Download Eco 301 Name_______________________________ Problem Set

Eco 301
Problem Set 11
Name_______________________________
7 December 2009
1. The demand curve for a monopolist is given by P = 350 - 7Q, and the short-run total cost curve is
given by TC = 500 + 70Q. What is the profit-maximizing price and quantity? Find the monopolist's
economic profit.
Marginal cost is equal to the slope of the straight line total cost curve: MC = 70
Marginal revenue has a slope which is twice as large as the slope of the demand curve.
MR = 350- 14Q
Set MC = MR: 70 = 350 – 14Q
Q = 280/14 = 20
P = 350 - 7(20) = 350 - 140 = 210
Profit = PQ – TC = 210(20) – [500 + 70(20)]
Profit = 4200 _ 1900 = 2300
2. A monopolist faces two separate demand curves: P1 = 65 – 2Ql and P2 = 35 – 3Q2. The total cost
curve is TC = 7 + 5Q. Find Q1, Q2, P1, P2.
MC = slope of TC = 5
MR1 = 65 - 4Q1
MR2 = 35 - 6Q2
Set MR1 = MR2 = MC
First solve for Q1 and P1: 65 - 4Q1 = 5
4Q1 = 60
Q1 = 60/4 = 15
P1 = 65 - 2(15) = 35
Next solve for Q2 and P2: 35 - 6Q2 = 5
6Q2 = 30
Q2 =30/6=5
P2 = 35 - 3(5) = 20
3. Find the price elasticities at the profit maximizing points for Problem 2.
elasticity l = ∆Q1/∆P1 (P1/Q1) = (-15/30) (35/15) = -1.167
elasticity 2 = (-5/15)(20/5) = -1.333
Check: MR= P(1 - 1/η)
MR1 = 35(1 - 1/1.1671) = 5
MR2 = 20(1 - 1/1.33) = 5
4. The price elasticity of demand for popsicles on a beach in a small east coast resort town is -5 in the
month of May, while in July the elasticity falls to -1.5. A single vendor supplies the popsicles to the
beachcombers. If the marginal cost per popsicle is $0.60, how much should the vendor charge per
popsicle in May and July?
Set MC = MR = $0.60
MR = P(1 - 1/elasticity)
P1 (May):
$0.60 = P1[1 – (1/5)]: $0.60 = 0.80 P1: P1 = $0.75
P2 (July):
$0.60 = P2[ 1 - (1/1.5)]: $0.60 = 0.333P2: P2= $0.60/0.333 = $1.80