A competitive firm sells its product at a price of $0.10 per unit. Its total and

Question

A competitive firm sells its product at a price of $0.10 per unit. Its total and marginal cost functions are:

            TC = 5 - 0.5Q + 0.001Q2

            MC = -0.5 + 0.002Q,                   

where TC is total cost ($) and Q is output rate (units per time period).

a.   Determine the output rate that maximizes profit or minimizes losses in the short term and calculate profits.

b.   If input prices increase and cause the cost functions to become

            TC = 5 - 0.10Q + 0.002Q2

            MC = -0.10 + 0.004Q,

what will the new equilibrium output rate be? Explain what happened to the profit maximizing output rate and the level of profits when input prices were increased.

Explanation / Answer

1. Profit maximizing output:

MR = MC

MR = Price

MC = -0.5 +0.002Q

0.10 = -0.5 +0.002Q

Q = 75

Profit = TR - TC

Profit = 6.875

2. Q = 50

Profit = 5

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