The theory of the firm under perfect competition Chapter 4

The theory of the firm under perfect competition Introduction

The theory of the firm under Perfect Competition Chapter 4 In the previous chapter, we studied concepts related to a firm’s production function and cost curves. The focus of this chapter is different. Here we ask: how does a firm decide how much to produce? Our answer to this question is by no means simple or uncontroversial. We base our answer on a critical, if somewhat unreasonable, assumption about firm behavior – a firm, we maintain, is a

ruthless profit maximizer. So, the amount that a firm produces and sells in the market is that which maximizes its profit. Here, we also assume that the firm sells whatever it produces so that ‘output’ and quantity sold are often used interchangeably. The structure of this chapter is as follows. We first set up and examine in detail the profit maximization problem of a firm. Then, we derive a firm’s

supply curve. The supply curve shows the levels of output that a firm chooses to produce at different market prices. Finally, we study how to aggregate the supply curves of individual firms and obtain the market supply curve.

Perfect Competition

To analyze a firm’s profit maximization problem, we must first specify the market environment in which the firm functions. In this chapter, we study a market environment called perfect competition. A perfectly competitive market has the following defining features: 1. The market consists of a large number of buyers and sellers 2. Each firm produces and sells a

The theory of the firm under perfect competition Chapter 4

homogenous product. i.e., the product of one firm cannot be differentiated from the product of any other firm. 3. Entry into the market as well as exit from the market are free for firms. 4. Information is perfect. The existence of a large number of buyers and sellers means that each individual buyer and seller is very small compared to the size of the market. This means that no individual buyer or

seller can influence the market by their size. Homogenous products further mean that the product of each firm is identical. So a buyer can choose to buy from any firm in the market, and she get the same product. Free entry and exit mean that it is easy for firms to enter the market, as well as to leave it. This condition is essential for large numbers of firms to exist. If entry was difficult, or restricted, then the number of firms in the market could be small. Perfect information implies that all

The theory of the firm under perfect competition Chapter 4

buyers and all sellers are completely informed about the price, quality, and other relevant details about the product, as well as the market. These features result in the single most distinguishing characteristic of perfect competition: price-taking behaviour. From the viewpoint of a firm, what does price-taking entail? A price-taking firm believes that if it sets a price above the market price, it will be unable to sell any quantity of the good that it produces. On the other hand, should the set price be

less than or equal to the market price, the firm can sell as many units of the good as it wants to sell. From the viewpoint of a buyer, what does price-taking entail? A buyer would obviously like to buy the good at the lowest possible price. However, a price-taking buyer believes that if she asks for a price below the market price, no firm will be willing to sell to her. On the other hand, should the price

asked be greater than or equal to the market price, the buyer can obtain as many units of the good as she desires to buy. Price-taking is often thought to be a reasonable assumption when the market has many firms and buyers have perfect information about the price prevailing in the market. Why?

Let us start with a situation where each firm in the market charges the same (market) price. Suppose, now, that a certain firm raises its price above the market price. Observe that since all firms produce the same good and all buyers are aware of the market price, the firm in question loses all its buyers

. Furthermore, as these buyers switch their purchases to other firms, no “adjustment” problems arise; their demand is readily accommodated when there are so many other firms in the market. Recall, now, that an individual firm’s inability to sell any amount of the good at a price exceeding the market price is precisely what the price-taking assumption stipulates.

Revenue

We have indicated that in a perfectly competitive market, a firm believes that it can sell as many units of the good as it wants by setting a price less than or equal to the market price. But, if this is the case, surely there is no reason to set a price lower than the market price. In other words, should the firm desire to sell some amount of the good, the price that it sets is exactly equal to the market price.

A firm earns revenue by selling the goods that it produces in the market. Let the market price of a unit of the good be p. Let q be the quantity of the good produced, and therefore sold, by the firm at price p. Then, the total revenue (TR) of the firm is defined as the market price of the good (p) multiplied by the firm’s output (q). Hence, TR = p × q.

To make matters concrete, consider the following numerical example. Let the market for candles be perfectly competitive and let the market price of a box of candles be Rs 10. For a candle manufacturer, Table 4.1 shows how total revenue is related to output. Notice that when no box is sold, TR is equal to zero; if one box of candles is sold, TR is equal to 1×Rs 10= Rs 10; if two boxes of candles are produced, TR is equal to 2 × Rs 10 = Rs 20; and so on.

We can depict how the total revenue changes as the quantity sold changes through a Total Revenue Curve. A total revenue curve plots

The theory of the firm under perfect competition Chapter 4

Profit Maximization

A firm produces and sells a certain amount of goods. 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). In other words:

π = TR – TC

Clearly, the gap between TR and TC is the firm’s earnings net of costs. A firm wishes to maximize its profit. The firm would like to identify the quantity ( q_0 ) at which its profits are maximum. By definition, then, at any quantity other than ( q_0 ), the firm’s profits are less than at ( q_0 ). The critical question is: how do we identify ( q_0 )?

For-profits to be maximum, three conditions must hold at ( q_0 ):

  1. The price, p, must equal MC.
  2. The marginal cost must be non-decreasing at ( q_0 ).
  3. For the firm to continue to produce, in the short run, the price must be greater than the average variable cost (p > AVC); in the long run, the price must be greater than the average cost (p > AC).

Condition 1:
Profits are the difference between total revenue and total cost. Both total revenue and total cost increase as output increases. Notice that as long as the change in total revenue is greater than the change in total cost, profits will continue to increase. Recall that the change in total revenue per unit

increase in output is the marginal revenue, and the 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. By the same logic, 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.

In other words, profits are maximum at the level of output (which we have called ( q_0 )) for which MR = MC.

For the perfectly competitive firm, we have established that MR = P. So, the firm’s profit-maximizing output becomes the level of output at which P = MC.

Condition 2:
Consider the second condition that must hold when the profit-maximizing output level is positive. Why is it the case that the marginal cost curve cannot slope downward at this point?

Supply Curve of a firm

A firm’s ‘supply’ is the quantity that it chooses to sell at a given price, given technology, and given the prices of factors of production. A table describing the quantities sold by a firm at various prices, with technology and prices of factors remaining unchanged, is called a supply schedule. We may also represent the information as a graph, called a supply curve. The supply

A firm’s ‘supply’ is the quantity that it chooses to sell at a given price, given technology, and given the prices of factors of production. A table describing the quantities sold by a firm at various prices, with technology and prices of factors remaining unchanged, is called a supply schedule. We may also

represent the information as a graph, called a supply curve. The supply curve of a firm shows the levels of output (plotted on the x-axis) that the firm chooses to produce corresponding to different values of the market price (plotted on the y-axis), again keeping technology and prices of factors of production unchanged. We distinguish between the short-run supply curve and the long-run supply curve.

Short Run Supply Curve of a Firm

Let us turn to Figure 4.7 and derive a firm’s short-run supply curve. We shall split this derivation into two parts. We first determine a firm’s profit-maximizing output level when the market price is greater than or equal to the minimum AVC. This done, we determine the firm’s profit-maximizing output level when the market price is less than the minimum AVC.

Case 1: Price is Greater Than or Equal to the Minimum AVC

Suppose the market price is ( p_1 ), which exceeds the minimum AVC. We start out by equating ( p_1 ) with SMC on the rising part of the SMC curve; this leads to the output level ( q_1 ). Note also that the AVC at ( q_1 ) does not exceed the market price, ( p_1 ). Thus, all three conditions highlighted in section 3 are satisfied at ( q_1 ). Hence, when the market price is ( p_1 ), the firm’s output level in the short run is equal to ( q_1 ).

Case 2: Price is Less Than the Minimum AVC

Suppose the market price is ( p_2 ), which is less than the minimum AVC.

Market supply Curve

The market supply curve shows the output levels (plotted on the x-axis) that firms in the market produce in aggregate corresponding to different values of the market price (plotted on the y-axis). How is the market supply curve derived? Consider a market with ( n ) firms: firm 1, firm 2, firm 3, and so on. Suppose the market price is fixed at ( p ). Then, the output produced by the ( n ) firms in aggregate is ([ \text{supply of firm 1 at price } p ] + [ \text{supply of firm 2 at price } p ] + … + [ \text{supply of firm } n \text{ at price } p ]). In other words, the market supply at a price ( p ) is the summation of the supplies of individual firms at that price.

Let us now construct the market supply curve geometrically with just two firms in the market: firm 1 and firm 2. The two firms have different cost structures. Firm 1 will not produce anything if the market price is less than ( p_1 ), while Firm 2 will not produce anything if the market price is less than ( p_2 ). Assume also that ( p_2 ) is greater than ( p_1 ).

In panel (a) of Figure 4.13, we have the supply curve of firm 1, denoted by ( S_1 ); in panel (b), we have the supply curve of firm 2, denoted by ( S_2 ). Panel (c) of Figure 4.13 shows the market supply curve, denoted by ( S_m ). When the market price is strictly below ( p_1 ), both firms choose not to produce any amount of the good; hence, market supply will also be zero for all such prices. For a market price above ( p_1 ) but below ( p_2 ), only firm 1 will produce, and the market supply will be equal to the supply of firm 1. For prices above ( p_2 ), both firms will produce, and the market supply will be the sum of the supplies of both firms.

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