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Geography/Planning 379 “Urban Growth & Development” Lecture 8: The Household Location Decision Indifference Curves

Geography/Planning 379 “Urban Growth & Development” Lecture 8: The Household Location Decision Indifference Curves Budget Lines The Effect of Commuting Costs The Equilibrium Solution “Real-World” Search Processes READING Optional: Thrall

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Geography/Planning 379 “Urban Growth & Development” Lecture 8: The Household Location Decision Indifference Curves

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  1. Geography/Planning 379 “Urban Growth & Development” Lecture 8: The Household Location Decision Indifference Curves Budget Lines The Effect of Commuting Costs The Equilibrium Solution “Real-World” Search Processes READING Optional: Thrall Print out and bring Practice Exams to class next time! Work ‘A’ (Spring 2007); We’ll go over ‘B’ (Fall 2007) “The greatest of all gifts is the power to estimate things at their true worth.” --La Rochefoucauld

  2. 1. Indifference Curves • Basic idea behind rent distribution in urban areas: Tradeoff between housing and transport costs -- Lower rents + higher transport costs farther out vs. higher rents +lower transport costs closer in • To see how this tradeoff works in detail, consider the residential choice decision of a single household • We’ll examine the rents they will be willing to pay in different parts of the city • Let’s look at the housing-choice decision faced by a typical American family – Mr. and Mrs. Yester…

  3. 1. Indifference Curves (Continued) • To study the Yester’s housing choice (where and how much to buy or rent) and their other consumption decisions need to know about their disposable income • Suppose Mr. Lester Yester is currently unemployed and sits home drinking beer and watching soap operas all day • Suppose Mrs. Polly Yester works at the XYZ Insurance Company downtown…

  4. 1. Indifference Curves (Continued) net (or disposable) $2.50 / hour after taxes • Her (and thus their joint) gross income: $10.00 / hour • She works: 8 hours / day; 5 days / week; 48 weeks / year • So, the Yester family’s monthly disposable income is: 2.50 x 8 x 5 x 48 / 12 = $400 / month • Assume there are only two things to spend this on: • Housing (H) • “Composite Consumer Good” (C)

  5. 1. Indifference Curves (Continued) • Following standard micro-economic theory (“the theory of the household”) there are tradeoffs between quantities of housing (H) and quantities of Composite Consumer Good (C) that provide equal satisfaction or utility • The Yesters are equally happy with any of these combinations, so we call the bundles of (H,C) corresponding to a given level of utility, U, an “indifference curve” Indifference curves are convex to the origin… What’s the opposite of convex? C A 50 Indifference curves cannot cross: cf. consumption bundles for points A and B Higher indifference curves correspond to higher utility: U3 > U2 > U1 40 30 B At Point A: U2 > U3But at Point B: U3 > U2Both of these cannot be true! U3 20 U2 10 U1 0 H 0 10 20 30 40 50 60

  6. 2. Budget Lines Let’s summarize what we’ve decided if they live in the center of the city, at distance x = 0 • How do the Yesters actually decide how much housing and how much composite consumer good to purchase? • Ideally, being good Americans, they want infinite amounts of both! • But they are constrained by their budget: $400 per month • If we know the prices of C and H (PC and PH) we can draw in a “budget line” to show feasible combinations they can purchase They should buy 20 units of C and 20 units of H:C*(0) = 20H*(0) = 20 U* = U1 PC(x) = $10 PH(0) = $10 PH(x) = ?(to be derived)… C If they blow all their income on Composite Consumer Good, how many units of C could they buy? 50 How about if they instead spend it all on housing? Budget Line for x = 0 40 Point of Tangency 30 What are theOPTIMAL amounts of C and H to buy? Want to obtain highest level of utility, subject to the budget constraint U3 20 But wouldn’t it be smarter to split purchases? Let’s draw in the entire budget line The Tangent Indifference Curve – Highest level of utility possible U2 10 FeasiblePurchases U* U1 0 H 0 10 20 30 40 50 60

  7. 2. Effect of Commuting Costs So how are they going to spend this $300 income on C and H? Now let’s summarize the results…C*(5) = 18 H*(5) = 24 U* = U1 Compared to if they lived in the center,the Yester’s buy less composite consumer good,but more units of housing at a lower price per unit… and end up being equally happy! So, if they choose to live 5 miles out what is now the Yester family’s disposable income? Let’s draw in the new budget line for x = 5 • Now let’s suppose the Yesters consider living farther out, say, 5 miles. So now x = 5 • Disposable income will be lower because of commuting costs • Suppose full costs of commuting are 50 cents / mile • What are monthly commuting costs? Monthly Income - Commuting Costs:$400 / month - $100 / month = $300 / month What if they spend all $300 on C? But we cannot ask the same question about H because we don’t knowPH(5): the price of housing 5 miles out $0.50 / mile x 5 miles / trip x 2 trips / day x 5 days / wk x 4 wks / month Budget Line for x = 5 = $100 / month C 50 Budget Line for x = 0 PC(x) = $10 40 Point of Tangency, x = 0 PH(0) = $10 30 Point of Tangency, x = 5 PH(5) = ?(to be derived)… $5 20 18 10 Equilibrium Assumption: Must be able to attain same utility level at all locations! U* PH(5) = 300 / 60 = $5 0 24 H 0 10 20 30 40 50 60

  8. 4. The Equilibrium Solution Composite consumer good: • Equilibrium assumption of equal level of utility at all locations • Suppose higher utility could be achieved at one location than others • More people would try to live there, which would bid up the price per unit of housing • People could afford to buy less housing, lowering utility achievable at that location • So the equilibrium assumption results in supply of housing equaling demand for housing at each distance x from the center • The city is thus “in balance” • Let’s review the properties we have derived for the various variables we’ve been dealing with in this analysis… PC(x) C*(x) x x Housing: PH (x) H*(x) x x Density: Utility: D(x) U*(x) x x

  9. 5. “Real-World” Search Processes X • What’s different in the “Real World”? aX + bY + cZ + … ? Photo Source: John Birdsall Social Issues Photo Library http://www.johnbirdsall.co.uk/catalogue.shtml

  10. POP QUIZ Name __________ The graph below shows the budget line and the point of tangencyof this line with an indifference curve for the Qwester family if they choose to live right at the center of Toosunny. Their monthly disposable income is $1200. What is the price per unit of composite consumer good, PC, and what is the optimal quantity of housing, H*(0), purchased by this household? PC = 1200/30 = $40 per unit H*(0) = 20 units 30 C 20 10 0 0 10 20 30 40 H

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