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If Duopoly Behaviour is One that is Described by Cournot, the Market Demand Curve is Given by the Equation Q = 200 − 4p and Both the Firms - Economics

ConceptOther Non - Perfectly Competitive Markets

Question

If duopoly behaviour is one that is described by Cournot, the market demand curve is given by the equation q = 200 − 4p and both the firms have zero costs, find the quantity supplied by each firm in equilibrium and the equilibrium market price.

Solution

Market demand curve

Q = 200 − 4p

When the demand curve is a straight line and total cost is zero, the duopolist finds it most profitable to supply half of the maximum demand of a good.

At P = Rs 0, market demand is

Q = 200 − 4 (0)

= 200 units

If firm B does not produce anything, then the market demand faced by firm A is 200 units.

∴ The supply of firm A = 1/2xx200 units

In the next round, the portion of market demand faced by firm B is 200 -200/2=200-100=100 units

∴ Firm B would supply 1/2xx(200-200/2) = 50 units

Thus, firm B has changed its supply from zero to 50 units. To this firm A would react accordingly and the demand faced by firm A will be 200-1/2xx(200-200/2)

= 200 − 50

= 150 units

∴ Firm A would supply = 150/2=75 units

The quantity supplied by firm A and firm B is represented in the table below.

 Round Firm Quantity Supplied 1 B 0 2 A 1/2[200-1/2xx200=100] 3 B 1/2[200-1/2xx200]=200/2+200/4 4 A 1/2[200-1/2(200-1/2xx200)]=200/2-200/4+200/8 5 B 1/2{200-1/2[200-1/2(200-1/2xx200)]}=200/2-200/4+200/8-200/16

Therefore, the equilibrium output supplied by firm A

= 200/2- 200/4+200/8-200/16+200/32-200/64+200/128+200/256+..............=200/3 units.

Similarly, the equilibrium output supplied by firm B = 200/3 units.

Market Supply = Supply by firm A + Supply by firm B

=200/3+200/3

Equilibrium output or Market Supply = Q = =400/3 units  ....... (1)

For equilibrium price

Q = 200 − 4p

4p = 200 − Q

p=50-Q/4

p=50-1/4(400/3)    .....(From(1)]

p=50-100/3

p=(150-100)/3

p = Rs 50/3

Therefore, the equilibrium output (total) is 400/3 units and equilibrium price is Rs 50/3.

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Solution If Duopoly Behaviour is One that is Described by Cournot, the Market Demand Curve is Given by the Equation Q = 200 − 4p and Both the Firms Concept: Other Non - Perfectly Competitive Markets.
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