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# Residential use of land in a monocentric city

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A powerpoint presentation I made for our class in Econ 196. It discusses residential land use in a monocentric city.

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### Residential use of land in a monocentric city

1. 1. Residential Use of Land in a Monocentric City Hannah Faith Enriquez
2. 2. Two steps in the analysis of residential land rent:  Housing-Price Function - indicates how much a household is willing to pay for dwellings at different locations in the city  Residential Bid-Rent Function - indicates how much housing producers are willing to pay per acre of land at various locations in the city
3. 3.  Assumptions in Residential Land Use:
4. 4.  HOUSING-PRICE FUNCTION  Price of housing – price per square foot of housing per month  Ex. 1,000 square-foot house Household rent – \$250 per month Price of housing – 25 cents/square foot (\$250 divided by 1,000 sq. foot)
5. 5.  2 Types of Housing-Price Function: a. Linear Housing Price Function: No Consumer Substitution a. Convex Housing Price Function: Consumer Substitution
6. 6.   Linear-Housing Price Function: No Consumer Substitution Assumptions: 1. Identical dwellings – every dwelling in the city has 1,000 square feet or living space 2. Fixed budget – the household has a fixed budget of \$300 per month ( on commuting and housing costs) 3. Commuting cost – monthly commuting costs are \$20 per mile/month  1 mile - \$20  2 miles - \$40
7. 7. Housing-Price Function for a City with Identical Dwellings (1,000 square-foot): No Consumer Substitution (LINEAR) \$ 0.30 Price of housing per square foot A  \$300 - housing  \$120 – commuting B  \$180 - housing 0.18 Housing-price function 0.06 6 City center Miles to city center 12 15
8. 8. Linear Housing Price Function: No Consumer Substitution a. Households are indifferent among all locations within the city Why?  Because differences in commuting costs are offset by differences in housing costs Slope: t – commuting cost/mile H – housing consumption/sq. foot P – change in price/sq. foot If: t = \$20 H = 1,000 sq. foot P= 0.02/sq.foot
9. 9.  Convex Housing Price Function: Consumer Substitution  A more realistic assumption: ◦ Household obeys the law of demand: decreases the quantity demanded as price increases As a household moves toward the city center, it pays a higher price for housing, so it occupies a smaller dwelling
10. 10.  As the relative price of housing increases, the household substitutes nonhousing goods
11. 11. Housing-Price Function for a City with Identical Dwellings : With Consumer Substitution (CONVEX) \$ Housing-price function: no consumer substitution 0.30 Price of housing per square foot Housing-price function: with consumer substitution 0.12 Distance to city center (miles) Housing consumpti on (sq. 3 400 6 600 9 750 12 1,000 0.06 foot) 3 6 9 Miles to city center City center 12 15
12. 12. Convex Housing Price Function: Consumer Substitution a. As the household moves toward the city center, housing consumption decreases, thus increasing the slope of the housing price-function. Slope: t H P u – commuting cost/mile – housing consumption/sq. foot – change in price of housing – distance to city center If: u = 9 miles t = \$20 H(u) = 750 sq. foot Slope = 0.0267/sq.foot
13. 13.  How rapid does the price of housing decrease as distance to the city center increases?  Housing-Price Gradient: percentage change in the price of housing per mile
14. 14.  Residential Bid-Rent Function - indicates how much housing producers are willing to pay per acre of land at various locations in the city  2 Types of Residential Bid-Rent Functions: a. Housing with Fixed-Factor Proportions b. Housing Firms engage in Factor Substitution
15. 15.  Residential Bid-Rent Function Equation: Given: P – price of housing u – distance to city center Q – square feet of housing T – acres of land K –nonland cost u – 6 miles T – 50 K - 50 consumption 3 R(u) = 1.98 Distance to city center (miles) Housing 400 0.24 6 600 0.18 9 750 0.12 12 1,000 0.06 (sq. foot) Price of Housing
16. 16.  Since P(u) decreases as u increases, R(u) declines as u increases. The bid rent function is convex since the housing price function is convex.
17. 17.  Bid-Rent Function: Fixed Factor Proportions The characteristics of the housing industry are as follows:  1. Production - each firm produces Q square feet of housing using land and non-land inputs. Once the firm erects a building, it can be used as a single dwelling (with Q square feet of space) or divided into x units each of which has (Q/x) square feet of living space.  2. Non-land Cost - Firms use (K) worth of non-land inputs for each building.
18. 18. Residential Bid-Rent Function: Fixed Factor Proportions \$ Total Revenue = P(u) times Q Cost of nonland inputs Bid-rent Function City center u* Miles to city center
19. 19.  3. Fixed Factor Proportions - Each firm produces its house, regardless of the price of land.  4. Housing Prices - the housing price function is negatively sloped and convex (i.e. slope gets steeper as location approaches city center)  5. Perfect Competition - the housing industry is perfectly competitive so each house builder makes zero economic profits in long run equilibrium.
20. 20.  Bid-Rent Function: Factor Substitution  Involves substituting non-land inputs for land as the price of land increases which means building progressively taller buildings as location approaches city center.  The flexible firm (with factor substitution) is able to produce housing more cheaply than the inflexible firm since the flexible firm uses less of the more expensive input at each location. Thus the flexible firm can always outbid the inflexible firm for land.
21. 21. Residential Bid-Rent Function: Factor Substitution \$ Bid Rent without factor substitution Bid Rent without factor substitution Bid rent (per acre) City center 3 6 9 Miles to city center 12
22. 22.  Residential Density- population density at different locations in the city Consumer substitution – price of housing decreases as distance to the city center increases b. Factor substitution – price of land decreases as the distance to the city center increases a.
23. 23.  Monocentric City 2 features: 1. Office firms occupy the central area of CBD (central business district) 2. Employment is concentrated in the CBD, not distributed throughout the city
24. 24. Land rent per acre Distance from city center
25. 25.  Why do all manufacturers and office firms locate at the CBD?  There are trade-offs: 1. Higher freight costs (transportation costs)  2. Lower wages 
26. 26. Suburbs City Center Low wages Higher transportation costs High wages Lower transportation costs Why? - Horse-drawn wagons are slower and more expensive Why? - Workers commute by streetcar and they are faster and more efficient
27. 27. Residential Bid Rent Functions Manufacturer Bid Rent Functions Office Bid Rent Functions Lowest transport costs Higher transport costs Highest transport costs Slope of Bidrent Function Flat Steeper Steepest Distance from City Center Farthest Closer Closest Transport Costs
28. 28. END