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Question:

If duo poly behavior is one that is described by Cornet, 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. 

Answer:

Market demand curve 

Q = 200 - 4p

When the call for curve is an immediate line and general price is 0, the duopolistic unearths it most worthwhile to deliver half of the maximum demand of an excellent.

At P =Rs zero, marketplace call for is Q = two hundred – 4 (0) = 200 units

If firm B does not produce anything, then the market demand confronted by means of company A is 2 hundred devices. consequently, The supply of firm A = ½ * 200 = a hundred gadgets within the next spherical, the portion of market call for faced via company B is 200 -200/2 = two hundred – one hundred = one hundred devices.

Consequently, firm B might supply ½ (two hundred – two hundred/2) = 50 units

accordingly, company B has modified its supply from 0 to 50 gadgets. To this company A might react thus and the demand faced through firm A can be 2 hundred -1/2*(two hundred-200/2) = two hundred – 50 = one hundred fifty devices consequently, firm A might supply = 150/2 = seventy five gadgets

The amount furnished through firm A and firm B is represented within the table under.

Round

Firm

Quantity Supplied

1

B

0

2

A

½ * 200 = 200/2 = 100

3

B

½ * ( 200 – ½ * 200 ) = 200/2 – 200/4

4

A

½ * 200–½(200–½∗200)200–½(200–½∗200) = 200/2 – 200/4 + 200/8

5

B

½ * {200 – ½ 200–(1/2200–½∗200)200–(1/2200–½∗200)} = 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

= 200 – Q

P = 50 – Q/4

P = 50 – ¼ (400/3) (from (1))

P = 50 – 100/3

P = 50-100/3

P = Rs. 50/3

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


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