Introduction
We first set up and examine in detail the profit maximization problem of a firm. Then, 0 we derive a firm’s supply curve. The supply curve shows the levels of output that 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 – Defining Features
In order to analyse a firm’s point 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:
- The market consist of a large number of buyers and sellers
- Each firm produces and sells a homogenous product. i.e., the product of one firm cannot be differentiated from the product of any other firm.
- Entry into the market as well as exit from the market are free for firms.
- 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 market, and she gets 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 the large number 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 buyers and all sellers are completely informed about the price, quality and other relevant details about the product, as well as the market.
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 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 good 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, 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 x q
We can depict how the total revenue changes as the quantity sold changes through a total revenue curve. A total revenue curve plots the quantity sold or output on the X-axis and the Revenue earned on the Y-axis. Three observation are relevant here. First, when the output is zero, the total revenue of the firm is also zero. Therefore, the TR curve passes through point O. second, the total revenue increases as the output goes up. Moreover, the equation ‘TR = p x q’ is that of a straight line because p is constant. Third, consider the slope of this straight line. When the output is one unit (horizontal distance Oq1 the total revenue therefore, the slope of the straight line is Aq1 / Oq1 = P.
The average revenue (AR) of a firm is defined as total revenue per unit of output. Recall that if a firm’s output is q and the market price is p, then TR equals p x q. Hence
AR = TR / q
= p x q /q
= p
Profit Maximisation – A firm produces and sells a certain amount of a good. The firm’s profit, denoted by 1 , is defined to be the difference between its total revenue (TR) and its total cost of production (TC). In other words
= TR – TC
Clearly, the gap between TR and TC is the firm’s earnings net of costs. A firm wishes to maximise its profit. The firm would like to identify the quantity q0 at which its profits are maximise. By definition, then, at any quantity other than q0 the firm’s profits are less than at q0. The critical questions is: how do we identify q0?
For profits to be maximum, three conditions must hold at q0 :
- The price, p, must equal MC
- Marginal cost must be non-decreasing at q0
- 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).
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, 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.
Case 1 – Price is greater than or equal to the minimum AVC – Suppose the market price is p1, which exceeds the minimum AVC. We start out by equating p1 with SMC on the rising part of the SMC curve; this leads to the output level q1. Note also that the AVC at q1 does not exceed the market price, p1. Thus, all three conditions highlighted in section 3 are satisfied at q1. Hence, when the market price is p1, the firm’s output price is p1 the firm’s output level in the short run is equal to q1.
Case 2 – Price is less than the minimum AVC – Suppose the market price is p2, which is less than the minimum AVC. We have argued (see condition 3 in section 3) that if a profit-maximising firm produces a positive output in the short run, then the market price p2 must be greater than or equal to the AVC at that output level. But notice from AVC strictly exceeds p2. In other words, it cannot be the case that the firm supplies a positive output. So, the market price is p2 the firm produces zero output.
Determinants of a Firm’s Supply Curve – in the previous section. We have seen that a firm’s supply curve is a part of its marginal cost curve. Thus, any factor that affects a firm’s marginal cost curve is of course a determinant of its supply curve.
Technological Progress – Suppose a firm uses two factors of production – say, capital and labour – to produce a certain good. Subsequent to an organisational innovation by the firm, the same levels of capital and labour now produce more units of output. Put differently, to produce a given level of output, the organisational innovation allows the firm to use fewer units of inputs.
Input Prices – A change in input prices also affects a firm’s supply curve. It the price of an input (say, the wage rate of labour) increases, the cost of production rises. The consequent increase in the firm’s average cost at any level of output is usually accompanied by an increase in the firm’s marginal cost at any level of output; that is there is a leftward (or upward) shift of the MC curve.
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: firm1, firm2, firm3, and so on. Suppose the market price is fixed at p. Then, the output produced by the n firms in aggregate is supply of firm 1 at price p + supply of firm 2 at price p + ….. + supply of firm n at price in other words, the market supply at price p is the summation of the supplies of individual firms at that price.
Price Elasticity of Supply – The price elasticity of supply of a good measures the responsiveness of quantity supplied to changes in the price of the good. More specifically, the price elasticity of supply, denoted by es, is defined as follows
Price elasticity of supply, es = Percentage change in quantity supplied / Percentage change in price
= ΔQ / Q X100 /ΔP / P X 100
= ΔQ / Q X P /ΔP
Where ΔQ is the change in quantity of the good supplied to the market as market price changes by ΔP.
To make matters concrete, consider the following numerical example. Suppose the market for cricket balls is perfectly competitive. When the price of a cricket ball is Rs.10 let us assume that 200 cricket balls are produced in aggregate by the firms in the market. When the price of a cricket ball rises to Rs.30, let us assume that 1,000 cricket balls are produced in aggregate by the firms in the market.
The percentage change in quantity supplied and market price can be estimated using the information summarised in the table below:
Percentage change in quantity supplied = ΔQ / Q1 x 100
= Q2 – Q1/ Q1 x 100
= 1000 – 200/200 x 100
= 400
Percentage change in market price = ΔP / P1 x 100
= P2 – P1 / P1 x 100
= 30 – 10 / 10 x 100
= 200
Therefore, Price elasticity of supply, , es = 400 / 200
= 2
