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Flashcards in BUSI 300 Lesson 4 Deck (13)
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1

Explain what the phrase "land is the residual claimant" means.

The phrase “land is the residual claimant” means that land rent equals what is leftover after all other
factors of production have been paid their opportunity costs. It is another way of saying that all land
rent is economic profit.

2

Consider a property developer who is trying to determine the feasibility of constructing a small mixed unit development on a vacant lot near the downtown of a large metropolitan area. All units in the project will be sold (rather than rented) and the expected proceeds from sales equal $80 per square foot. The fixed cost of the project is $300,000. The only variable cost is construction cost, which equals $40 per square foot. The initial proposal calls for 10,000 square feet of saleable space.

(a) The asking price for the lot is $200,000. Is the project feasible? Why or why not?

(b) What is the maximum amount that the developer should be willing to pay for the lot?

(c) What is the minimum size (in terms of saleable square feet of space) at which the project is feasible if the price of the lot is $300,000? Explain your reasoning.

(a) If the developer pays 200,000 for the lot, then her profit equals 80(10,000) - 300,000 - 40(10,000) - 200,000 = -100,000. The project is not feasible at the asking price for the lot.

(b) The maximum amount that the developer should be willing to pay for the lot is given by her profit before land, which equals 100,000.

(c) Letting S represent square feet of saleable space, profit under these conditions can be written
as 80S - 40S - 600,000 = 0. The maximum size would be the value of S at which this
expression equals 0, so 40S - 600,000 = 0 implies S =600,000/40 = 15,000 square feet.

3

Consider the location of the production of three agricultural products (indexed by i = 1, 2, 3) around a central market. Assume that:
(i) all land is homogeneous and each farm occupies one unit of land;
(ii) non-land production costs per unit of output are constant and represented by ci ;
(iii) all output is shipped to a central market;
(iv) the cost of shipping one unit of product i one kilometre is a constant, represented by ti;
(v) the opportunity cost of urban land is zero;
(vi) all markets are perfectly competitive;
(vii) quantity is represented by qi and price by pi

To begin, let qi , pi , ci , and t take on the following values:
qi pi ci ti
Product 1 15 40 10 3
Product 2 10 40 10 2
Product 3 5 40 10 1

a) Derive and graph the bid rent functions. Hint: the example in the textbook uses fixed production costs, while this example uses variable production costs. The formula must be altered slightly as follows:
ri(d) = (pi -ci)qi - (ti)(qi)(d).

b) Solve for the boundaries between the agricultural zones and the outer boundary of the cultivated area and label on the diagram from part (a).

c) Show the equilibrium allocation of land between the three products and the equilibrium land rent function in your diagram from part (a).

d) How does the land allocation and equilibrium land rent change if q decreases to 10? Use a 1 new diagram to support your answer.

(a) For each product i, profit equals pi = (pi - ci )qi - (ti)(qi)(d) - ri(d) and setting profit equal to zero implies ri(d) = (pi - ci)qi - (ti)(qi)(d). Then, inserting the values given above, we have r1(d) = 450 - 45d, r2(d) = 300 - 20d, and r3(d) = 150 - 5d. The graph should look like Figure 5.9.
Diagram located in R&D answers Lesson 4 Question 3 (a)

(b) The boundary between products 1 and 2 occurs where
r1 (d) = r2 (d), which implies d = 6. The boundary between products 2 and 3 occurs where r2 (d) = r3 (d), which implies d = 10. The boundary between product 3 and the hinterland occurs where r 3(d) = 0, which implies d = 30.

(c) Land is allocated to the highest bidder, and equilibrium land rent is the highest of the bid rents for any parcel. The graph should look like Figure 5.9.

(d) The bid rent of product 1 becomes r1 (d) = 300 - 30d, which lies everywhere below the bid rent of product 2. Thus, product 1 can no longer successfully bid for land, and will disappear from the region, while product 2 will occupy all land up to d = 10. Equilibrium land rent is
now just the upper envelope of r2 (d) and r3 (3).
Diagram located in R&D answers Lesson 4 Question 3 (d)

4

In the long run, the equilibrium of a competitive industry is where the ______, ______, and ______ are all equal.

(1)price, marginal cost, average cost
(2) price, marginal revenue, average cost
(3) demand, marginal revenue, price
(4) marginal revenue, total cost, marginal cost

Answer: (1) The basic characteristics of a competitive industry are that, in the long run, all firms in the industry earn normal profits or zero economic profits. To maximize profit, the firm produces where price equals marginal cost. However, in the long-run, profit must equal zero since there is “free entry” and this implies that price must also equal average cost. Thus, in the long-run equilibrium of a competitive industry, we have price = marginal cost = average cost.

5

Which of the following is NOT correct when discussing the "leftover principle"?

1) All land rent is economic profit.
2) Land is the residual claimant.
3) Land rent is what is left over after all other factors of production are paid their opportunity costs.
4) Farmers living on higher-quality land will make more profit than farmers living on low-quality land.

Answer: (4) The excess profit that farmers make on higher-quality land is paid in land rent. This profit is the maximum amount that anyone would be willing to pay to rent the land from the owner. It is the amount the farmer could receive by renting the higher-quality land to someone else. We must include this opportunity cost in the higher-quality land costs, resulting in economic profits of zero. Farmers on higher-quality land will make the same profits as farmers on low-quality land because the higher profits that farmers make is spent on rent for using the higher-quality land.

6

Clark is planning to build an apartment building. The municipality will allow Clark to build a building to a maximum of 1,100 square feet per unit with 40 units. It will cost Clark $600,000 for the property and construction costs are $170 per square foot. There is also a charge of $4,200 per unit that goes directly to the municipality to cover costs that the municipality will incur because of the development.

Clark plans to build an apartment building with 40 units, each of 1,100 square feet. If Clark plans to sell each unit for $225,000, how much money will he make or lose on his investment?

(1) He will lose $920,000.
(2) He will lose $132,000.
(3) He will make $752,000.
(4) He will make $1,227,600.

Answer: (3) The costs that Clark pays are $600,000 for the property, $170 per square foot × 40 units × 1,100 square feet = $7,480,000 for construction, and $4,200 per unit × 40 units =$168,000 to the municipality. If he sell the units for $225,000 each, he will make ($225,000 × 40 units) ! $600,000 - $7,480,000 - $168,000 which equals $752,000.

7

Clark is planning to build an apartment building. The municipality will allow Clark to build a building to a maximum of 1,100 square feet per unit with 40 units. It will cost Clark $600,000 for the property and construction costs are $170 per square foot. There is also a charge of $4,200 per unit that goes directly to the municipality to cover costs that the municipality will incur because of the development.

Assume that the building is now complete. Clark puts all 40 units up for sale for $225,000. None of the units sell. What is the lowest price that Clark can sell each unit for without losing any money?

1) $125,200
2) $92,300
3) $206,200
4) $4,748,500

Answer: (3) Clark incurs costs of $600,000 for property, $7,480,000 for construction, and $168,000 from the municipality. The total costs are $600,000 + $7,480,000 + $168,000 = $8,248,000. Therefore, the minimum that Clark can sell each unit for without losing any money is $8,248,000/40 units = $206,200.

8

Mark is a chickpea farmer in Peru. He produces 1,000 tonnes of chickpeas per year and sells all of them to the market at $60 dollars per tonne. The non-land production costs total $20,000 and each farmer occupies 1 acre of land. It costs Mark $0.15 per tonne to transport 1 tonne of chickpeas 1 kilometre. (When solving this problem, use these assumptions in a stylized version of von Thunen's model of a spatial land market).

Given perfect competition, what is the maximum amount that a farmer at a distance of 10 kilometres from the market will pay for a unit of land?

1) $1,500
2) $38,500
3) $40,000
4) $39,850

Answer:(2)
The bid rent function for land is r(d) = (p × q - c)/l - ((t × q)/l) × d and therefore, r(10) = ($60 per tonne × 1,000 tonnes - $20,000)/1 - {(0.15 per tonne × 1,000 tonnes)/1) × 10 km} = ($40,000/1) - $1,500 = $38,500.

9

Mark is a chickpea farmer in Peru. He produces 1,000 tonnes of chickpeas per year and sells all of them to the market at $60 dollars per tonne. The non-land production costs total $20,000 and each farmer occupies 1 acre of land. It costs Mark $0.15 per tonne to transport 1 tonne of chickpeas 1 kilometre. (When solving this problem, use these assumptions in a stylized version of von Thunen's model of a spatial land market).

If agricultural land is not used, it earns no rent. Farming of agricultural land will occur up to a distance where it is no longer profitable. What is the boundary of the cultivated area?

1) 40,000 kilometres
2) 26.67 kilometres
3) 38,500 kilometres
4) 266.67 kilometres

Answer: (4)
The cultivated land extends out to the point where equilibrium land rent is zero. The boundary of the cultivated area is the distance at which r(d) = 0. r(d) = ($60 per tonne × 1,000 tonnes - $20,000)/1 - ((0.15 per tonne × 1,000 tonnes)/1) × d. Therefore, 40,000/1 - 150d = 0 and, 40,000 - 150d. Solving for d, d = 266.67 km. The boundary of the cultivated land is 266.67 kilometres. Beyond this distance, transport costs are so high that farmers cannot break even, even if they pay no land rent.

10

Mark is a chickpea farmer in Peru. He produces 1,000 tonnes of chickpeas per year and sells all of them to the market at $60 dollars per tonne. The non-land production costs total $20,000 and each farmer occupies 1 acre of land. It costs Mark $0.15 per tonne to transport 1 tonne of chickpeas 1 kilometre. (When solving this problem, use these assumptions in a stylized version of von Thunen's model of a spatial land market).

Now, assume that the agricultural land is surrounded by a dense forest that cannot be cut down and that the boundary of the cultivated area is 1,500 kilometres. What is the area under cultivation if the actual area is a circle with the market in the middle? (The equation for area of a circle is: radius × r2 ).

1) 7,068,577.5 square kilometres
2) 4,712.385 square kilometres
3) 837.77 square kilometres
4) 225,000 square kilometres

Answer: (1)
The actual area under cultivation is a circle with the market at the centre. The radius of the circle is equal to the boundary of the cultivated area. Using the equation for the area of a circle, 3.14159 × 1,500^2 = 7,068,577.5 square kilometres.

11

What happens to the bid rent curve if more effective means of transporting goods are created and the marginal cost of transport decreases?

(1) This causes the slope of the bid rent function to steepen and causes the boundary to move inward decreasing the area.
(2)This causes the slope of the bid rent function to steepen and causes the boundary to move outward increasing the area.
(3)This causes the slope of the bid rent function to flatten and causes the boundary to move outward increasing the area.
(4) This causes the slope of the bid rent function to flatten and causes the boundary to move inward decreasing the area.

Answer: (3)
A decrease in marginal transport costs makes the rent function flatten, but does not affect its vertical
intercept. This causes the outer boundary of the area to move outward. It is now feasible to farm in
locations farther away from the market because total costs of farming are now lower.

12

The city of Jokers has two types of land users, kings and queens. Queens have a bid rent function of r(d)=10,000 - 600d and kings have a bid rent function of r(d) = 7,500 - 300d. Assuming these are the only land users, where is the boundary of the city? (All distances are in kilometres.)

1) 8.33 kilometres
2) 25 kilometres
3) 16.67 kilometres
4) 20.835 kilometres

Answer: (2)
There will now be two distinct rings around the market. Queens are willing to spend more money on
rent for land closer to the centre because they have high transport costs. Kings are willing to spend
more money on rent for land farther from the city because they have less to lose than queens by locating
at a distance from the centre. The land that is not used by kings and queens earns no profit, and
therefore the city extends out to a point where equilibrium land rent is zero. The outer ring of the city
is occupied by kings. The distance at which the kings would be willing to spend $0 on rent is ,
r(d) = 7,500 - 300d, r(d) = 0 at the boundary so,
0 = 7,500 - 300d, therefore d = 25 kilometres.

13

Which of the following are TRUE with respect to bid rent curves?

A) If possible, firms will economize on inputs that are relatively more expensive.
B) If land becomes less expensive as we move away from the market, lot sizes should increase as distance to the market increases.
C) The bid rent curve will be steeper near the market and flatter further away.
D) If firms can substitute other inputs for land, then land rent should decline very quickly at first as distance from the market increases, and firms should use land most intensively near the market.

1) Only Statements A and D are correct.
2) Only Statements B and C are correct.
3) Only Statements A, B, and C are correct.
4) All of the above statements are correct.

Answer: (4)
If firms can substitute one input for another, then they will economize on inputs that are relatively more
expensive. Input substitution changes the shape of the bid rent function for land. Firms will use less
land if they locate close to the market and more land if they locate further away. Thus, lot size should
not be constant. Rather, since land becomes less expensive as we move away form the market, lot sizes
should rise as the distance to the market increases. The bid rent function is steeper near the market and
flatter further away. With input substitution, the bid rent function takes a convex shape, land rent will
decline very quickly at first as distance from the market increases, and firms will use land most
intensively near the market.