Consider a price taking firm that produces a homogeneous, divisible product in an industry characterized by...

Consider a price taking firm that produces a homogeneous, divisible product in an industry characterized by no transaction costs and no barriers to entry/exit.

The cost function is given by :

C(q)=800+10q +q^2 , Where q is the firm’s output.

(a)Find the average variable cost (AVC) and average total cost (ATC).

(b)Find the marginal cost function.

(c) Suppose the market price for the product (i.e. the price the firm will receive per unit sold) is $40. Will the firm be willing to produce at this price in the short-run? If yes, how much will it produce?

Solutions

Expert Solution

C = 800+ 10q + q²

(a) TVC = 10q + q²

AVC = TVC/q = (10q +q²)/q

AVC = 10 +q

ATC =TC/q = (800+ 10q + q²)/q

ATC = 800/q +10 +q

(b) MC= dTC/dq

MC = 10 +2q

Under perfectly competitive firm :P=MC

40 = 10+2q

q = 15 units.

At this output : AVC = 10+15= $25

Because P>AVC . Therefore, firm will produce in the short run.

Rahul Sunny answered 2 years ago

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