Short run equilibrium of the firm perfect competition

The short-run equilibrium of the firm can be illustrated by combining the short-run cost curve with 
the demand curve (AR curve) faced by the firm.Since the firm is price- taker, it has to decide 
the amount of output it should produce at the given price so as to maximise its profits.
Thus, the firm is output adjuster under perfect competition.
In order to determine the profit maximising output, the firmhas to meet two conditions :

1) Short run marginal cost curve = Marginal revenue, and SMC curve cuts the MR curve from below.

Since in perfect competition MR = AR = price (p), it follows that SMC = P.

This is the profit maximisation rule.
2) Perfect competition firms may be earning super-normal profits, incurring losses or 
just earning normal profits.Whether a firm makes abnormal profits or normal profits or losses 
depends on its cost and revenue conditions.Three equilibrium conditions can be seen.

a) AR > SAC, it means the firm is earning abnormal or supernormal profits.

As shown by the graph above, as short run average cost is below the P = AR = MR 
line at equilibrium, the firm earns super – normal  or pure profits as shown by the shaded area.

As the firm is covering all its cost thereby earning abnormal profits.

b) AR < SAC (but > AVC), then the firm is incurring losses

If the AR (P) > AVC, then he is covering entire variable costs and part of fixed costs as well. 

Here, losses in production would be less than losses in case of shut down, and the firm will definitely produce.

As shown by the below graph:

As explained above, SAC lies above the price ( P= AR= MR), the firm is incurring losses shown by the shaded area. Since price exceeds AVC, the firm continues to produce in the short run (since loss is of fixed factors only so continue production) 

c) AR = SAC, it means firm is making only normal profits.

As shown by the graph above, SAC is tangent to P = AR = MR line, the firm covers 
only its SAC,which includes normal profits. The firm, therefore earns normal profits 
(no profit no loss situation)

Short run supply curve of the firm in perfect competition

In a state of perfect competition, price is given to a firm.

Implying that, AR is constant for different levels of firm’s output.

Constant AR implies that AR=MR, 

so that the equilibrium condition that MR=MC can also be stated as P=MC.

At a given Price (P) a firm strikes its equilibrium when P=MC and MC is rising. Supply curve of the 
firm shows that various quantities of a commodity a firm is willing to supply at different prices.

The quantity which a firm is willing to supply at a particular price is determined by the equality 
of SMC and MR (=AR=P). By finding out equilibrium output at different prices and by joining 
different equilibrium points we an derive the short-run supply curve of the firm as shown by the 
below graph:

1) At P_o price (P_o = AR_o = MR_o), SMC curve cuts MR_o from below at E_o, giving  E_o as 
the equilibrium point and OQ_o as the equilibrium quantity. 
At P_o price, firm is able to cover only variable cost since P=AVC.
The firm will not operate below this point and stop production since P <  AVC (firm is unable to 
cover variable as well as fixed cost). 
Eo is known as shut-down point because the firm would not like to operate below this.

OQ_o is the minimum supply of the firm in the short run.

2) If the price rises to P₁, equilibrium point shifts to E₁, where SMC = MR, and AR = SAC, and the 

equilibrium quantity increases to Q₁.

Point E₁, where SMC curve cuts the minimum point of SAC, is known as ‘break-even point’ 

because the firm is able to cover all costs at OP₁ price.

Firm is just covering all its cost i.e. AR = AC.

At P₁ price the firm will supply OQ₁ quantity.

3) At P₂ and P₃ prices, equilibrium is at E₂ and E₃ respectively, and the amount supplied is OQ₂ and 

OQ₃ respectively. While producing OQ₂ and OQ₃ quantities of output, the firm is earning super 

normal profits since AR > SAC.

4) By joining E_o, E₁, E₂ and E₃, we get the firm’s short run supply curve.

The part of short run MC curve which lies above the minimum point of AVC curve is the 

supply curve of the firm in the short run.

Supply curve of the firm in the short run is always upward sloping.