BUSI 300 Lesson 5 Flashcards
Consider a monocentric city in which every household occupies one-fifth of an acre of land (l* = 0.20). Suppose that the cost of commuting is $50 per mile per month, round trip (t = $50). Finally, suppose that a 0.20 acre lot 10 miles from the city centre (d = 10) rents for $1,000 per month.
(a) What is the slope of the household bid rent function?
(b) What is bid rent per acre at d = 5?
(c) Calculate the sum of land rent and commuting cost for someone living at d = 10. Calculate the sum of land rent and commuting cost for someone living at d = 5. Comment on the significance of your findings.
(d) Derive an expression for the bid rent function in this case and illustrate the function in a diagram. [Hint: Recall that r(d) = r(0) - t/l*(d), where r(0) is the rent at city centre.]
(a) By equation (6.4), r/d= -t/l* = -50/0.20 = - 250
(b) Moving five miles closer to the city centre will cause bid rent to rise by 1,250. Since bid rent
at d = 10 is 5,000, bid rent at d = 5 must be 6,250 per acre or 1,250 per lot.
(c) Someone living at d = 10 pays 1,000 per month in rent and 500 per month in commuting cost,
so the total is 1,500 per month. Someone living at d = 5 pays 1,250 per month in rent and 250
per month in commuting cost, so the total is again 1,500 per month. This illustrates the
concept of a spatial equilibrium: rents change along the bid rent function so that identical
households get the same level of utility regardless of where they locate. Rents change along
the bid rent function so that no one has an incentive to move.
(d) The bid rent function is a line with a slope of -250, so
r(d) = r(0) - 250d, where r(0) is the vertical intercept, or the rent at the city centre. Then, r(10) = 5,000 implies 5,000 = r(0) - 250(10), so r(0) = 7,500, and the bid rent function is r(d) = 7,500 - 250d (any other point
on the curve will allow you to solve for r(0)). The diagram should look like Figure 6.7.
Diagram located R&D answers Question 1 d
Consider a closed monocentric city with a population of 100,000 in which each household occupies 0.25 acres of land. Agricultural land rent is $1,000 per acre per year, and commuting cost is $250 per mile per year round trip.
(a) Find the border of the city (in miles).
(b) What is the annual rent per acre on land at the border?
(c) What is the annual rent per acre on land at the city centre?
(d) Carefully illustrate the land rent function by using a graph.
(a) The total demand for land is 25,000 acres, or approximately 39.1 square miles. The total
supply of land within a circle of radius b is πb^2. If everyone is to have a place to live, we must
have 39.1 = 3.14 b^2, which implies b is equal to approximately 3.5 miles.
(b) Since the residential and agricultural bid rent functions intersect at the border, we must have
r(3.5) = 1,000 per acre.
(c) The slope of the bid rent function is -250/0.25 = -1,000, so the rent on land at the city centre must be 1,000 + 3.5(1,000) = 4,500 per acre.
(d) Diagram located R&D answers Question 2 d
Explain intuitively why lot sizes vary within a city. Explain how flexible lot sizes, or more generally substitution between land and other goods, impacts the slope of the bid rent function. When will lot sizes be smaller?
If consumers can substitute other goods for land, then, as the price of land rises, they will consume less
land and more of other goods. This implies that lot sizes will be smaller where land prices are higher.
Since lot size is in the denominator of the slope of the bid rent function, substitution or flexibility will
cause the slope to decrease (in absolute value) as lot size increases. This implies that the bid rent
function will be convex: steeper near the city centre and flatter near the city boundary.
Consider a monocentric city with two land uses: manufacturing firms and households. Suppose that each manufacturing firm produces 1,000 units of output (Q = 10), has total non-land costs of $500 (C = 5), and occupies one acre of land (L = 1). The price of output is $2 per unit, and shipping costs are $0.20 per unit of output per mile. The household or residential bid rent function is r(d) = 1,000 - 100d with $100 representing the commuting cost per mile.
(a) Derive the firms’ bid rent function for land, and show both this and the residential bid rent function on a diagram. Refer to Equation 6.9 in deriving the firm’s bid rent function.
(b) Calculate the sum of expenditures on land and shipping costs for a firm located at d = 1 and a firm located at d = 2. Comment on the significance of your findings.
(c) Find the location of the border between the commercial and residential districts. How many firms does the city contain?
(d) How would the size of the commercial district change as a result of each of the following? Explain each case briefly, using a diagram.
(i) An increase in the price of output; (ii) An increase in shipping costs.
(a) Profit is P(d) = 2,000 - 500 - 0.2(1,000)d - R(d), and so setting profit equal to zero implies a commercial bid rent function of R(d) = 1,500 - 200d.
Diagram located in R&D answers Question 4 A
(b) For a firm located at d = 1, expenditures on land equal 1,500 - 200 = 1300 and shipping costs equal 200 for a total of 1,500. For a firm located at d = 2, expenditures on land equal 1,500 - 400 = 1,100 and shipping costs equal 400 for a total of 1,500. This illustrates the concept of a spatial equilibrium: rents change along the bid rent function so that identical firms earn the same level of profit (in this case zero) regardless of where they locate. Rents change
along the bid rent function so that no one has an incentive to move.
.
(c) The location of the border satisfies 1,500 - 200d = 1,000 100d, so 100d = 500 or d =5. The area of the commercial ring is thus 3.14(25) = 78.5 square miles or 50,240 acres.
Since each firm occupies one acre, this is also the number of firms in the commercial district
(d) (i) The firm bid rent function would shift upward, and the size of the commercial district
would increase.
(ii) The firm bid rent function would become steeper, and the size of the commercial
district would decrease.
Which of the following statements are CORRECT?
A) As we move to the left along an indifference curve, the utility obtained by the household increases.
B) A utility curve holds different combinations of goods that give the same utility.
C) Higher indifference curves (i.e., indifference curves positioned higher and to the right) represent higher utility.
D) The only way to obtain a higher utility is to make more money.
1) Only Statements A and D are correct.
2) Only Statements B and C are correct.
3) Only Statements B, C, and D are correct.
4) All of the above statements are correct.
Answer: (2)
Utility functions are described by their indifference curves, which are combinations of goods that give the same level of utility. Higher indifference curves represent higher utility. Statement A is incorrect because as we move along an indifference curve, we are changing the combinations of goods while keeping the utility constant. Statement D is incorrect because you could also obtain a higher utility if the price of any of the goods change. A change in price will change the budget line, which could result in the new budget line now being tangent to a higher indifference curve.
Why do land prices increase as we move closer to the city?
1) Households are willing to bid more for land closer to the city centre because commuting costs are lower.
2) Identical households must reach the same level of utility in equilibrium. Otherwise, someone will have an incentive to change their behaviour. If houses closer to the city are not more expensive, all households will want to move there.
3) Land prices increase as we move closer to the city because lots are maintained better.
4) Both (1) and (2) are correct.
Answer: (4)
Households are willing to bid more for land closer to the city because commuting costs are lower. The difference in land rents is just large enough so that utility at the two locations is the same. Thus, no one will have an incentive to move.
Consider a monocentric city in which every household occupies one-fifth of an acre of land (l* = 0.20). Suppose that the cost of commuting is $50 per mile per month for a round trip (t = $50). Finally, suppose that a 0.20 acre lot 10 miles from the city centre (d = 10) rents for $1,000 per month.
What is the slope of the household bid rent function?
(1) -1,000
(2) +50
(3) -250
(4) -50
Answer: (3) The equation for the slope of a household’s bid rent function is -t/l* {the change in r(d)/(the change in distance)}. The change in r(d) is 50 and the change in distance is 0.2. Therefore -50/0.20 = -250.
Consider a monocentric city in which every household occupies one-fifth of an acre of land (l* = 0.20). Suppose that the cost of commuting is $50 per mile per month for a round trip (t = $50). Finally, suppose that a 0.20 acre lot 10 miles from the city centre (d = 10) rents for $1,000 per month.
What is the bid rent per acre at a distance of 5 miles?
(1) 1,250 per acre
(2) 5,500 per acre
(3) 6,250 per acre
(4) 7,500 per acre
Answer: (3) Since each lot contains 0.20 acres of land, bid rent per unit of land at d = 10 is $5,000. (5 × $1,000) because there are 5 lots per acre each renting for $1,000. The slope of the bid rent is -50/0.20 = -250. At a distance of 5 miles, which is 5 miles closer to the city centre than d = 10, the change in distance is now equal to 5. Moving from d=10 to d=5 will cause the price of houses to rise by (-250)× (-5)=1,250. Since bid rent at d=10 is $5,000, bid rent at d = 5 must be $6,250 per acre ($5,000 + $1,250).
Consider a monocentric city in which every household occupies one-fifth of an acre of land (l* = 0.20). Suppose that the cost of commuting is $50 per mile per month for a round trip (t = $50). Finally, suppose that a 0.20 acre lot 10 miles from the city centre (d = 10) rents for $1,000 per month.
Calculate the sum of land rent and commuting cost for someone living at a distance of 10 miles.
1) The land rent would be $1,000 per month and the commuting cost would be $500 per month.
2) The land rent would be $1,250 per month and the commuting cost would be $250 per month.
3) The land rent would be $500 per month and the commuting cost would be $1,000 per month.
4) The land rent would be $1,500 per month and the commuting cost would be $0 per month
Answer: (1) Someone living at d = 10 pays $1,000 per month in rent and $500 ($50 × 2 × 10 miles) per month in commuting cost.
Consider a closed monocentric city with a population of 100,000 in which each household occupies 0.25 acres of land. Agricultural land rent is $1,000 per acre per year, and commuting costs are $250 per mile per year round trip. (There are 640 acres in a square mile).
Where is the border of the city in miles?
1) 3.5 miles
2) 6.25 miles
3) 12.45 miles
4) 39.1 miles
Answer: (1)
The total demand for land is 25,000 acres (100,000 people × 0.25 acres of land), which is approximately 39.1 square miles (25,000 acres/640 acres in a mile = 39.1 square miles). The total supply of land within a circle of radius b is pie × b^2 . If everyone is to have a place to live, we must have 39.1 = 3.14 b^2 , which implies b is equal to approximately 3.5 miles.
Consider a closed monocentric city with a population of 100,000 in which each household occupies 0.25 acres of land. Agricultural land rent is $1,000 per acre per year, and commuting costs are $250 per mile per year round trip. (There are 640 acres in a square mile).
What is the annual rent (per acre) on land at the border?
1) $1,875 per acre
2) $125 per acre
3) $1,000 per acre
4) $500 per acre
Answer: (3) Since the residential and agricultural bid rent functions intersect at the border, we must have r(3.5) = $1,000 per acre.
What is the impact of a transportation improvement on the bid rent curve in a city with a fixed population and flexible lot sizes?
1) The decrease in commuting costs leads to an increase in equilibrium land rent for all properties because the reduction in transportation costs leaves residents at all locations with more money to spend on land rent.
2) The decrease in commuting costs leads to a increase in equilibrium land rent for properties in the outskirts of the city and a decrease in land rent for properties near the city centre.
3) A transportation improvement will cause the city to grow because land is now less expensive near the city boundary.
4) There is no impact on the bid rent curve if transportation is improved because it affects all individuals the same.
Answer: (2) The decline in commuting cost leads to an increase in equilibrium land rent for properties far away from the city centre and a decrease in equilibrium land rent for properties near the city centre.
What will be the effect on the bid rent curve for an industrial firm if the selling price of the product increases?
1) An increase in the selling price of the firm’s product will cause the firm’s bid rent curve to move up and in because it is now more profitable to produce large quantities.
2) An increase in the selling price of the firm’s product will cause the firm’s bid rent curve to become convex as the firm substitutes away from selling other goods and produces the product with a higher selling price.
3) An increase in the selling price of the firm’s product will cause the firm’s bid rent curve to shift upward in a parallel fashion.
4) There will be no effect on the firm’s bid rent because it affects all parts of the curve the same.
Answer: (3)
An increase in the selling price or a decrease in the non-land costs will shift the bid rent function
upward in a parallel fashion. A higher selling price or a lower cost leaves a larger residual to be paid
in land rent
The capital-to-land ratio is:
(1) higher in the city centre than it is in the agricultural region.
(2) lower in the city centre that it is in the agricultural region.
(3) exactly the same in the city centre and in the agricultural region.
(4) approximately equal in the city centre and in the agricultural region.
Answer: (1)
The capital-to-land ratio is higher in the city centre than in the agricultural region because land is more
expensive in the city core. Therefore, firms substitute away from land and build structures that are
high.
