Suppose we have a perfectly competitive market where at the equilibrium price the total market demand...

Suppose we have a perfectly competitive market where at the equilibrium price the total market demand is 300 units. Each individual firm in the market has a cost function C(Q) = 50 -2Q + 0.4Q^2. The number of firms this market can support in the long run is _____?

Solutions

Expert Solution

The long-run output of a firm is the output level where the average total cost is minimum.

The minimum average total cost output level is found by differentiating the ATC function and equating to zero.

ATC=TC/Q=(50-2Q+0.4Q^2)/Q=50/Q-2+0.4Q

dATC/dQ=-50/Q^2 +0.4=0

0.4Q^2=50

Q^2=125

Q=11.1803399

the number of firms in the market =market output /individual firm output

=300/11.1803399

=26.8328157

=26.83

there will be 26.83 firms in the market.

Rahul Sunny answered 1 year ago

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