# Derivation of Short-Run and Long-Run Supply Curves for an Industry

## Introduction

Supply curves are derived from cost curves because supply depends on cost of production. The concept of supply curve is relevant only under perfect competition. In a competitive market price is determined by the two forces of demand and supply. Since in a perfectly competitive market the supply of each seller is only negligible portion of the market supply, he has no control over the price. Like an individual consumer, he is a price-taker; as an optimistic seller, he believes that he can sell any quantity he is able to produce at the prevailing price. If the price rises, he supplies more. In the case of monopoly or imperfect competition, the producer can fix the price. The producer will choose that price-output combination which maximizes his profit. However, a competitive producer has to adjust his supply as per the change in price.

## Supply Curve of an Industry in the Short-Run

A competitive industry is a collection of firms producing a homogeneous product. Thus, firms in a perfectly competitive market all taken together form an industry. The industry’s supply curve is obtained by summing up the individual firm’s supply curves. The industry supply curve portrays the functional relationship between the price of a good, and various quantities of the goods offered for sale by all the firms in the market.

A competitive firm always adjusts its output until the price is equal to its marginal cost so that it can maximize its profits. The marginal cost curve therefore gives the relationship between price and the quantity supplied by the competitive firm. Price must exceed AVC, otherwise the firm will cease its operations. Quantity supplied by the firm at any price below AVC will be zero. The competitive firm’s short-run supply curve is therefore that portion of its marginal cost curve, which is above the minimum point of the AVC curve.

Close Down Range

If the price is lower than the minimum AVC, the firm should shut down its operations. Since price cannot cover even AVC, continuing the operations of the firm will invite the shutdown of the firm.

Loss Minimization of Range

If the price is equal to AVC, then the firm has to decide whether to run the firm or close it down. However, the firm will continue its operations due to various reasons.

1. A higher valuation is given to a going concern than to a closed firm.
2. More prestige is attached to the owner or manager of a going concern than to that of a firm that has ceased to operate.
3. By keeping the operation going, the firm will not lose its competent personnel.

Thus, if the price is above AVC and below AC, the firm is in the range of loss minimization. At OP1 price, the firm will produce and supply OM1 output. If there are 100 firms in the industry, the industry as a whole will supply OM1 × 100 outputs.

Profit Maximization Range

At price OP2, the firm will produce and supply OM2 level of output. Between price OP2 and OP3, there is an area of profit maximization. At OM2 output marginal cost is equal to price. The industry as a whole will be supplying OM2 × 100. Similarly, at OP3 price, the output will be OM3 × 100.

Since the individual firm is a ‘price taker’ and ‘quantity adjuster’ the price line AR is a horizontal line and MR = AR. Hence, when MC is equal to price, it is equal to MR also.

The short-run supply curve of the industry is shown in figure 1(B). It is derived by the lateral summation of supply curves of all the firms in the industry. The short-run supply curve has a positive slope indicating that supply increases as price increases. At OP1, price industry’s supply is OQ1, at OP2 price it is OQ2 and at OP3 price it is OQ3.

## Supply Curve of an Industry in the Long-Run

In order to discuss the long-run pricing, it is necessary to understand how the entry of new firms into an industry affects the prices of the factors of production.

An industry is a constant cost industry if the prices of the factors of production remain constant as the industry’s output expands. An industry is an increasing cost industry, if the prices of the factors of production increase as the industry’s output expands. An industry is a decreasing cost industry if the prices of the factors of production decrease as the industry’s output expands.

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Constant Cost Industry

If external economies and diseconomies exactly balance, the cost of production will become constant. The duration of the supply curve of a constant cost industry is illustrated as follows:

The pencil-making industry is often quoted as an example. This industry uses an insignificant portion of the total demand for wood and lead, which are the main inputs of the pencil making industry – a relatively large increase in the industry’s demand for wood and lead will not affect their prices. Similarly, the increased demand for labor as a result of the expansion of the pencil-making industry will not raise the wages of labor employed by it.

It can be seen from the left hand side diagram that at the price OP1, the firm is in the long-run producing OM output. The price OP1 is equal to the long-run average and marginal costs. If we assume that there are 100 firms in the industry and the cost curves of all firms are identical at price OP1, the whole industry will supply OM × 160 quantity of the product, which may be represented by OQ1.

Now if the demand for the product increases more firms will enter into the industry in the long-run to meet the increased demand. Since constant costs are assumed to prevail, the price will remain at OP1. If the number of firms becomes 160, the quantity supplied by the industry will increase to OM × 160, which is represented by OQ2.

Increasing Cost Industry

An industry is said to be an increasing cost industry if its long-run supply curve has a positive slope, indicating that the prices of factors increase as the industry’s output expands. In the case of an increasing cost industry, the external diseconomies will overweigh the external economies.

Suppose the industry is operating under the law of increasing cost or diminishing returns. The entry of new firms increases the demand for factors. In case the supply of factors is inelastic to the industry, the increased demand for the factors will result in higher prices of the factors, thus shifting the cost curve upwards.

Initially the firms are in equilibrium at E. the price is OP1 and output is OM1. The price OP1 becomes equal to LAC1 and LMC1. Suppose we assume that all the 100 firms in the industry have identical cost curves. The industry’s supply will be OM1 × 100, which is represented by OQ1.

Suppose the price rises to OP2. This attracts new firms into the industry and the firms increase to 160. There will be net external diseconomies as a result of an increase in input prices. Given the new cost curve LAC2 and LMC2, the firms are in equilibrium at point E1. At the price OP2, each firm will be producing an output OM2. At this output, the price OP2 becomes equal to both LAC2 and LMC2. The total output of the industry will be OM2 × 160 = OQ2. This is shown in the right hand side of the figure. The supply curve (LRS) slopes upwards to the right indicating that supply extends with a rise in price.

Decreasing Cost Industry

An industry is said to be a decreasing cost industry, if its long-run supply curve has a negative slope indicating that the prices of factors fall as the industry’s output expands.

In the case of a decreasing cost industry, the entry of new firms may provide a larger pool of trained labor, so that the cost associated with the hiring of workers is reduced. Entry of new firms may also provide the critical mass of industrialization, which permits the development of a more efficient transportation and communication network. These cost reductions are called external economies, which accrue to the industry as well as to the firms.

The original equilibrium is at point E when the firms supply OM1 quantity at OP1 price. At OP1 price, if there are 100 firms (with identical cost curves) the total output will be OM1 × 100 = OQ1. This is shown on the right hand side of the figure. (4(B)).

Suppose there is an increase in the demand for the product, new firms enter into the industry. Because of the emergence of external economies, cost curves shift downwards from LAC1 to LAC2 and LMC2. The firms will be in equilibrium at point E1, where OM2 output is supplied by the firms at OP2 price. The total output of the industry is OM2 × 160 (assuming that the number of firms are 160). It is equal to OQ2 as shown in the right hand side of the figure. The long run supply curve is the line AB that has negative slope. This implies that if there are strong external economies the industry’s supply can expand in the long run at a decreasing price.