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.

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.  

More on Water and Scarcity

Earlier, I posted a story about the increasing tension in water markets, especially in more arid regions.  I think it is safe to say that water allocation decisions will become a much more important policy topic in the years to come.

On his New York Times blog titled "Economix," David Leonhardt posted (May 3, 2011) an interview with Charles Fishman about how we have treated water allocation in the past and, more importantly, the implications of those policies on usage patterns today and going forward.

http://goo.gl/UnEPt

The interview is quite revealing.  Currently, the average U.S. homeowner pays a monthly water bill of $34 and uses about 300 gallons of fresh water per day. That amounts to a price of about $.004 (4 tenths of a cent) per gallon.  As the column indicates, that is "free" water when compared to the $7.70 per gallon you pay when you buy a bottle of water at the Kwik-E-Mart.

Economic theory tells us that when something is under-priced, it will be inefficiently over-used.  To quote from the Leonhardt column:

"Free water — water so cheap you never think about cost when making water use decisions — is a silent disaster. When something is free, the message is: It’s unlimited.

Free water leads to constant waste and misallocation. Farmers and factory managers, hotels and gardeners never consider how much water they are using, and whether they are using it smartly — because the water bill itself sends no signal to be careful. (Half the water used by farmers worldwide is wasted.) There’s no incentive for efficiency."

Endangered Species and Markets

In an earlier post, I talked about the Great Hamster of Alsace. These hamsters thrive in fields of wheat and alfalfa.  Unfortunately for the hamsters, contemporary French farmers have switched to more profitable crops such as wine and corn.  These crops do not provide the shelter for the hamsters and the population of these creatures is plummeting.  In response, the French government is considering a policy to force farmers to return to the less lucrative uses of their land so that the hamsters will be protected.

If you are thinking that such interventions seem to be growing, you would be correct.  The Thursday April 21, 2011 edition of the New York Times carried the following story concerning U.S. experiences with endangered species.

http://goo.gl/Ce7fE

The Fish and Wildlife Service is so overwhelmed by the explosion in requests to add species to the endangered list that it has told Congress it has become paralyzed and unable to perform its tasks. Adding to the mounting problem is a concurrent explosion in litigation against the Fish and Wildlife Service for missing multiple deadlines in each application, deadlines written into the Endangered Species Act passed in 1973.

The groups filing these numerous requests for intervention are trying to be the voice for the unrepresented species.  They ask for government intervention to restrict market outcomes, arguing that the socially optimal outcome demands incorporating the costs imposed on these species (how these "costs" are measured is a different and very complex issue).   Just two weeks ago, the April 13, 2011 issue of the New York Times ran a story about the recent efforts in Congress to remove a species from the endangered list.

http://goo.gl/4LVHT

This is notable because it is the first time Congress has directly intervened on the endangered species list.  Environmental groups are alarmed at this "political" intervention.   But, as the amount of economic activity impacted by the endangered list grows, you can expect to see more and more such congressional scrutiny.

Scarcity and the Proper Pricing of Water

Recall the famous diamond-water paradox.  While water is absolutely essential to human life, no one really needs a diamond to survive.  Yet, diamonds are many times more highly valued than water.  Of course, this seeming paradox is explained by the supply side.  Water is plentiful and diamonds are scarce.

This article appeared in the April 12th, 2011 issue of New York Times.  The article discusses the growing demands for water, especially in the southwest.

http://goo.gl/IElbu

As we know, you cannot just wish away scarcity.  The existence of scarcity means that some system must be used for deciding allocation.  Normally, we rely on markets and prices to handle that.  But, there really are very few markets for water in the U.S.  The single biggest use of freshwater in the U.S. is irrigation and mostly in arid western states.  But the water for such uses is provided at no charge.  (Careful here:  people using irrigation do pay a price, but that is for access and delivery cost recovery.  The original grant of water into the irrigation system is generally not priced.)

The story indicates that water (more accurately, the scarcity of water) will become an increasingly important issue.  Of course, scarcity (and the handling of the resulting allocation problem) is not something new.  But, the combination of a very important item (water) facing an era where pricing will begin to reflect opportunity costs brings the potential for great disruptions in how we produce food as well as locate our communities.

The Fundamental Law of Demand

In considering the demand for, say, widgets, there are many things to consider.  And, we know that one of the key factors in the demand for widgets would be changes in prices of markets for goods economists call substitutes or complements.   Economic theory predicts that if the price of a substitute for widgets increases (decreases), the demand for widgets will increase (decrease).  And, of course, any changes in a complementary product's price will have the opposite effect on the demand for widgets.

The following story is from the March 29, 2011 business section of the New York Times.

http://goo.gl/SOK8T

Most travelers need to carry clothing and supplies to their destination, and there are substitute methods to accomplish this transport.  You can check your bag or you can take extra carry-on bags.  This story shows dramatically how the increase in the price of checking your bag has lead to a large increase in demand for a substitute to checking your bag: carry-ons.  And, if you were to read the story you would find examples of the negative externality effect of congestion.  Each person who increases his or her carry-ons is adding to an overall social cost of congestion, both at the TSA lines and in the nerve wracking boarding process where people try to fit bags seemingly twice their body size into the overhead compartments.

Pricing Assets In Perpetuity: the Case of Farmland

A recent article in The Progressive Farmer indicates that the price of farmland in the midwest is skyrocketing.

http://goo.gl/rjzIb

$11,000 per acre may seem to be pretty pricey for farmland. However, there is a way to understand the imputed market value of an acre of land.  First, recall that when we thought about the price of a share of stock of a company, we considered the present value (PV) of the long run stream of profits you could expect to earn as an owner of the company. Suppose you thought profits would be x0 this year, x1 next year, x2 the year after that, and so forth. The PV of this stream of returns over time out to time = T would be the sum of

PV = x0  +  x1/(1+r)  +  x2/((1+r)^2)  +  x3/((1+r)^3)  +  ...  +  xT/((1+r)^T)

Lets make things simple and assume for the moment that the returns in each period were some constant x (that is, we assume that x0 = x1 = x2 = x3 = ... = x).  Farmland is a special asset, one that is an "asset in perpetuity" since the owner can bequest it to her heirs, etc.  The good news is that we know for very large T, the equation simplifies to

   x/r

In other words, if you expected to earn $100 per year forever, and the interest rate was .05, then the PV of that infinite series would be $100/.05  =  $2000.  That is the same thing as saying that "the discounted stream of an annual series of $100 annuities would be comparable to $2000 in the bank today" which is the same thing as saying "if you gave me $2000 today and I put it in the bank at a guaranteed annual rate of 5% forever, I could continue to take $100 out on Jan 1 of each year, forever...."

So back to our farmland story.  The same story cited above indicates that owners of farmland can simply rent the land (this is called "cash rent") for as much as $450 per acre in McLean county.  This is pure profit to the owner; the renter pays this for the right to use the land and that same renter incurs all production costs on top of this land cost and then keeps any and all profits after selling the corn.

We know the price of land ($11,000) represents the present value of the long run stream of annual profits ($450 per year) you could earn by simply keeping the land in your ownership.  Or, the $11,000 per acre today is what it would take to compensate you for giving up the $450 per acre into perpetuity.  Does that make sense?  Lets check:

Since we know the formula is:   PV = x/r   then we are asking does   $11,000 = $450/r

To make that equation work, we would need an interest rate, r, equal to 4 percent.  Is that reasonable? Well, if you look at the interest rate on long term bonds today, you see that the rate on 20 year bonds is about 4.3% which makes the $11,000 number quite reasonable.