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Economics – Assume there are three farms in a county

Question
Urban
Economics
Problem Set
#5
no late problems
sets

Question 2
Assume there are three farms in a county growing corn in a perfectly competitive market.
The overall global market supply of corn is given by QS=P. The demand function
equals QD=100-P. The marginal cost functions for the farms are given by MC1=48+Q,
MC2=46+Q and MC3=42+Q. Assume there is no fixed cost of production.
a) Calculate the overall market equilibrium quantity and the corresponding
market clearing price.
b) How much corn does each farm produce?
c) What is each firm’s annual profit?
d) Assuming a discount rate of 4% and a profit growth rate of 1.5%, what is the
land of each firm worth?
e) Now assume, due to better climatic conditions, marginal cost for each firm falls
by $2. Calculate the new marginal cost functions, quantities, profits and the
new land values assuming the same discount rates as under (d). What was the
sum of the tree land values before and after the change?

Question 3
A firm that produces metal occupies four hectares of land. The firm produces 10 tons of
output per day and sells its output at a price of $240 per ton. The firm does not engage in
factor substitution as the price of land changes. Intra-urban transportation is on trucks,
with a unit cost of $12 per ton per mile. The firm’s non-land cost is $560 per day. The
firm exports its output via circumferential highway (i.e., beltway around the city). That is,
the firm would like to be located at or near the beltway.
(a) Draw the firm’s bid-rent curve for land for different distances from the beltway, from
a distance zero to five miles.
(b) What is the bid-rent at the beltway? What is the slope of the bid-rent function? Show
your work.

Question 4
Is in your textbook, Ch. 6, Applying the Concepts # 9:
Consider a region with two cities: Obeyburg (B) and Vioville (V). The cities differ
in the individual demand curves for housing. Consumers in Obeyburg obey the
law of demand with negatively sloped individual demand curves. Consumers in
Vioville violate the law of demand, with positively sloped individual demand
curves. Draw the housing price curves for the two cities (labeled PB for Obeyburg
and PV for Vioville) under the assumption that PB=PV at a distance of 5 miles from
the city center. Hint: How does conventional consumer substitution affect the
shape of the housing-price curve and how would contrary consumer substitution
affect the shape?

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