Economics (NCERT) Notes → Class XII

4.4 Profit Maximization-II

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)
•Third condition has two parts:
     •one part applies in the short run
     •Second part applies in the long run.
 
Case 1: Price must be greater than or equal to AVC in the short run
•We will show that the statement is true by arguing that a profit maximising firm, in the short run, will not produce at an output level wherein the market price is lower than the AVC.
•At the output level q1, the market price p is lower than the AVC.
•Firm’s total revenue at q1
     TR = Price × Quantity
     = The area of rectangle OpAq1
•Firm’s total variable cost at q1
     TVC = Average variable cost × Quantity
     = The area of rectangle OEBq1
Firm’s profit at q1 is TR – (TVC + TFC);
=[the area of rectangle OpAq1] – [the area of rectangle OEBq1] – TFC
•At the output level q1, the market price p is lower than the AVC.
•Firm’s total revenue at q1
TR = Price × Quantity
= The area of rectangle OpAq1
•Firm’s total variable cost at q1
TVC = Average variable cost × Quantity
= The area of rectangle OEBq1
Firm’s profit at q1 is TR – (TVC + TFC);
=[the area of rectangle OpAq1] – [the area of rectangle OEBq1] – TFC
 
Case 2: Price must be greater than or equal to AC in the long run
•We will show that the statement is true by arguing that a profit-maximizing firm, in the long run, will not produce at an output level wherein the market price is lower than the AC.
•At the output level q1, the market price p is lower than the (long run) AC.
     •Firm’s total revenue, TR, at q1 is the area of the rectangle OpAq1
     •Firm’s total cost, TC , is the area of the rectangle OEBq1  
•Since the area of rectangle OEBq1 is larger than the area of rectangle OpAq1, the firm incurs a loss at the output level q1.
•But, in the long run set-up, a firm that shuts down production has a profit of zero.
•Hence, the firm chooses to exit in this case.
 
The Profit Maximisation Problem: Graphical Representation
•Equating the market price with the (short run) marginal cost, we obtain the output level q0.
•At q0, SMC slopes upwards and p exceeds AVC.
•Since the three conditions discussed earlier are satisfied at q0, we maintain that the profit-maximising output level of the firm is q0.
•At q0, the total revenue of the firm is the area of rectangle OpA q0 (the product of price and quantity) while the total cost at q0 is the area of rectangle OEB q0 (the product of short run average cost and quantity).
•So, at q0, the firm earns a profit equal to the area of the rectangle EpAB.



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