in the cheapest manner.  By sticking thousands of straws down in the reservoir and sucking as hard as you can on your straw, the aquifers pushed in too rapidly, leaving vast quantities of oil stuck in hidden pools and fissures that were inaccessible.  This outcome was very inefficient.  This is the nature of Common Pool Resource problems and the resulting market failure.

Recently, the January 30, 2013 issue of the New York Times had an Op-Ed by Callum Roberts titled “Keep the Fishing Ban in New England.”  The article discusses a phenomenon similar to the oilfield disaster described above but occurring in the great fishing beds off the coast of New England.  Again, the common pool problem arose.  The sea was full of fish but if any one fisherman showed restraint in extracting fish, the other fishers would simply get a larger share of the finite pool of fish below the surface.  The result was over-fishing, just as the oilfield saw over-extraction of the oil. Every fishing firm had an incentive to fish with as many boats and as many nets as possible to get a larger share of the fish swimming below the surface.  The result was disastrous, as the stocks got dangerously low.

Policy makers have shown a willingness to intervene in market transactions when they feel that some group will be impacted by the transaction but that very same group does not have power to be heard in the negotiations.  For example, consider a housing developer offering a farmer on the edge of the community enough money that the farmer agrees to sell her cornfield to the developer.  This appears to be a very efficient and desirable transaction; both the buyer and the seller voluntarily agree to a transaction that brings both of them some gain. However, if it turns out that putting houses on the former cornfield would destroy the natural habitat of a small wetlands creature, policy makers might consider intervention to stop this form of urban sprawl.

Economists have noted the increasing pressure to have a third-party agency join in transactions in order to have “…someone who will speak for the XXX…”  where you can substitute the XXX with “spotted owl” or “grizzly bears” or whatever animal that is being disadvantaged as a result of a willing and voluntary transaction between two entities.  My favorite quote in the Times story on the New England fishing issue is:

Federal law delegated to the New England Fishery Management Council authority to manage the fishery from 3 miles to 200 miles off the coast, but the council didn’t see its job as speaking up for fish.

The author of the Op Ed very much wants the fish to be fairly represented as the Federal Government mulls opening up fishing areas that have closed for decades.  It is a debate we will continue to see more frequently, in various venues, moving forward.