Chapter 6 Perfect competition in a single market

6.1 Introduction

The analysis of consumer behaviour in Chapter 2 showed how we can derive the demand curve in a market. In the first part of this chapter, we analyse the behaviour of competitive firms, and show how we can derive the supply curve in a market. In the second half of this chapter, we study the partial equilibrium competitive model that puts demand and supply together to derive the equilibrium in individual markets. Note that this is different from a ‘general equilibrium’ analysis that considers all markets in an economy together, which we do in the next chapter. The partial equilibrium approach allows us to understand in a simple setting how small price-taking agents (both buyers and sellers) come together in a competitive market. Furthermore, we can use this ‘supply-demand’ model to carry out a partial equilibrium analysis of the impact of policy on specific markets.

In this chapter we aim to study the behaviour of competitive firms and the outcome under competition in specific markets. In other words, we analyse the partial equilibrium competitive model here. We aim to show that even though such competition is an idealised extreme, the model is very useful in studying a variety of markets and policy initiatives.

* explain the supply decision of a price-taking firm in the short run and in the long run
* derive the industry supply curve in the short run and in the long run
* calculate the market equilibrium price and quantity given supply and demand curves
* analyse the impact of entry and exit decisions of firms and their impact on industry supply
* relate the nature of input costs to the long-run industry supply curve explain supply elasticities
* explain the concept of producer surplus and use this in conjunction with consumer
surplus as a measure of welfare
* use the measure of welfare to evaluate the impact of a variety of tax and subsidy policies on the market
* explain the concept of the incidence of a tax or a subsidy
* use the measure of welfare to evaluate the impact of policies: examples include price ceilings (such as rent control), price floors (such as minimum price guarantees for agricultural products), permits and quotas, price support policies as well as trade policies involving tariffs and quotas.

6.3 A general comment on zero profit

In this and other chapters, we refer to firms earning a zero profit. You might wonder whether this assumption makes sense – after all, why would a firm bother producing if it makes no profits at all? However, the assumption of zero profits does not imply the absence of an accounting profit. Each factor of production must cover at least their opportunity cost, which is the amount the factor would earn in its next best use.

In accounting terms there will be a ‘normal’ level of profit that covers such opportunity costs. The zero-profit assumption simply means that there are no profits beyond this normal level. This is why sometimes the assumption is stated as ‘no super-normal profits.’

6.4 Supply decision by a price-taking firm

In discussing markets, we often talk about market supply and market demand and how the intersection of the two determines market equilibrium. But does any kind of market structure produce a market supply curve? In fact, this is not true. A market supply curve is an appropriate concept only when the firms in an industry are price-takers. In this case, we can associate a specific firm and industry output to each price and, therefore, trace out firm and industry supply curves, respectively. But if a firm has control over price, that is, if the market price depends on firm output, the firm would consider market demand and see at which point on market demand it should produce. In this case, there is no unique relationship between price and output. As demand conditions vary, so would the price-quantity pair of a firm vary. Therefore, we cannot trace out a supply curve.

Short-run supply

A price-taking firm faces a notional perfectly-elastic demand curve. Essentially, the firm can sell any amount at the given price, P . The idea is that a firm in a competitive market is a very small part of the overall market so that whatever amount such a firm produces is a very small part of the overall supply in the market. Therefore, variations in the output of a single firm have a vanishingly small impact on the market price, hence the notional firm demand curve is horizontal.

Short-run profit maximisation by a competitive firm. The demand curve facing the firm is perfectly elastic at price P (i.e. the firm is a price-taker). Profit is maximised at P = MC and the maximised value of profit is (P − AC(Q^∗ )) Q^∗ .

The (inverse) supply curve of a price-taking firm is given by: P = MC for P > AVC.

In other words, the supply curve is the part of the short-run MC that is above the AVC curve.

Long-run supply

In the long run, all factors are variable. Therefore, the (inverse) supply curve is given by the LRMC curve above the minimum point of the LRAC curve:

P = LRMC for P >= LRAC_min .

6.5 Market supply and market equilibrium

Short run

The short-run market supply curve can be obtained by summing individual firm supply curves.

The intersection of market demand and market supply determines the market equilibrium price and quantity.

Long Run

If there is a fixed number of firms in an industry, and no entry is possible, the long-run
firm supply curve is simply:

P = LRMC. for P >= LRAC_min

and the long-run market supply is simply the firms’ supplies added together.

However, once we allow entry and exit, this is a little different. The process of entry and exit implies that firms always end up earning a zero profit and producing at the minimum long-run average cost. How this minimum behaves as the market output expands determines the shape of the long-run market supply curve.

If input costs do not rise as new firms enter, the long-run supply curve is horizontal at the minimum LRAC. In this case the long-run market supply equation is:

P = LRAC_min .

If input costs rise, we have an increasing-cost industry and you should be able to show that in this case we get a long-run market supply curve that slopes upwards. Similarly, if we have a decreasing-cost industry, the long-run market supply curve slopes downwards (rare, if they exist at all).

Just as we can calculate demand elasticities, we can calculate supply elasticities in the
short and long runs. The elasticity of supply is simply:

ε_S = (P/Q^S)(dQ^S/dP)

This is positive in all cases other than for the long-run supply under a decreasing-cost industry (if this is at all possible).

Furthermore, the long-run supply curves are more elastic than their short-run counterparts

6.6 Producer surplus

Just as we derived consumer surplus using demand curves, we can describe producer surplus using upward-sloping supply curves. Understanding consumer and producer surplus thoroughly is very
important for working through the variety of applications of the competitive model of supply and demand.

6.7 Applications of the supply-demand model: partial equilibrium analysis

Much of our understanding of tax and subsidy policies, as well as price control policies, derives from this fairly simple model. The simplicity of the model and yet its capacity to accommodate a large number of variations makes it a powerful tool of analysis.

However, there is also a limitation. We are looking at the impact of policy on the specific market on which it is aimed. For example, if the government announces a rent control policy, we look at the impact on the market for house rentals. This type of analysis is known as since we are not considering the impact of a policy on other markets, or the feedback effect from these other markets on the original market.

Tax: deadweight loss and incidence

One of the most important applications of the supply-demand model is to study the impact of taxes and subsidies. There are two aspects that you should understand. The first is the impact on efficiency. A per-unit tax (or subsidy) creates a deadweight loss. Second, there is the question of incidence, i.e. which side of the market actually pays the tax or enjoys the subsidy in equilibrium.

Price ceiling

A different type of intervention involves setting a price ceiling. Rent control is an example of such a policy. Of course, to be effective, the ceiling needs to be below the price that would, in the absence of any control, clear the market. It is clear that rent control works well (generates a lower efficiency loss) when supply is relatively inelastic. This would happen, for example, if suppliers do not have many alternative uses for the existing housing stock.

The analysis above makes one implicit assumption that is unlikely to be true in practice. Note that at the ceiling price, demand exceeds supply. In other words, more consumers are queuing up for the object (rent-controlled apartments, say) than the number of objects available for sale. It is assumed implicitly that the consumers who value the object the most are the ones who obtain it. In other words, the analysis above is the most optimistic case.

Price floor

A minimum wage is the most well-known price floor policy. Note that some of the surplus is lost, and out of the rest, some of the consumer surplus is shifted to suppliers. Note also that there is an implicit assumption that the sellers with the lowest cost (those at the lowest end of the supply curve) are the ones supplying in the market. However, this need not be the case: all sellers up to production level Q 2 would be happy to supply the product at the price floor, therefore a misallocation is possible, which would raise the deadweight loss further.

Quota

Note that, as in the case of a price floor above, some of the surplus is lost, and out of the rest, some of the consumer surplus is shifted to suppliers. Note also that there is an implicit assumption that the sellers with the lowest cost (those at the lowest end of the supply curve) are the ones who obtain the quota. Again, a misallocation would raise the deadweight loss. However, irrespective of the initial allocation of quotas, if they are tradeable, it is likely that they would end up in the hands of the most efficient sellers. In this respect, the implicit assumption is perhaps not too restrictive in this case.

Price support policy

Under a price support policy for agricultural products, the government maintains a minimum market price in order to ensure a minimum income level for farmers. To ensure that the price does not fall below the announced support price, the government buys up any excess supply at the support price.

More generally, this shows why income generation for farmers through price support policies (the EU common agricultural policy is an important example) is inefficient. The policy gets farmers to produce more (even though demand is less at a higher price) and then spends government revenue to buy up the unsold amount. This is, of course, a poor use of resources.

A better solution is to simply give the amount of money to farmers directly, and not interfere with the market. This avoids the unnecessary excess production, and incurs no deadweight loss.

Tariffs and quotas

Suppose that the government wants to raise the price of a commodity on the domestic market by reducing imports. Assume that the importing country is a price-taker in world markets. Below, we compare the welfare effects of an import tariff with an import quota.

Reading: Nicholson, W., Synder, C., Intermediate Microeconomics and its application (eleventh edition), South-Western, Cengage Learning, 2010

Chapter 9: Perfect Competition in a Single Market

In the analysis of price determination, it is important to decide the length of time that is to be
allowed for a supply response to changing demand conditions. The pattern of equilibrium prices will be different if we are talking about a very short period of time during which supply is essentially fixed and unchanging than if we are envisioning a very long-run process in which it is possible for entirely new firms to enter a market.
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Supply response: The change in quantity of output supplied in response to a change in demand conditions.
Market period: A short period of time during which quantity supplied is fixed.
Equilibrium price: The price at which the quantity demanded by buyers of a good is equal to the quantity supplied by sellers of the good.
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Short-run market supply curve: The relationship between market price and quantity supplied of a good in the short run.
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Re asons for a Shift in a Demand or Supply Curve
DEMAND
Shifts outward (->) because
• Income increases
• Price of substitute rises
• Price of complement falls
• Preferences for good

Shifts inward ( • Income falls
• Price of substitute falls
• Price of complement rises
• Preferences for good diminish

SUPPLY
Increase Shifts outward (->) because
• Input prices fall
• Technology improves

Shifts inward ( • Input prices rise
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Short-run elasticity of supply: The percentage change in quantity supplied in the short run in response to a 1 percent change in price.

Short-run supply elasticity = % in quantity supplied/ % change in price

For example, if the short-run supply elasticity is 2.0, each 1 percent increase in price results in a 2 percent increase in quantity supplied. Over this range, the short-run supply curve is rather elastic. If, on the other hand, a 1 percent increase in price leads only to a 0.5 percent increase in quantity supplied, the short-run elasticity of supply is 0.5, and we say that supply is inelastic.
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Marshall’s Scissors
Marshall’s scissors analogy is just a folksy way of referring to simultaneous equations (see the Appendix to Chapter 1). It is a reminder that demand and supply relations must be solved together to arrive at equilibrium price and quantity. One way to do that is by using a graphical approach as in Figure 9.6. Another way would be to use a purely algebraic method. No matter what approach you take, however, you have not found a market equilibrium until you check that your solution satisfies both the demand curve and the supply curve.

In perfectly competitive markets, supply responses are more flexible in the long run than in the short run for two reasons. First, firms’ long-run cost curves reflect the greater input flexibility that firms have in the long run. Diminishing returns and the associated sharp increases in marginal costs are not such a significant issue in the long run. Second, the long run allows firms to enter and exit a market in response to profit opportunities.
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As before, we assume that firms seek maximum profits. Because each firm is a price taker, profit maximization requires that the firm produce where price is equal to (long-run) marginal cost. This first equilibrium condition, P = MC, determines both the firm’s output choice and its ch

In graphic terms, long-run equilibrium price must settle at the low point of each firm’s long-run average total cost curve. Only at this point do the two equilibrium conditions hold: P = MC (which is required for profit maximization) and P = AC (which is the required zero-profit condition).
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Constant cost case: A market in which entry or exit has no effect on the cost curves of firms
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Contrary to the short-run case, the long-run supply curve does not depend on the shape of firms’ marginal cost curves. Rather, the zero-profit condition focuses attention on the low point of the long-run average cost curve as the factor most relevant to long-run price determination. In the constant cost case, the position of this low point does not change as new firms enter or leave a market. Consequently, only one price can prevail in the long run, regardless of how demand shifts, so long as input prices do not change. The long-run supply curve is horizontal at this price. After the constant cost assumption is abandoned, this need not be the case. If the entry of new firms causes average costs to rise, the long-run supply curve has an upward slope. On the other hand, if entry causes average costs to decline, it is even possible for the long-run supply curve to be negatively sloped.
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The entry of new firms may cause the average cost of all firms to rise for several reasons. Entry of new firms may increase the demand for scarce inputs, driving up their prices. New firms may impose external costs on existing firms (and on themselves) in the form of air or water pollution, and new firms may place strains on public facilities (roads, courts, schools, and so forth), and these may show up as increased costs for all firms.

Increasing cost case: A market in which the entry of firms increases firms’ costs.
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Long-run elasticity of supply: The percentage change in quantity supplied in the long run in response to a 1 percent change in price.

An elasticity of 10, for example, would show that a 1 percent increase in price would result in a 10 percent increase in the long-run quantity supplied. We would say that long-run supply is very price elastic: The long-run supply curve would be nearly horizontal. A principal implication of such a high price elasticity is that long- run equilibrium prices would not increase very much in response to significant outward shifts in the market demand curve.

A small supply elasticity would have a quite different implication. If the elasticity were only 0.1, for example, a 1 percent increase in price would increase quantity supplied by only 0.1 percent. In other words, the long-run supply curve would be nearly vertical, and shifts outward in demand would result in rapidly rising prices without significant increases in quantity.
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Whether it is possible for long-run supply curves to be negatively sloped has been a subject of debate among economists for decades. Of course, it is well known that supply curves can shift downward if input costs fall. But the declining prices that result from such changes lie on many different supply curves, not on a single, downward-sloping curve. Whether it is possible to devise a reasonable theory to explain why prices might move downward along a single supply curve remains an open question for economists.
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Consumer surplus: The extra value individuals receive from consuming a good over what they pay for it. What people would be willing to pay for the right to consume a good at its current price.
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Producer surplus: The extra value producers get for a good in excess of the opportunity costs they incur by producing it. What all producers would pay for the right to sell a good at its current market price.
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Ricardian rent: Long-run profits earned by owners of low-cost firms. May be capitalized into the prices of these firms’ inputs
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Economically efficient allocation of resources: An allocation of resources in which the sum of
consumer and producer surplus is maximized. Reflects the best (utility- maximizing) use of scarce
resources.
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Tax incidence theory: The study of the final burden of a tax after considering all market
reactions to it.
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A specific commodity tax of amount t lowers the after-tax demand curve to D 0 . With this
‘‘new’’ demand curve, Q 2 will be produced in the short run at an after-tax price of P 2 . In the
long run, firms will leave the industry and the price will return to P 1 . The entire amount of
the tax is shifted onto consumers in the form of a higher market price (P 4 )

Long-Run Shifting of the Tax In the long run, firms do not continue to operate at a loss. Some firms leave the market bemoaning the role of oppressive taxation in bringing about their downfall. The industry short-run supply curve shifts leftward because fewer firms remain in the market. A new long-run equilibrium is established at Q 3 where the after-tax price received by those firms still in the industry enables them to earn exactly zero in economic profits. The firms remaining in the industry return to producing output level q 1 . The price paid by buyers in the market is now P 4 . In the long run, the entire amount of the tax has been shifted into increased prices. Even though the firm ostensibly pays the tax, the long-run burden is borne completely by the consumers of this good. 9
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Incidence and Elasticity A bit of geometric intuition suggests that the relative sizes of the price changes shown in Figure 9.13 depend on the elasticities of the demand and supply curves. Intuitively, the market participant with the more-elastic response is able more easily to ‘‘get out of the way’’ of the tax, leaving the one with less elastic response still in place to pay the most.
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More generally, if demand is relatively inelastic, whereas supply is elastic, demanders pay the bulk of a tax in the form of higher prices. Alternatively, if supply is relatively inelastic but demand is elastic, producers pay most of the tax.... For example, the producer’s share of a tax on gold or silver would be largely paid by mine owners because the supply of mining land to this industry may be very inelastic.
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Deadweight loss: Losses of consumer and producer surplus that are not transferred to other parties.
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With Taxes, Suppliers and Demanders Pay Different Prices
Taxes create a wedge between the price demanders pay and what suppliers receive. Whenever you are dealing with a tax problem, you must decide whether P will represent the price suppliers receive (as it did in our numerical application where demanders paid P + t) or the price demanders pay. If you opt for P to represent the price demanders pay, then suppliers will receive P - t. The final conclusions will be the same in either case—it is the size of the tax wedge that matters for the analysis, not the specifics of how it is modeled.
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Opening of International Trade Increases Total Welfare

Opening of international trade lowers price from P D to P W . At P W , domestic producers
supply Q 2 and demanders want to buy Q 1 . Imports amount to Q 1-Q 2 . The lower price
results in a transfer from domestic producers to consumers (shaded dark) and a net gain of
consumer surplus (shaded light).
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Tariff: A tax on an imported good. May be equivalent to a quota or a nonquantitative restriction on trade.
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