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Student Number:
QUIZ 5
Econ 212-Section B
Question 1. [6 marks] Suppose in a perfectly competitive market, a firm’s short-run total
cost curve is given by
STC  60Q 2  25 Q  30
a) [3 marks] What is the equation for the firm’s short-run supply curve? Show your
work.
Answer:
First, we find the minimum of average variable cost by setting average variable cost
equal to short-run marginal cost.
120Q  25  60Q  25
Q0
At Q  0 , average variable cost is AVC  60Q  25  60(0)  25  25 . The supply curve
is the short-run marginal cost curve above the minimum point of average variable cost.
Thus setting, 120Q  25  P We get:
 P  25

S ( P )   120
0
P  25
P  25
where the notation is S ( P )  Q ( P ) , the quantity supplied.
b) [3 marks] Given that there are 240 identical firms in the industry (with above given
short-run total cost function), and the demand function is given by D( P )  385  P ,
calculate equilibrium price and the quantity demanded in this industry. Show your work.
Answer:
With 240 firms, setting demand in the industry equal to aggregate supply, we have
240
P  25
 385  P  3P  435  P  145  Aggregate Q  240
120
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Question 2. [4 marks] In the competitive market for compact discs, market demand is
given by Q d  300  10 P and quantity supplied is given by Q s  25  15P where
quantity is given in millions of compact discs sold per year.
a) [1 mark] What is the market equilibrium price and quantity?
Answer:
To find the market equilibrium, set quantity demanded equal to quantity supplied.
300  10 P  25  15P
25P  325
P  13
At this price, the equilibrium quantity will be Q  300  10(13)  170 . Consumers
will purchase 170 million compact discs.
b) [2 marks] Suppose the government decided to support this “high-tech” industry by
providing a $10 subsidy per compact disc. What would the new equilibrium quantity be?
What price would consumers pay? What price would sellers receive?
Answer
In equilibrium, two conditions must be satisfied. First, markets must clear so that
Q d  Q s . Second, there will be a wedge between the price that consumers pay and
the price that sellers receive; in particular, P d  P s  10 . Together these imply
300  10( P s  10)  25  15P s
25P s  425
P s  17
This is the price sellers will receive. Consumers will pay P d  17  10  7 , and the
equilibrium quantity will be Q  230 , or 230 million compact discs per year.
c) [1 mark] What will this subsidy cost the government?
Answer:
To determine the total cost, take the amount of the subsidy, $10, and multiply it by
the market quantity, 230 million. The total cost will be $2,300 million.
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