Introduction to Land Rent © Allen C. Goodman, 2006

Key Idea Land rents adjust to equalize either utility or profits across all parcels! Desirable land  higher fertility, or higher utility. The land owner will reap the benefits in higher rents. Users will not benefit from being on one parcel or another!

We’ve talked about density It’s important to be near a transportation hub. It will get more crowded near the hub. What will happened to ratio of (labor/land)? What will happen to ratio of (capital/land)? What might we guess will happen to rents for the land?

Values and Rents Market Value = Present value of rental income. Look at a piece of land that generates $20 of net income per year. PV =  R/(1 + interest rate) t PV = 20/(1 + r) + 20/(1+r) 2 + … + 20/(1+r) n Paid at the end of the year

Values and Rents PV = 20/(1 + r) + 20/(1+r) 2 + … + 20/(1+r) n (1) (1+r) PV = /(1+r) + … + 20/(1+r) n-1 (2) Subtract (2) - (1) (1+r) PV - PV = /(1+r) n rPV = /(1+r) n As n gets very large the second term goes to 0, so: rPV = 20 PV = 20/r.

Land Rent and Fertility Fixed prices of inputs and outputs. Zero economic profit. Three types of land –high fertility –medium fertility –low fertility Land to highest bidder. Zero transport costs.

Fig Fertility and Land Rent MC AC Corn Mkt.High Fert.Med. Fert.Low Fert. Rent $

Fig Fertility and Land Rent MC AC Corn Mkt.High Fert.Med. Fert.Low Fert. Rent $

Land Rent and Accessibility Again, fixed prices. Central mktplace, costs t/mile to get there. Distance to mktplace = u. Competitive markets All land is equally fertile, so production costs are the same everywhere. A little algebra:

Land Rent and Accessibility Profit = Total Revenue – Other Cost – Transp Costs - Rent  = PQ - C - tQu - R If we have perfect competition, what happens to profits  ? They go to zero! So: 0 = PQ - C - tQu - R, or: R = PQ - C - tQu

Land Rent and Accessibility R = PQ - C - tQu What happens to rents as distance increases? A> They fall. Why? An example -- Worksheet for Figure 7.3 Fill in some numbers.

Land Rent and Accessibility If we want to look at Rent/acre, we now have: RT = PQ - C - tQu What happens to rent/acre as distance increases? R = (PQ - C - tQu)/T

Flexible Production Distance Rent A farmer with fixed production methods faces a linear rent curve. Pick a point A, with a certain technology. If we move 1 mile further away, we’ll remain on the red rent curve. Since land is cheaper, here, if we can substitute it for labor or capital, we can make higher profits. Others can do the same, so the rent we’ll be bid UP.

Flexible Production Distance Rent Do the same going the other way. We get a convex land rent function.

Competing for Land Producers of Type 1 will have the highest bids for land, up to two miles away. Producers of Type 2 will have the highest bids for the land further away.