Answers: August 06 Final
1 This question was discussed in class Feb. 6-7, 2007.
(a) Total revenue from the demand curve with u = 160, p = $50,000 = $8Million.
The payment to capital is obtained from the u = 160 isoquant (LC = $128 m) as
follows. With a fixed land supply = 40 acres, capital cost = $128m / 40 =
$3.2 million. The limit on building permits does not interfere with factor
substitution, so equilibrium land rent will make the industry isocost line tangent
to the u = 160 isoquant at the point L = 40, C = $3.2 million. From the slope
expression (MRTS = - $128 million / L
), we have slope = rent per acre = $128m /
(40 X 40) = $80,000. That makes total spending on land = 40 acres X $80,000 =
$3.2 million. (This particular isoquant specification gives equal spending on both
factors, which is not a general result.)
With the limit on building permits we have a barrier to competition, so economic
profit is possible. Economic profit is total revenue minus spending on capital and
land ($3.2 million on capital, $3.2 million on land: total $6.4 million), leaving $1.6
million economic profit.
Part (a) should include an isoquant / isocost line showing the u = 160 isoquant, a
tangent isocost line at the point on that isoquant with L = 40.
The tangent isocost
line has slope = - $80,000 and an intercept on the C axis = $6.4 million.
(b) We need a zoning policy that will limit output to 160 units. With 40 acres of
land, a minimum lot size of 0.25 acres will achieve this result.
With the zoning policy, economic profit is no longer possible. Any "wannabe"
firm from outside the model can get a permit and bid for land.
As a result of removing the barrier to competition, land rent will increase until
there is zero economic profit. Output is the same (160 units) as in (a) so total
revenue is still at $8 million. However, all of that revenue not paid to capital will
go to land rent, eliminating the economic profit in (a). So the $8 million goes $3.2
million to capital and $4.8 million to land rent. Economic profit = zero.
(c) The diagram that is useful to solving this part is Figure 1 in the web-site
Chapter 9 notes (page 14 in the edition posted March 2007).
With the August 06
exam question, however, the supply curve (marginal cost) would go through the
origin instead of being as shown in Fig. 1. The reason is that rent and
capital payments as determined in part (a) were equal ($3.2 million each).
The total of rent and capital payments in part (a) is the rectangle zncj (6.4
The capital half of that rectangle is the area under the supply curve,
and the rent half is the area above it. The supply curve has to be the diagonal of
the rectangle for these two amounts to be equal.