•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.

•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 *q*_{1}, the market price *p *is lower than the AVC.

•Firm’s total revenue at *q*_{1}

TR = Price *× *Quantity

= The area of rectangle *OpAq*_{1}

•Firm’s total variable cost at *q*1

TVC = Average variable cost *× *Quantity

= The area of rectangle *OEBq*1

Firm’s profit at *q*1 is TR – (TVC + TFC);

=[the area of rectangle *OpAq*1] – [the area of rectangle *OEBq*1] – TFC

•At the output level *q*_{1}, the market price *p *is lower than the AVC.

•Firm’s total revenue at *q*_{1}

TR = Price *× *Quantity

= The area of rectangle *OpAq*_{1}

•Firm’s total variable cost at *q*1

TVC = Average variable cost *× *Quantity

= The area of rectangle *OEBq*1

Firm’s profit at *q*1 is TR – (TVC + TFC);

=[the area of rectangle *OpAq*1] – [the area of rectangle *OEBq*1] – TFC

•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 *q*1, the market price *p *is lower than the (long run) AC.

•Firm’s total revenue, TR, at *q*1 is the area of the rectangle *OpAq*1

•Firm’s total cost, TC , is the area of the rectangle *OEBq*1

•Since the area of rectangle *OEBq*1 is larger than the area of rectangle *OpAq*1, the firm incurs a loss at the output level *q*1.

•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.

•Equating the market price with the (short run) marginal cost, we obtain the output level *q*_{0}.

•At *q*_{0}, SMC slopes upwards and *p *exceeds AVC.

•Since the three conditions discussed earlier are satisfied at *q*_{0}, we maintain that the profit-maximising output level of the firm is *q*_{0}.

•At *q*_{0}, the total revenue of the firm is the area of rectangle *OpA q*_{0} (the product of price and quantity) while the total cost at *q*_{0} is the area of rectangle *OEB q*_{0} (the product of short run average cost and quantity).

•So, at *q*_{0}, the firm earns a profit equal to the area of the rectangle *EpAB*.

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