econ 135 fall08 lecture3

econ 135 fall08 lecture3 - Urban Economics Lecture 3 How...

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1 Urban Economics Lecture 3 How are activities arranged within cities? Land rent versus land value (defn.): land rent is the price of using land for a year; land value is the value at which the land sells. Land rent is a flow; land value is a stock. Can translate between the two using present value, the value of land is the discounted present value of future rents. PV = value of land = .. . 3 ) 1 ( 2 ) 1 ( ) 1 ( + + + + + + r R r R r R ... = r R / where r is the discount rate.
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2 So if rent is $1000/mo and the discount rate is .03, then the value of land is (12)($1,000)/.03 = $396,000. Since land rent and land value are related by the discount rate, when we know one we can compute the other. Question: if you own your own house, who is the renter? Note: we’ll make this model more realistic when we talk about housing.
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3 Even though this is an urban economics course, let’s consider a rural example. What factors affect the value of land/rent on land for rural land? For farmland, the land’s fertility (how much of particular crops an acre can produce). This depends on whether the land is irrigated. For farmland, the distance/cost of transporting crops to market. (what about the cost of transporting inputs such as seed and fertilizer?) The technology of growing any particular crop—how much seed, fertilizer, water and time on a tractor are applied to each acre of farmland. Assume initially that the technology is fixed. Potential renters are willing to pay the amount of rent that allows them to make zero profit, but no more. Profit = revenue minus total costs, so maximum rent = profit. This assumes that there is competition in the land/farming market and the land is rented to the highest bidder.
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4 Suppose all farmers grow cotton and they sell it in Ames, IA. All the land around Ames is identical in terms of fertility. How much profit do cotton-farmers make per acre? Profit/acre R tdQ C PQ - - - = where P = price of cotton/bale (fixed by the national market for cotton) Q = output in bales per acre of cotton around Ames R = rent/acre C = cost of growing an acre of cotton around Ames t = cost/mile of transporting a bale of cotton (assume straight line travel from farm to Ames). d = distance from farm to Ames Assume that farmers bid up the rent on farmland to the point where profit = 0 for all farmers. Then solve for the amount of rent that farmers offer for land (the bid rent function): tdQ C PQ R - - =
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5 [Question: What do economists mean by zero profit?] Graph this with d on the horizontal axis. It’s a linear function (straight line) that falls as distance increases. So rent on land adjusts to fully compensate farmers for transport costs! Question: How large is the area around Ames that is devoted to farming? The edge of the farming area occurs where R = 0. Now suppose some flower farmers think about locating in Ames.
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econ 135 fall08 lecture3 - Urban Economics Lecture 3 How...

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