Problem Set 6
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Jan 9, 2024
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Urban Economics, Fall 2023, Problem Set #6
Due Friday, Dec 8, 11pm, online on Brightspace
no late problem sets,
one single file submission only
Word, Excel, or PDF formats only
Question 1: The Shape of Bid Rent Curves
For the following cases say whether the resulting Bid Rent Curves are linear, convex, concave,
or undetermined. No explanation needed.
a) A firm enjoys decreasing marginal travel cost and engages in factor substitution.
b) A firm has constant marginal travel cost and does not engage in
factor substitution.
c) A firm incurs increasing marginal travel cost and does not engage in
factor substitution and
needs to have regular lunch meetings with its peers of the same industry.
d) A firm engages in factor substitution and faces increasing marginal travel cost.
Question 2: Bid Rent Functions
Office firms, office workers, and agricultural firms compete for land. Their respective bid rent
functions are given by:
office firms R
o
=222-5x,
office workers R
w
=192-2x, and
agricultural firms R
a
=120.
where R denotes the bid rent and x the distance from the city center.
a) Where does each bidder locate? (calculate the respective distances from the city center)
b) Now assume that the city imposes a fuel tax on offices and on office workers resulting in an
increase in their corresponding marginal transportation cost by 1. How does this change your
answer to (a)? Who locates where?
c) Now assume that, in addition to (b), some revenue from the fuel tax is paid to office workers
(to office workers only, not to offices). The government sends out checks resulting in an income
growth of $3 for each worker. How does this change the bid rent functions and the respective
locations?
d) Now assume that, in addition to all effects mentioned under (b) and (c ), climate change
reduces farm profits and lowers the bid rents of agricultural firms by $3 (to $117). How does this
change the respective locations. Who located where?
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Related Questions
Can I get the answer for this?
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Given the input-output matrix below, find the output matrix if final demand changes to 400 for water, 180 for electric power, and 800 for agriculture.
Industry
Electric
Water
Power
Agriculture Final Demand
Water
100
360
360
220
Industry:
Electric Power
200
120
480
170
Agriculture
300
60
240
500
Other
400
60
120
The output matrix is X =
(Round to two decimal places as needed.)
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Which firm would have more ability to respond to a change in input prices, one where inputs are perfect substitutes or one where they are combined in proportions? Use graphs to help demonstrate answer
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Larry’s Lumber Mill sells lumber in a perfectly competitive product market. However, Larry’s Lumber Mill is the only employer of labor in the small community where it is located. The labor market is depicted by the graph above.
(a) Using the labels from the graph above, identify each of the following.
(i) The optimal quantity of labor Larry’s Lumber Mill will hire
(ii) The wage rate Larry’s Lumber Mill will pay
(b) Using the labels from the graph above, identify the number of workers Larry’s Lumber Mill would hire if the labor market were perfectly competitive.
(c) Because of growing housing demand, the price of lumber increases. What will happen to each of the following?
(i) Larry’s Lumber Mill’s demand for labor. Explain.
(ii) The supply of labor
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Practice Question 7.2
A) The figure below shows the bid rent curves for land for use in housing (R), commercial
purposes (Rc), and agricultural purposes (Ra) in a city. The figure also shows the
boundary for the city's Commercial District (X) and the City itself (X2). On the same
figure, show how the bid rent curves for housing and commercial use would shift if there
is a decline in commuting costs in the city. Further, show any shift in the boundary of the
Commercial District and the City. Assume that the city is a "closed city."
Land rent
Re
Re
Re
Distance to city center
B) What are the reasons that the bid rent curve for land used in housing is curved rather than
a straight line?
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A firm gives electricity to the neighborhood. The firm buys two inputs: green energy (G) and fossil fuel energy (F). The function is given by: Q(G, F) = 4(G + F) a) Find the marginal product per dollar spent on F and G for the firm when PG = 20 and PF = 20. b) Find the cost-minimizing combination(s) of fossil fuels and green energy for the firm to make Q' units of output (a fixed level). c) The government subsidized green energy. What is the new cost-minimizing combination(s) of fossil fuels and green energy for the firm to produce Q' of output (a fixed level).
Give typed Answer ASAP correctly with proper explanation.
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Suppose that the market for dress shirts is a competitive market. The following graph shows the daily cost curves of a firm operating in this market.
(?)
50
45
40
35
30
ATC
25
20
15
AVC
10
MC
5
+
2
4
6.
8
10
12
14
16
18
20
QUANTITY (Thousands of shirts)
For each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that
quantity, using the data from the graph to identify its total variable cost. Assume that if the firm is indifferent between producing and shutting down,
it will produce. (Hint: You can select the purple points [diamond symbols] on the graph to see precise information on average variable cost.)
Price
Quantity
Total Revenue
Fixed Cost
Variable Cost
Profit
(Dollars per shirt)
(Shirts)
(Dollars)
(Dollars)
(Dollars)
(Dollars)
12.50
7,500
135,000
27.50
135,000
45.00
135,000
If the firm shuts down, it must incur its fixed costs (FC) in the short run. In this case, the firm's fixed cost is…
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– A certain cleaning company cleans professional offices and believes its staff can clean up to 300 office units a week at a labor and supply cost of $58 per unit. Preliminary pricing surveys indicate that if that if the company charges $100 per unit, it will have clients for 300 units. For every $5 price increase it can expect a demand of 10 fewer units.
Assume the demand, s, is a linear function of price p. Find an equation for demand as a function of price.
Find the Revenue and Cost functions, both of which are dependent on price p.
Write the Profit function.
Using Desmos, graph the Revenue, Cost, and Profit functions on the same coordinate plane. Label the axes and the functions and use an appropriate scale.
Find the break-even points graphically and confirm algebraically. Label the regions of profit and loss on the graph.
Algebraically find the price that results in a maximum profit.
Conclusion:
A price of $_________ results in a quantity of _____________ units…
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None
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What are the concepts of microeconomic theory with respect to the supply and demand of the inputs required to produce the good/s and the good/s itself. Consider relating to elasticity/inelasticity; substitutes and complements; derived demand; marginal costing; rival / non-rival goods; price formation.
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Use the following general linear supply function:
Qs = 40 + 6P - 8PI + 10F
where Qs is the quantity supplied of the good, P is the price of the good, PI is the price of an input, and F is the number of firms producing the good.If PI = $20 and F = 60 what is the equation of the supply function?Group of answer choices
Qs = 480 + 6P
Qs = 40 + 8P
P = 480 + 6Qs
Qs = 400 + 6P
none of the above
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Show the effect this hurricane on the sweat shirt
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Price (Dollars per Bushel)
950
900
850
D
800
750
700
650
600
550
500
450
400
350
300
250
200
150
100
50
0
0
3 6 9
12
15
S
18
21
24
27
Bushels of Corn (Billions)
The graph above shows hypothetical demand and supply functions for corn in the U.S. Oil
prices increase due to some political problems in middle east. This causes the marginal cost
of producing each bushel of corn to increase by $150.00. This is because, oil is used to
produce gasoline that farmers use to operate tractors, groundwater water pumps, and other
farming equipment. Higher gasoline prices also affect the costs of transporting corn to
consumer centers. This number may, of course, be unrealistic. But it will make the graph less
messy and calculations less cumbersome.
Calculate the following:
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A demand curve is given by p = 660-3x. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. Graph the profit function, M(x)=550x-3x²-8000, and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number):
selling price:
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The cost of renting tuxes for the Choral Society's formal is $21 down, plus $87 per tux. Express the cost C as a function of x, the number of tuxedos rented.
C(x) =
Use your function to answer the following questions.
(a) What is the cost of renting two tuxes?
%$4
(b) What is the cost of the second tux?
$4
(c) What is the cost of the 4,098th tux?
2$
(d) What is the variable cost?
%24
What is the fixed cost?
$4
What is the marginal cost?
%24
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\beta < 1. 16. A firm uses two inputs, X1 and X2, to produce a good that is described by the production function: Q = f (X1, X2) = X1/2X1/4 12 The firm sells its output at $80 per unit: P = $ 80. The cost of input 1, X1, is $4. The cost of input 2. X2, is $2. (a) Solve for the profit - maximizing input mix, output, and profit. (b) Check the second-order conditions to verify that the profit is at a maximum
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Please answer fast
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please do the graphs and the questions below
the choices for the following are
Sean 1. (should, should not) increase production from 4 to 5 fire engines, because the 2.( output effect, price effect) dominates in this scenario.
thankyou!!!!
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3. Optimal inputs: A firm has a production function, y = ln(l, k) in a market with prices
Py = 20, pe = 4, Pk = 5. Find the firm's profit maximizing choice for y, l, and k. How
much profit do they earn?
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Draft a numerical example using the following prompt:
Create a numerical example of a two-commodity market with linear demand and supply curves. The two goods should be substitues and the example should model actual goods found in the real world. The solution should have a price and quantity solution with a reasonable economic interpretation
(i.e. no negative prices or quantities)
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Please see the image.
1. Derive the cost function.2. Directly use the cost function to derive the output supply function
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1. If the cost function of
producing a commodity is:
40 + 50x + Vx2 +1 10 C (x) = =
where x represents the number
of units produced. Calculate
the marginal cost of producing
20 units.
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