1. Introduction to Land Rent © Allen C. Goodman, 2006

2. 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?

3. 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

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

5. 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.

6. Fig. 7.1 - Fertility and Land Rent MC AC Corn Mkt.High Fert.Med. Fert.Low Fert. Rent $

7. Fig. 7.2 - Fertility and Land Rent MC AC Corn Mkt.High Fert.Med. Fert.Low Fert. Rent $

8. 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:

9. Land Rent and Accessibility  = PQ - C - tQu - R So, if we have perfect competition, what happens to profits  ? They go to zero! So: 0 = PQ - C - tQu - R, or: R = PQ - C - tQu

10. 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.

11. 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

12. 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.

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

14. 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.