Question

Two teenagers in my neighborhood, Randy and John, are the only ones offering to mow people’s lawns, so they are a duopoly.

(a) Initially, they are competing as Cournot oligopolists – making simultaneous decisions of how many lawns to mow. The market inverse demand is P = 150 − Q. Randy's constant marginal and average cost is $10 per lawn because he has a new mower. John’s marginal and average cost is $20 per lawn because his mower is old and constantly jams and stalls, and mowing takes him much longer and requires more effort. What are Randy and John’s profit-maximizing quantities of lawns and the market price? How much profit does each earn?

(b) Suppose Randy wants to acquire John’s business and become a monopoly in the neighborhood. If that happens, the new firm will serve the entire market and use Randy’s mower (so the firm will have his MC = $10). How much would Randy be willing to offer Steve to buy him out? (Hint: how much extra profit can the monopoly earn above what the oligopolist earned?)

(c) Would our neighborhood gain or lose if the acquisition described in part (b) happened? Discuss taking into account improved efficiency (lower cost of operation) vs. less competition (monopoly vs. duopoly).

Answer 1

a) P = 150 − Q  

Randy's constant marginal and average cost is $10

John’s marginal and average cost is $20 per lawn

Let quantity of Randy=q1 and quantity of John=q2

So Q=q1+q2

For cournot equilibrium:

Total revenue(Randy)= q1*P= 150q1-q12-q1q2

Differentiate with respect to q1

MR(Randy)= 150-2q1-q2

Condition for equilibrium:

MR=MC

150-2q1-q2=10

140=2q1+q2 Equation 1

Now for John:

Total revenue(John)= q2*P= 150q2-q22-q1q2

Differentiate with respect to q2

MR(John)= 150-2q2-q1

Condition for equilibrium:

MR=MC

150-2q2-q1=20

130=2q2+q1 Equation 2

Solve equation 1 and 2:

150=3q1

q1=50

q2=40

Q=50+40=90

Price= 150-90= 60

Profit(Randy)=(P-AC)q1= (60-10)50= 2500

Profit(John)= (P-AC)q2= (60-20)40= 1600

(b) To calculate monopoly profit for Randy:

AR=P=150-Q

MR= 150-2Q

MC=10

Condition is MR=MC

150-2Q=10

2Q=140

Q=70

P= 150-70= 80

Profit= (P-AC) Q= (80-10)70= 4900

So the profit as a monopolist (Randy) is 2400 extra as compared to as a part of oligopoly market so he is willing to provide atleast the amount which John was earning that is $1600.

(c) Generally the movement from oligopoly to monopoly create inefficiency because a monopolist has less or no competition so it has a power of price making and as an only seller it increases its price which cause some part of consumer surplus to eliminate. So here as well neighborhood lose if the acquisition described in part (b) happened and as the marginal cost is less which means more producer surplus and less consumer surplus.