This question is based on pages 200-201 in the text and on Chapter 9 Notes
posted on Course Documents.
Mark allocation is 10 for (a), 15 for (b) (i), and 10
for (b) (ii).
Zoning constraints are binding only if they limit output to less than 120 units
(12 units per acre on the 10 acre land supply).
That is because the demand
function and the marginal cost of capital (output supply) function intersect at u =
The industry will not expand output beyond the point where price =
We note that with the land market in equilibrium (all 10 acres rented to housing
firms), capital is the industry’s only variable input.
The capital input is measured
in dollars per year spent on capital (bricks, glass, concrete etc.).
cost is the industry’s additional capital cost if output is increased by one unit.
(The points noted in this paragraph do not have to be specifically noted – they
are just here for background information.)
With a 5 unit per acre zoning limit, industry output cannot go above 5 X 10 acres
= 50 units (houses).
Total revenue is then quantity times price = 50 X ($40,000 –
200 X 50) = $1.5 million / year.
Total capital cost is the area under MC from u =
0 to u = 50.
This area is made up of the rectangle $10,000 X 50 = $500,000; and
the triangle 0.5 X (12,500 - $10,000) X 50 = $62,500.
($12,500 is MC at u = 50.)
Firms will make zero economic profit in equilibrium, so land rent absorbs all of
the difference between total revenue and non-land (capital) cost.
Thus total land
rent is $1,500,000 minus $562,500 = $937,500 ($93,750 / acre).
As an alternative to calculating total revenue as price times quantity from the
demand function, it can be calculated as area under the industry MR function to
the left of u = 50.
This would be the rectangle $40,000 X 50 minus the triangle
0.5 ($40,000 - $20,000) X 50.
That is, total revenue = $1.5 million (the same
number calculated as price times quantity).
Calculated similarly, the answer to (ii) is $96,000 / acre; and the answer to (iii) is
$36,000 / acre.
The answer to (iv) is also $36,000 / acre.
That is because the
zoning constraint is non-binding above 12 units per acre (upa).
12 upa maximum to 15 upa maximum will not affect output or land rent.
Answers using the marginal revenue function may note that to the left of the MC /
MR intersection, upzoning will increase land rent.
To the right of that
intersection, up to the intersection of MC with demand, upzoning will decrease
They could also note that MR = 0 at u = 100, and is negative to the
right of that point.
However, none of the points in this paragraph were
specifically requested so mentioning them is optional.