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4.3 Profit Maximization-I

Profit of a firm (π)
•The firm’s profit (denoted by π) is defined to be the difference between its total revenue (TR) and its total cost of production (TC ).
•Mathematically, Profit  = TR – TC
 
Maximization of Profit
•A firm wishes to maximise its profit.
•The firm would like to identify the quantity q0 at which its profits are maximum.
•By definition, then, at any quantity other than q0, the firm’s profits are less than at q0.  
 
Conditions for the profits to be maximum
•Three conditions must hold at q0:
     1. The price, p, must equal MC
     2. Marginal cost must be non-decreasing at q0
     3. For the firm to continue to produce,
        •In the short run, price must be greater than the average variable cost (p > AVC); 
        •In the long run, price must be greater than the average cost (p > AC)
 
Condition 1 (The price, p, must equal MC)
•Profits are the difference between total revenue and total cost.
•Both total revenue and total cost increase as output increases.
•As long as the change in total revenue is greater than the change in total cost, profits will continue to increase.
•We know that
     •Change in total revenue per unit increase in output is the marginal revenue; and
     •Change in total cost per unit increase in output is the marginal cost.
•Therefore, we can conclude that as long as marginal revenue is greater than marginal cost, profits are increasing.
•Similarly, as long as marginal revenue is less than marginal cost, profits will fall.
•It follows that for profits to be maximum, marginal revenue should equal marginal cost.
•Hence, profits are maximum at the level of output (q0) for which MR = MC
•For the perfectly competitive firm, we have established that the MR = P
•So the firm’s profit maximizing output becomes the level of output at which P=MC.
 
Condition 2 (Marginal cost must be non-decreasing at q0)
•At output levels q1 and q4, the market price is equal to the marginal cost.
•However, at the output level q1, the marginal cost curve is downward sloping.
•We claim that q1 cannot be a profit-maximising output level.
•Why?
•For all output levels slightly to the right of q1, the market price is higher than the marginal cost.
•Hence, the company is making more profit by selling more than q1
•This being the case, q1 cannot be a profit-maximising output level.
 
Condition 3
•Condition 3: For the firm to continue to produce,
     •in the short run, price must be greater than the average variable cost (p > AVC); 
     •in the long run, price must be greater than the average cost (p > AC)
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