Perfect Competition - Short Run Equilibrium

In the model of price and output determination under perfectly competitive market conditions, price is determined by the impersonal market forces of supply and demand, and not by individual actions of buyers and sellers. The individual firm in such a market may be said to be a price-taker. Perfect competition is used by economists not so much as an attainable goal, but as a pure state against which all other markets can be measured.

For a market to be perfectly competitive, the following necessary conditions must, in general, prevail.

1. There must be many firms acting independently. Each firm is small enough relative to the size of the market, so that a single firm's decision to either stop production entirely or to produce to full capacity will not have any perceptible effect on market supply to cause a change in market price.

2. Entry and exit from the market are free and frictionless for both the firms and consumers.

3. The products offered for sale are homogeneous and divisible into small units.

5. Buyers and sellers have perfect knowledge about the market conditions.

6. Price is determined by the impersonal market forces of supply and demand, and not by individual actions of buyers and sellers. The individual firm in such a market may be said to be a price-taker.

7. There is perfect knowledge among consumers about the price at which goods are being sold in the market. Sellers thus cannot manipulate the commodity price and thereby exploit the consumer.

8. There is perfect mobility of goods and factors of production among firms. Uniformity in factor prices is prevalent in the market.

If these necessary conditions prevail, the firm can lose its entire market if it sets its price above the market price. It can also expect no gain by lowering price, since it can sell all it wishes to produce at the market price. The competitive firm has no price discretion. Market price will not be affected by the independent action of a single firm. No firm is able to influence market price.

The objective of each firm is to maximize profit. Profit is the difference between revenue and cost of production. Marginal cost (MC) is the cost incurred to produce an additional unit of the product. If the per unit price of a commodity is greater than the marginal cost, the firm will be interested in producing more of the commodity. On the other hand if price falls below marginal cost, the firm will curtail its production.

Equilibrium condition will prevail at a point where profit is maximized. This happens where price is equal to marginal cost (P = MC). Also at the point of equilibrium, the marginal cost curve must be upward sloping.

Average Revenue (AR) = Total Revenue/No. of units sold.

Since the price is set by impersonal forces of supply and demand and every individual firm is a price taker, the average revenue (AR) curve is a straight line, parallel to the X-axis. Price always remains the same and is equal to AR. Marginal revenue (MR) is the price at which an additional unit may be sold. Since this can be done only at the current market price, marginal revenue is equal to average revenue (MR=AR) and the marginal revenue curve is the same as the average revenue curve (MR curve = AR curve). This is the demand curve for the firm. It is perfectly elastic as it is parallel to the X-axis.

The short run is a period of time in which the quantity of at least one input is fixed and the quantities of the other inputs can be varied. In the short run an increase in the variable input results in an increase in the marginal productivity of the variable input. When first few quantities of a variable input are added to a fixed input, marginal returns from the variable input flow in an increasing rate.

As marginal returns flow in an increasing rate and average fixed cost starts declining, the marginal cost per unit starts falling and the marginal cost curve shows a downward slope. After some time, as more and more of the variable input is combined with the fixed input, the marginal productivity of the variable input eventually starts declining.

So with diminishing returns, the marginal cost per unit starts increasing and the marginal cost curve starts showing an upward trend. This explains the U-shape of the marginal cost curve.

Short Run Equilibrium of a perfectly competitive firm

In the short run total fixed cost remains unchanged. So any change in total cost is caused by changes in the total variable cost in the short run. Marginal cost is the cause of change in total cost or total variable cost. Marginal cost is defined as additional variable cost incurred due to an additional change in output.
Similarly the average cost curve also takes an U-shape like the marginal cost curve. As production increases, both marginal cost curve and the average cost curve rises due to the Law of Diminishing Marginal Productivity. As the MC curve lies below the AC curve, while rising it cuts the AC curve at its minimum point. A perfectly competitive firm's supply curve is the portion of its marginal cost curve that lies above the minimum of the average (variable) cost curve.

In the short run, the demand curve, namely the average revenue curve, and the supply curve, namely the marginal cost curve, intersects at two places, E' and E. The profit maximizing P = MC is satisfied at both the points. If the firm continues to produce even after E', it will still be able to increase its revenue as marginal revenue or price will continue to be greater than marginal cost till the point E. So the firm continues production up to point E. Thus E is the point of profit maximization. E' is the point of loss minimization since until E' the marginal cost curve lies above the marginal revenue curve. E is the profit-maximizing point where the MC (supply) curve cuts the MR (demand) curve from below. Equilibrium output is OB and equilibrium price is OC. Rectangle OCEB shows the total revenue and rectangle OADB shows the total cost. Profit is shown by the rectangle ACED, which is basically 'economic profit'.

A few points

1. Price = Marginal cost (P=MC) shows the economic efficiency of the firm.
2. Marginal cost=Marginal revenue (MC=MR) is the standard condition for profit maximization. This gives the highest economic profit to the firm.
3. Price=Average revenue=Marginal revenue (P=AR=MR) shows that
a) a perfectly competitive firm has no market control
b) price is determined by the combined forces of demand and supply. The firm can sell any or all of its production at this going market price.
c) the firm is a price-taker.
d) the firm faces a perfectly elastic demand curve equal to market price.

Also read: Perfect Competition - Long Run Equilibrium
Shut down Conditions of a firm