Determinants of landowner income    (for APEC 460)             by Prof. Kilkenny       

 

The income (a flow of money per period) that the owner of a parcel of land obtains is a pure rent.  

Rent on a parcel of land reflects (1) its current use value and (2) its asset value.

 

(1)   Current use value:  The Bid Rent function:

 

Current use value reflects a parcel’s productivity (see Ricardo) and its location (see vonThunen or Alonso).

 

The portion of rent due to the value of a parcel in farm, business, or residential use reflects the productivity of the soil (denoted Q for output per unit land), the proximity of the parcel to the market, or the proximity of the parcel to jobs or shopping.   With d denoting distance between the parcel and the destination, P the output’s price at the destination, C the average production cost,  and t the cost per unit output per unit distance, we can express land rent (R) as follows.   Freedom of entry (into farming, the industry, or the neighborhood) drives the farm or industry product (output) price down, costs of production up, or land rents up --- until profits in the activity are zero: 

           

            Profit = PQ – CQ – tdQ –R = 0.    Rearrange this equation to solve for R :

 

… R = (P-C)Q – tdQ.   This equation is called the bid rent function .

 

The bid rent function provides a static measure of the flow value of parcels at different distances from the market during one period.

Graphing it:

 

 

 

 

 

 

 

 

 

 

 

The bid rent function formalizes that land rents are higher where

            value-added is higher, or

            higher prices are paid for output (or more subsidies are collected),

            there is higher productivity,

            the costs of production are lower (or larger input subsidies are provided); and

            transport costs are lower, or

            the parcel is closer to the market. 

 

Consider the return to arable land in the U.S. Midwest.  89% of the total land in the state of Iowa, for example, is in farms.  So, Iowa provides a good test case for the theory of land rent determination.  The source of the data used below is Iowa State University Extension (2001) “Cash Rental Rates for Iowa.” 

 

The choropleth map below is darker in counties where farm land rents are relatively high, and lighter where land rents are low. 

In fact, farm land rents are higher in counties close to the Mississippi River (the destination), for example Clinton and Scott counties on the East.  Counties that have a lot of food and kindred processing activity (Carroll, Black Hawk, Keokuk Counties) are also destination counties, so rents are higher there too.  The lowest rental rates are found where the soil is less productive, which is south central Iowa.  Yields are only 117 bu/acre even on the best acres in Wayne county, compared to 145 bu/acre or more in Ida, Buena Vista, or Sioux counties (in the Northeast).   These real world data is just what we would predict using bid rent theory.  

 

(2) Land’s value as a asset

 

An asset is a storage of value: an asset offers either a stream of flow values over time or a final value at a later date (or both).   The asset value of a land parcel consists of its current rental value (R) plus expected future capital gains.  

 A capital gain is the difference between the sale price (VT) and the purchase price (V0):                      capital gain  = (VT-V0).

The capital gain rate is the percentage increment of the future sale price over the purchase price:   (VT-V0)/V0  ,   or equivalently:  (VT/V0)  - 1.

 

Land is an asset that either provides the owner a flow of net revenues (Rents), or, saves them from having to pay rents to someone else.  In addition, it may also offer a capital gain.

 

Details: if no-one expects the flow value of a parcel to increase (or decrease) over time, then the price someone would be willing to pay for a parcel reflects just the stream of rents over time:

DPV of rents, V = R + R/(1+i) + R/(1+i)2…= ∑t R/(1+i)t.

Because people can choose among various assets (saving accounts, bonds, stocks), and they’ll choose the assets that give them the best expected rates of return, given the riskiness and the liquidity (ease of conversion back into cash) of the alternatives, the expected rate of return “eRoR” on all assets move together over time.  Measure the rate of return all assets have in common by the interest rate “i”.  Rearrange the above equation, and use this interest rate to determine the discounted present value of current plus future rents.  Furthermore, given the mathematical fact that ∑t 1/(1+i)t  = 1/i for t approaching infinity,  the equation above simplifies to show that

 

the current value of a parcel that offers an unchanging flow rents over time is    V = R/i.     In the case of constant flow value over time, a parcel’s price, V, is higher for higher rent parcels and lower for lower rent parcels.  So:  land prices reflect the same things that land rents reflect. 

 

But if people expect the flow value of a parcel to rise later, then the price of the parcel will be expected to raise later too.  If the parcel’s future price is expected to be higher, then the owner not only earns rents but also expects capital gains on the parcel.  As with all assets, this expected future gain will cause the parcel’s value to rise today.  (Also, a capital loss expected in the future will cause the asset’s price to fall today.)

 

Taking into account expected capital gains eVt+1, the current value of a parcel is:  Vt  =  (R+eVt+1)/(1+i).

 

Note that rather than taking the trouble to calculate the exact discounted present value of the stream of changing future rents, which would necessarily entail making many guesses (“guesstimates”) about expected future rents and expected future capital gains, we rely simply on one guess.  We assume that the expected future price, eVt+1, reflects all of the expected future changes in flow values.    It won’t be exact, because neither buyers nor sellers can have perfect information about the future.  But we can’t find better current information than that.  The information about what a parcel or asset will really be worth later won’t be revealed to anyone until later.

 

The formula above makes it clear that the price of land as an asset also reflects expected future rents and opportunity cost of other assets (the target expected rate of return, eRoR, or i), infinitely into the future. 

The green choropleth map here shows how Iowa farmland values or prices varied across counties in 2000.

 

Farm land values reflect the rental rates with a few exceptions—they are highest where there are more opportunities to convert farm land to urban uses (Story, Grundy, Cedar, and Scott counties).  Those landowners expect capital gains.

 

Our theory of land rent is confirmed again.

By the same token, we often observe very low-rent uses of land right next to very high rent uses.  How come?  Because of capital gains. 

 

The current, one period expected rate of return (eRoR) to the parcel owner is comprised of the flow value (the rental rate: R/V) plus the capital gain rate:

            eRoR =  R/Vt       +   eVt+1/Vt - 1        

 

Given that asset holders treat all assets as substitutes, we can replace eRoR  = i in that formula, and rearrange.  This gives us another useful equation:

R = Vt(1+i)  - eVt+1 

which says that the rent a landlord will charge on a parcel today reflects the current parcel use value, the expected future value of the parcel (which reflects all expected future rents), and the economy wide rate of return on other assets.  It also makes it clear that a landlord will charge a lower rent on parcels that offer newly expected future capital gains. 

 

This expression for R provides important insights into the phenomenon of uneven urban land use such as idle land downtown.  The downtown landlord who rents his real estate, for example, to a used-car lot operator is willing to accept low rent today because of the higher capital gain he expects later. 

 

…Similarly, people buy stocks that don’t even pay dividends today if they believe they can sell the stock later for a capital gain.  Capital gains will not materialize, however, on land or stock or any other asset that does not, ultimately, generate revenues in excess of costs. (Which is why the NASDAQ equity index tanked when people finally realized that many IT companies were not profitable and probably never would be.)