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Answers: August 08 Exam
Question 1 (a)
First solve for the equilibrium intersection of supply and demand.
This intersection tells
us how much output will be produced if the city lets the market reach its own
equilibrium, with no growth control policy.
MC = 6000 + 50u = P = 43,500 – 200u so
250u = 37,500.
Thus u = 150.
Since there are 50 acres of land in the land supply and a
minimum lot size = 0.25 acres, the zoning regulation is limiting total output to no more
than 200 units.
This is more than the unregulated equilibrium output (150), so the
zoning regulation is nonbinding.
The supply/demand diagram should show intersection
of supply and demand at u = 150, P  $13,500.
Total revenue is $2.025 million and
capital cost (area under MC from 0 to 150) is $1,462,500.
Total land cost = $2,025,000
 $1,462,500 = $562,500 (rent = $11,250 / acre).
The industry isoquant/isocost diagram should show the u = 150 isoquant with tangent
isocost line (slope = $11,500).
Given the absence of a binding zoning constraint, factor
substitution can operate ensuring the isocost/ isoquant tangency condition.
The Caxis
coordinate of the tangency point should be $1,462,500 and the Laxis coordinate should
be 50 acres.
The Caxis intercept of the tangent isocost line should be at total revenue
= $2,025,000 since with an unregulated market there is zero economic profit.
The firm isoquant/isocost diagram should show the isoquant for u = 5 (the firm’s fixed
output as given in the question.
There are 30 firms since total output = 150.
Thus each
firm’s land input is 50 / 30 = 1.67 acres.
Each firm’s capital input is $1,462,500 / 30 =
$48,750.
These inputs should be shown as coordinates of the isoquant/isocost
tangency point.
The Caxis intercept of the isocost line is the firm’s total revenue
($2,025,000 / 30 = $67,500).
(b) With this higher position of the demand curve the zoning regulation is binding. The
intersection of supply and demand would be at u = 250, but the zoning does not allow
output to go above u = 200.
The supply/demand diagram should show a vertical region
of the supply curve at u = 200.
Equilibrium price is at $28,500, so total revenue = $5.7
million.
Total capital cost = area under MC from u = 0 to u = 200 = $2.2 million.
Thus
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total land cost is $5.7 million minus $2.2 million = $3.5 million (rent = $3.5 million / 50 =
$70,000 / acre.
The industry isoquant/isocost diagram should show the industry producing on the u =
200 isoquant at the point where L = 50 acres, C = $2.2 million.
A nontangent isocost
line should connect this point to $5.7 million on the C axis, since there is zero economic
profit with the zoning policy (no barrier to competition).
The nontangency condition is
due to no factor substitution with the zoning policy in effect (industry cannot temporarily
use less than 50 acres of land which would create excess supply, leading to lower rents
until tangency is reached).
The firm’s isoquant/isocost diagram should show the u = 5 isoquant, this time with each
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 Summer '10
 Peterson

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