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1. Math 116.01 - Quiz 1 Solutions
(1) A farm can produce a bushel of wheat for $7 (including labor, fertalizer, and water expenses), and it can sell wheat for $7.50. If the lease on the land costs $3500 per year (a
fixed cost), how much wheat must the farm produce and sell in a year to make a profit?
Suppose the farm produces and sells q bushels of wheat. Then the variable costs for the
farm are V C = 7q. The fixed costs are F C = 3500. Since the farm can sell wheat at $7.50
per bushel, revenue is r = 7.50q. So profit is
P = r − c = 7.50q − (3500 + 7q) = 0.5q − 3500.
For the farm to make a profit, we must have 0 < P , so solve
0<P
0 < 0.5q − 3500
3500 < 0.5q
7000 < q.
So the farm must produce and sell more than 7000 bushels.
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1
2
10
2
and the supply is given by p = − + 2,
q
q
find the price and quantity sold when the market is in equilibrium.
(2) If the demand curve in a market is given by p =
Recall that a market is in equilibrium when supply equals demand. So we must solve
2
10
=− +2
q
q
2
10
= − +2 ·q
q·
q
q
10 = −2 + 2q
12 = 2q
q = 6.
So the market is in equilibrium when the quantity produced and sold is q = 6. The price
for this quantity is
10
5
10
=
=
p=
q
6
3