Determine the best level of output for a perfectly competitive firm that sells its product at...

Determine the best level of output for a perfectly competitive firm that sells its product at

P =$2.50and faces TC = .05Q³ - 1.2Q² + 21Q + 10

Will the firm produce at this level of output? Why?

Apply MR = MC rule to find loss-minimizing (it will be a loss) output.
Check the use of the rule—does price cover average variable cost (AVC) at MR = MC? If not then the MR = MC rule is inappropriate and the firm should shut down.

Solutions

Expert Solution

Total Cost TC= 0.05Q3-1.12Q2+21Q+10

Marginal Cost MC = d/dQ TC = d/dQ (0.05Q3-1.12Q2+21Q+10) = 0.15Q2-2.24Q+21

Price = $2.5

In a perfect competition, Price = Marginal Revenue (MR)

So Equating MR = MC

0.15Q2 - 2.4 Q + 21 = 2.5

=> 0.15 Q2 - 2.4Q + 18.5 = 0

=> Q = - (-2.24) + sqrt( (-2.4)^2 - 4 * 0.15 * 18.5) / (2*0.15)

From the above equation, we do not get any real value of Q or any real value of production.

So it is not possible to have a best level of output for the firm.

Rahul Sunny answered 1 year ago

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