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QUIZ 5
Econ 212-Section A
Question 1. [6 marks] Suppose market demand is given by Qd  50  2P and market
supply is given by Q s  3P .
a) [2 mark] With no tax, what is the market equilibrium price and quantity?
Answer:
To find the equilibrium, set quantity demanded equal to quantity supplied.
50  2 P  3P
5P  50
P  10
b) [3 mark] Now suppose the government imposes an excise tax of $10 per unit. What
will the new equilibrium quantity be? What price will the buyer pay? What price will
the seller receive?
Answer:
With an excise tax, two conditions must hold. First, the market must clear so that
Q d  Q s . Second, there is a tax wedge of $10, so P d  P s  10 . Together, these
conditions imply
50  2( P s  10)  3P s
5 P s  30
Ps  6
This implies P d  P s  10  16 and the equilibrium quantity will be (substituting into
demand) Q  50  2(16)  18 .
c) [1 mark] At the equilibrium calculated in part b), what will the government’s total tax
receipts be?
Answer:
To calculate tax receipts, take the amount of tax, $10, and multiply by the equilibrium
quantity, 18. Tax receipts will be $180.
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Question 2. [4 marks] Assume that a monopolist sells a product with a total cost
function:
TC  400  Q 2
The market demand curve is given by the equation, P  500  Q .
a) [2 marks] Find the profit-maximizing output and price for this monopolist. Show your
work.
Answer:
To find the profit-maximizing price and quantity, set MR  MC .
MR  500  2Q
MC  2Q
2Q  500  2Q
4Q  500
Q  125
Plug Q into the demand curve to find P .
P  500  Q
P  500  125
P  375
b) [2 marks] Now suppose the government imposes a tax of $8 per unit of the output
produced by the monopolist. What will the new profit maximizing output and price be?
Show your work
Answer:
MR = MC implies 500-2Q = 2Q + 8 which gives Q = 123 and P = 377.
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