A price-taker firm has an average total cost function given by ATC = 972 / q...

A price-taker firm has an average total cost function given by ATC = 972 / q + 5 + 3q . Calculate the price at which the firm would zero profits.

Expert Solution

Zero profit means P = ATC. For a price taker firm the price is equal to ATC athe minimum point of ATC. So, ATC will be minimum when the first order derivative of ATC function is equal to zero. Thus,

ATC = 972/q + 5 + 3q = 972q^-1 + 5 + 3q

The first order derivative of ATC = -972q^-1-1 + 0 + 3

= -972q^-2 + 3

= -(972/q²) + 3

So, -(972/q²) + 3 = 0

972/q² = 3

q² = 972 / 3 = 324

q = = 18

So, ATC = 972/q + 5 + 3q = 972/18 + 5 + 3(18) = 54 + 5 + 54 = $113

Thus, the price at which the firm would earn zero profits is $113.

Rahul Sunny answered 2 years ago

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