Extra Material complementing Pindyck and Rubinfeld Chapter 8 and 9Dr. Kris De Jaegher

Pindyck and Rubinfeld:Chapter 4:

Consumer Surplus, pp.132-134Chapter 8:

Perfectly Competitive Markets, pp.271-273

Demand and Marginal Revenue for a Competitive Firm, pp.277-279 Producer Surplus in the Short Run, pp.291-292 Long-Run Profit Maximization, pp.293-294 Long-Run Competitive Equilibrium, pp.294-297 Constant-Cost Industry, pp.299-300

Chapter 9:

Application of Consumer Surplus and Producer Surplus, pp.311-314

The Effects of a Specific Tax (excluding the pass-through formula), pp.335-338Learning Objectives1. Understand under which conditions perfect competition exists;

2. Understand why firms and consumers consider prices as given, while demand is downward sloping, and supply is upward sloping;

3. Understand how equilibrium is established in the short- and in the long-run in perfect competition;

4. Understand why the long-run supply function could be horizontal;

5. Understand what the consumer surplus measures;

6. Understand what the producer surplus measures;

7. Understand the concept of Pareto (in)efficiency;

8. Understand that the equilibrium in perfect competition is Pareto efficient (both for the case of one good and of two goods);

9. Understand what deadweight loss measures;

10. Understand that price ceilings and price floors are Pareto inefficient;

11. Understand that the deadweight loss of a per unit tax depends on the elasticity of demand and supply;

12. Apply welfare analysis to real-world problems (includes water-diamond paradox).

Key Concepts

Conditions for perfect competition (PR pp.271-273, Perfectly Competitive Markets)In Lecture week 47, we assumed that consumers consider the prices of goods as given. In Lecture week 48, we assumed the same for firms. It is now time to justify these assumptions, which apply when there is perfect competition. The conditions for perfect competition are the following: Price-taking behaviour: consumers and firms consider prices as given. Considering prices as given is justified for individual consumers and firms who are small compared to the market.

The good in the competitive market is a standardised (or: homogeneous) product. It does not matter for the consumer from which firm he or she buys the product.

Free entry and exit, or perfect mobility of factors of production (capital, labour). When profits are being made in a certain market, new firms are able to enter into the market, and are able to attract factors of production to exploit these profits. When losses are being made, firms can lay off factors of production, and move out of the market.

Both firms and consumers have perfect information. When one firm sets a higher price for the product than another firm, consumers know about this. When a firm can make higher profits in another market, the firm knows about this.

Apparent paradox, and its solution ( PR, pp.277-279, Demand and Marginal Revenue for a Competitive Firm)Firms assume that they can sell as much as they want at the current price, that is, they assume that the demand they face for their goods is perfectly elastic. Yet, consumers are only willing to buy more goods if prices go down, i.e. market demand is downward sloping.

Consumers assume that they can buy as much as they want of a good at its current price, that is, they assume that the supply that they face is perfectly elastic. Yet, firms are only willing to supply more of the good if they get a higher price, i.e. market supply is upward sloping.

This does not mean that consumers or firms are wrong in the assumptions that they make. Simply, they are each so small compared to the market that, individually, they will not affect the price. The individuals firms decision to supply more of the good will not result in any observable decrease in the price if the firm is only one of many firms; the individual consumers decision to demand more will not boost the price up if the consumer is only one of many consumers. Individual consumers and producers can safely consider the price as given. Overall, however, the equilibrium price is determined by the intersection of the downward sloping market demand curve, and the upward sloping industry supply curve.

Short-run equilibrium ( PR, pp.293-294, Long-Run Profit Maximization)As firms make different decisions in the long and in the short run (see Lecture week 48), we must model both short- and long-run equilibrium. We start by modelling short-run equilibrium. In the short run, the amount of capital is fixed, as well as the number of firms in the market.

The short-run equilibrium price pSR is determined by demand and supply, where supply is the horizontal summation of SMC curves of all the firms that are currently in the market. pSR in turn is the individual firms marginal revenue (MR). In Figure 1, the optimal short-run output of the individual firm, qSR, is found where MR equals SMC. The total supply is then QSR (note that qSR could e.g. be measured in hundreds, and QSR in thousands). As can be seen from the position of the SATC curve, the individual firm is making profits. Profits equal (pSR SATC)*qSR. Along with the short-run cost curves, the long-run cost curves are also presented in Figure 1. The relative position of the short-run and long-run cost curves was explained in Lecture week 48.

There are two things to note about this short-run equilibrium. First, in the long run, the fact that profits are being made will attract new firms. Second, the individual firm in the market is producing on too large a scale. In the long run, it could save on costs by using less capital, thus achieving lower average costs.

Figure 1 Short-run equilibrium where too few firms produce too much.

Consider next the alternative short-run equilibrium in Figure 2. The short-run equilibrium price is again determined by demand and supply, which in turn determines the MR, and individual output qSR. The individual firm is making a loss, but the firm still continues to produce, given that the fixed costs are sunk and given that the firm is still covering its average variable costs. In the short run, it will not shut down. However, this is not sustainable in the long run. First, some firms will leave the market. Second, the individual firms that stay in the market can benefit from producing on a larger scale (using more capital).

Figure 2 Short-run equilibrium where too many firms produce too little. Long run equilibrium (PR, pp.294-297, Long-Run Competitive Equilibrium)

Figure 3 Long-run equilibrium.Finally, consider the long-run equilibrium. In Lecture week 48, we focussed on the fact that all inputs can be changed in the long run. We now add the feature that firms can enter or exit in the long run. In the long-run equilibrium 1) firms are making zero profits; 2) firms are producing at the minimum efficient scale (see Lecture notes week 48). If 1) is not met, more firms enter. If 2) is not met, even if all other firms are making zero profits, one firm could compete other firms out of the market by producing at minimal LAC. It follows that, starting from the situation in Figure 1, the short-run industry supply curve will shift to the right in the long run, from S to S. In the situation in Figure 2, the industry supply curve will shift to the left in the long run, from S to S.

Because economic profits are necessarily zero in the long run equilibrium, economists refer to these as normal profits. Positive economic profits are referred to as supernormal profits.

Horizontal long-run supply (PR, pp.299-300, Constant-Cost Industry)The supply curves in Figures 1 to 3 are all short run supply curves. What is now the shape of the long-run supply curve? In any case, the long-run supply will be flatter than the short-run supply function. This is, first, because in the long run, firms can adapt both capital and labour levels, and therefore will have lower costs of producing more. Second, in the long run, price increases will cause entry, and a price increase will therefore be associated with a larger increase in output.

To concretely derive the long-run supply, note that a supply curve can be seen as giving us the equilibrium price for several possible demand schedules. Let us therefore assume that, starting from the long-run equilibrium in Figure 3, there is shift to the right in demand to D (at every price, more is bought), and let us investigate how this affects long-run equilibrium, in order to obtain a second point on the long-run supply curve.

We look first at the short-run, and then at the long-run effect of the shift in demand. In the short run (Figure 4), both the number of firms and the amount of capital used by each individual firm is fixed. The individual firm sets the new MR equal to SMC, and thereby earns supernormal profits.

Figure 4 Shifts in demand curve and derivation of long-run supply.However, these short-run supernormal profits will attract new firms in the market. Moreover, the individual firm will realise that it could make even higher profits by producing on a smaller scale (by using less capital). A moment of reflection teaches us that, in the long run, the situation of the individual firm must be identical to the situation before the demand shift. This is because it must continue to be the case in the long run that each firm is producing at the minimum efficient scale. Therefore, the only thing that will have changed in the long run is that more firms have entered the market. The corresponding shift in short-run supply (S, see Figure 5) must be such that more is produced in the market (QLR), but must leave the price before the demand shift unchanged. It follows that the long-run supply must be a horizontal line.

It should be noted, however, that this analysis is based on the assumption that all firms have identical costs. In reality, the firms that enter after the demand shift may have higher costs (e.g., they could be located further away from consumers). Also, the analysis is based on the assumption that input prices are fixed. It may only be possible to increase output at the cost of higher input prices. For these reasons, the long-run supply will often have an increasing slope.

Figure 5 Adjustment and long-run supply.The analysis so far reveals a first important feature of perfect competition: goods are produced at the lowest cost they possibly could be produced. A second important feature of perfect competition is that, as economic profits are zero, consumers do not pay one cent too much for the goods that they buy: the firms profits are equal to their opportunity costs of making the goods. A third feature of perfect competition is that all the gains from trade between firms and consumers are exhausted (the analysis in Lecture week 46 was already suggestive of this). To better understand this third feature, we need to introduce some new concepts.

Consumer surplus (PR, pp.132-134, Consumer Surplus)Reconsider Figure 1 from Lecture week 46, Supply and Demand, where the market demand for student rooms in a certain neighbourhood of Utrecht was derived using six students reservation prices. Let the equilibrium price be equal to 300. Then Abe, Ben, Cathy and Dave rent a room. We can now directly read the surplus that these consumers derive from renting a room rather than not renting one as a surface in Figure 6. To see why, consider the fact that Abe is willing to pay at most 600 for a room. Since, at a price of 600, Abe is indifferent between renting a room or not renting one, 600 is nothing but the benefit that Abe derives from renting a room. Abes cost of renting a room is 300. It follows that Abes surplus from renting a room rather than not renting one is 600 300 = 300. Similarly, Bens surplus from renting a room rather than not renting a room is 200, Cathys surplus is 100, and Daves surplus is zero.

Figure 6 Market demand for student rooms.

The surplus that all consumers derive from consuming the good rather than not consuming it is known as the consumer surplus, and is equal to the area under the demand curve up to the equilibrium quantity, minus expenditure. This makes intuitive sense. The demand curve can be seen as representing the consumers marginal benefit of consuming an extra unit of the good. The sum of all these marginal benefits is nothing but total benefit. Total cost is simply the expenditure on the good. Therefore, the consumer surplus is the somewhat triangular area indicated in Figure 7.

Figure 7 Consumer surplus.

For a continuous demand, the consumer surplus is literally a triangular area (see Figure 8). In general, consumers will consume several units of a good, at each point on the demand curve, we read the marginal benefit of the marginal consumer (the last consumer who would be willing to consume at the corresponding price). By adding up all these marginal benefits, we obtain nothing but the consumers total benefit from consuming the equilibrium consumption level. By subtracting the total expenditure on the good, we obtain consumer surplus. For the continuous demand in Figure 8, at an equilibrium price p* and an equilibrium output q*, the consumer surplus is the indicated triangle. Example: consider the inverse demand curve . Let p* = 6. Then the consumer surplus equals (6*4)/2 = 12 (= half of the surface of a 6 by 4 rectangle).

Figure 8 Consumer surplus for a continuous demandNote the reason why there is a consumer surplus. The price that consumers pay is equal to the marginal benefit of the last unit consumed by the consumer who is just still willing to buy some of the good. As marginal benefit is decreasing, this means that individual consumers earn a positive benefit on the first units of the good that they consume. Moreover, this means that consumers with a higher willingness to pay than the marginal consumer earn an extra benefit, because the price is adapted to the marginal consumer.

Circumstances under which the consumer surplus is a valid measure

Having treated the intuition for the consumer surplus, we need to be more precise about the circumstances under which we can use consumer surplus as a measure of consumer welfare. We have argued that the inverse demand measures the marginal utility to the marginal consumer of an extra unit of the good. Yet, the inverse demand for good x is only equal to marginal utility of good x if the utility function takes the form u(x, y) = v(x) + y, where y is the other good, and where v(.) is a concave function of x. Let the price of good y be 1, and denote the price of good x by px. Along the budget line, it is then met that y = m pxx. As a utility maximising consumer will choose a bundle on the budget line, we can plug the equation for the budget line into the utility function, to obtain the function v(x) + m pxx. This function is maximised when dv(x)/dx = px. But dv(x)/dx is nothing but the marginal utility of good x. Note that this means that consumer surplus is only valid as a measure if the income effect on the consumption of good x is zero.

In terms of Figure 7, suppose that the one reason why Abe is willing to pay 600 for a room, and that Dave is only willing to pay 300 for a room, is that Abe has a higher income. We could not pretend then that Abe derives a surplus of 300 from renting a room at 300, and that Dave obtains a surplus of 0 from renting one at the same price. This is because we are in part measuring Abes benefit of having a higher income then. The consumer surplus strictly speaking is only a valid measure if the sole reason that some consumers have a higher willingness to pay is that they attach a higher value to a good. However, income effects are often small, meaning that consumer surplus is often still a valid measure.

Formally, with a price of good y equal to 1, it is the case that px = [du/dx]/[du/dy]. If Abe has a higher income than Dave, Abe will buy more of good y than Dave. Given that marginal utility decreases, du/dy will be smaller for Abe than for Dave. Unless du/dy = 1, given that px = [du/dx]/[du/dy], px overestimates Abes marginal utility of an extra unit of good x.Example: let . Let pY = 1. Then , . The inverse demand for good X is. There is no income effect, and the consumer surplus can be calculated for this example.

Producer surplus (PR, pp.291-292, Producer Surplus in the Short Run)

Figure 9 Industry supply of student rooms.Reconsider the supply curve of the market introduced in Lecture notes week 46 for our fictional student room market in Utrecht, derived by plotting the minimum price that landladies want to receive before they are willing to rent out a room. This means that, at the given prices, landladies are each time indifferent between renting out a room and not renting out one. It follows that what is measured on the vertical axis is nothing but the landladies cost of renting out a room. Yet landladies do not only face costs, but also get benefits from renting out a room, in the form of monthly rent received. Let the monthly rent be 300. Then Agatha, Bertha, Cecile and Deirdre rent out a room. Berthas surplus of renting out a room rather than not renting one out is 300 100 = 200. Similarly, Agathas surplus is 300, Ceciles surplus is 100, and Deirdres surplus is zero.

The total surplus of the landladies of renting out a room rather than not renting one out at a rent of 300, or producer surplus, is the somewhat triangular area above the supply curve and below the equilibrium price level. This makes sense, as the supply curve represents the landladies marginal costs. Adding up all marginal costs yields us total cost. Total benefit is revenue, and is equal to the rectangular area obtained by multiplying number of student rooms by rent. The difference between these two areas is the producer surplus.

Figure 10 Industry supply of student rooms.

In general, producers will produce more than one unit, and their costs will range over a continuum of cost levels. The corresponding smooth supply curve measures the marginal cost of the last unit produced by the marginal producer (the last producer who is willing to supply a unit at the current price). The sum of all these marginal costs up to a certain output level are then the firms variable costs of jointly providing the specified output level. Their benefits are equal to price times output. Producer surplus is the difference between these two surfaces, and is literally a triangle. This is illustrated in Figure 11, for an equilibrium price of p* and an equilibrium quantity of q*.

Figure 11 Producer surplus for a continuous supplyNote: the producer surplus is nonzero. Yet, we have seen that, in perfect competition, profits must be zero. To understand why the producer surplus is still positive, note that supply is equals to marginal cost. Marginal costs concern variable costs, and leave out fixed costs. It follows that adding up marginal costs yields us variable costs. The producer surplus is therefore equal to profits plus fixed costs. With zero profits, the producer surplus that the firms get from producing rather than not producing is the benefit of being able to cover ones fixed costs rather than not covering them.

Total welfare (sum of consumer surplus and producer surplus) maximised in perfect competition/all benefits from trade exhausted

The area under the demand curve is the benefit that consumers derive from consuming the good; the consumers costs are their expenditure. The producers benefits are the consumers expenditure; their (variable) costs are the area under the marginal cost curve. It follows that the total benefit that society derives from the exchange between consumers and producers is consumer benefit minus producer costs (consumer expenditure cancels out when summing consumer and producer surplus), or is the area under the demand curve and above the supply curve.

As demand measures consumers marginal benefit from consuming an extra unit, and as supply measures producers marginal cost from producing an extra unit, when demand equals supply, benefit minus costs is maximised, and with it societal welfare. This is illustrated in Figure 12 for our student room market. In Figure 12a, total welfare is maximised when four rooms are rented out. If only two rooms are rented out (Figure 12b), total welfare is smaller, as no welfare is created by an exchange between Cathy and Cecile. If five rooms are rented out (Figure 12c), the total welfare equals the light grey area (identical to total welfare in Figure 12a) minus the dark grey area. The dark grey area is a net cost to society, because Evelyns cost of renting out a room is larger than Edies benefit. In the same manner, total welfare is maximised when the continuous demand function in Figure 13 intersects the continuous supply function.

The fact that total welfare is maximised can be stated in another way. When total welfare is not maximised, it is possible to make at least one agent (= consumer or producer) better off without making anyone worse off. Consider the case in Figure 12b. Here, Cathys benefit of renting a room is larger than Ceciles cost of renting out a room. If Cathy and Cecile are allowed to trade with one another, the room will be rented from Cathy to Cecile at some price between Cathys benefit and Ceciles cost. This trade will make both Cathy and Cecile at least as well off as they were before, and will not make anyone worse off.

Similarly, consider the case in Figure 12c, where Evelyn is somehow forced to rent out a room to Edie, and where Edie is forced to rent a room from Evelyn. Let p be the rent that Edie pays to Evelyn. Even if this transfer from Edie to Evelyn is maintained, both players are better off if Evelyn pays a bribe to Edie for not occupying the room. This is because Evelyns benefit of not having Edie in her house is larger than Edies cost of not having a student room. Evelyn can then always pay a bribe lower than her benefit, but higher than Edies cost, to get Edie out of her house. Both Evelyn and Edie can thus get better off without making anyone worse off.

When some agents can be made better off without anyone worse off, there is what economists call Pareto inefficiency. Pareto efficiency in turn occurs when nobody can be made better off without making someone else worse off. The attractiveness of this efficiency concept is that it allows us to make statements about efficiency without making any value judgments on how resources should be distributed among people (equity). The output levels in the markets in Figures 12a and 13 are Pareto efficient. In general, competitive markets are Pareto efficient. It is not the case that there are unexploited gains from trade to be made that would make some agents better off without hurting the other agents.

Figure 12 Perfect competition maximises total welfare

Figure 13 Perfect competition maximises total welfare: continuous supply and demand Deadweight loss of taxes (PR, pp.335-338, The Effects of a Specific Tax (excluding the pass-through formula))We have already seen in Lecture week 46 that, if a per unit tax is imposed, and if some consumers and producers were exempted from the tax, then everybody would be better off. The government would get the same tax revenues, and the producer and consumer who were exempted from the tax would be able to make a mutually beneficial transaction.

Now that we have introduced the concept of consumer surplus and producer surplus, we are better able to assess the effect of the tax. In the example of the student room market, consider a tax on consumers of 400, illustrated in Figure 14. Then the deadweight loss is the part of total welfare that gets lost because of the tax. Concretely, Cathy could have rented a room from Cecile, thereby increasing total welfare by 200. As this exchange did not occur, the deadweight loss is 200. Put otherwise, the tax is Pareto inefficient. Figure 10 also indicates the consumer surplus (CS), the producer surplus (PS), and the tax revenue of the government. Note that the tax revenue itself is not considered to be a loss. The government spends the tax revenue, and it is therefore not lost to the economy.

Figure 14 Tax imposed on consumers

Figure 15 makes the same analysis for the case of a continuous demand, where T indicates tax revenue, CS consumer surplus, and PS producer surplus. t is the tax per unit, pd is the price paid by consumers, and ps is the price received by suppliers.

Figure 15 Tax imposed on consumers: continuous demand and supplyIt should be clear that the deadweight loss is larger the more price elastic is demand and/or supply. The problem with a tax is that output that would otherwise have been produced and consumed to the mutual benefit of producers and consumers is now no longer on the market. The more elastic supply or demand, the larger therefore the deadweight loss. This is illustrated in Figure 16 for a tax on yachts, presumably a price elastic good (the fact that yachts are a luxury makes the income effect large). It follows then that, from the point of view of total welfare, it is best to tax goods with an inelastic demand and/or an inelastic supply. For instance, given that the demand for cigarettes, alcohol and fuel is price inelastic, it makes sense to tax these commodities, as is done in the real world. An extreme example with a completely inelastic demand for fuel, where a tax is imposed on suppliers, is given in Figure 17. The entire burden of the tax is suffered by consumers, but there is no deadweight loss.

Given that the demand for luxuries such as yachts is price elastic (because of the large income effect), from a welfare point of view, it is not a good idea to tax these. Summarising, from a welfare point of view, it is better to tax necessities than to tax luxuries. However, from the point of view of equity, one may want to do the opposite.

Figure 16 Tax in case of elastic demand

Figure 17 Tax in case of inelastic demand Taxing all goods is better than taxing a few goods

The fact that taxes create deadweight losses suggests that as few goods as possible should be taxed. This intuition is wrong, however. In Figure 18, consider a consumer who consumes beer and other goods, where the consumption of other goods is measured in euros. Without any taxes, the consumer chooses bundle A. When a tax is imposed on beer, the consumers budget line tilts downwards, and consumption bundle B is consumed.

If the consumer would not have had to pay the tax, he would have been able to consume consumption bundle C, on his old budget curve. As other goods are measured in euros spent on other goods, the vertical distance between B and C must necessarily be the amount of taxes that the consumer pays. But the government could now get the same amount of taxes from the consumer by taxing both goods to the same extent, so that the original proportion between the price of beer and of other goods is maintained. The new budget line is then the dashed budget line through bundle B, parallel to the budget line through A. As this budget line lies in part above the indifference curve that is achieved when only beer is taxed, the consumer will be doing better than in case only beer is taxed (bundle D). Clearly, when all goods are taxed to the same extent, we have what would seem to be a lump-sum tax (see problem 6 in the problem set of week 39). In reality, however, taxing all goods to the same extent will still distort the consumers decision on how much to work. Effectively, there is always a distortion. The consumers decision on how much to work is treated in Lecture week 2.

Figure 18 Two taxes better than one

Deadweight loss of price ceiling (PR, pp.311-314, Application of Consumer Surplus and Producer Surplus)

Figure 19 Deadweight loss of rent control in student room marketLet the city council impose a price ceiling in the student room market, illustrated in Figure 19 (see also Lecture week 46). All students then want to rent a room, but only Agatha and Bertha rent out rooms. Assume that the consumers with the highest willingness to pay are still the ones to get the rooms, meaning that Abe and Ben rent from Agatha and Bertha.

When comparing Figure 19 to Figure 12a (where consumer surplus is the part of total welfare above the price level of 300, and producer surplus is the part of total welfare below the price level of 300), it becomes clear that Abe and Ben win from the price control, while Cathy loses from it. Abe and Ben win more than Cathy loses, so that on average, consumers are better off. All producers are worse off. Finally, the price ceiling comes at the cost of a deadweight loss, as the sum of consumer and producer surplus is reduced. Concretely, Cathy and Cecile would both be better off if Cecile were allowed an exception to the price ceiling, and were allowed to rent out a room to Cathy at a rent between 200 and 400.

It should be noted that the analysis in Figure 19 may underestimate the true deadweight loss. The analysis assumes that, while there is excess demand, it is still the consumers with the highest willingness to pay who get to rent a room. This need not be the case. For instance, it may instead be Frank and Edie who get to rent a room. The deadweight loss is then even larger, because of the high benefits that Abe and Ben get from renting a room. Application of welfare analysis: why are diamonds more expensive than water?Diamonds are more expensive than water. Yet it is clear that we derive more value from water than diamonds: we could live without diamonds, but not without water. This is known as the water diamond paradox. How to explain this paradox?

The explanation consists of two parts. First, there is a large supply of water, but a small supply of diamonds. Second, by nature, the marginal benefit of the first unit of water consumed is enormous. But because of the large supply, the marginal benefit of the last unit consumed is very small, and with it the price of water. Still, because of the large benefits of the first units of water consumed, the consumer surplus for water is very large. The marginal benefit on the first units of diamonds consumed is never as large as it is for the first units of water consumed; this is what causes the consumer surplus on diamond consumption to always be smaller than it is for water. Yet, because there are few diamonds, the marginal benefit of the last unit consumed is high, and with it the price of diamonds. This is illustrated in Figure 20.

Figure 20 Water diamond paradox. Perfect competition exploits all potential gains from trade: the case of two goods In Figures 12 and 13, it was shown for one good that perfect competition exploits all potential gains from trade (leads to a Pareto efficient outcome). We now show the same for the case of two goods. Consider again the example from Lecture week 47 of consumers who only consume beer and pizza. Assume that beer and pizza are also the only goods produced, and this using capital and labour. We consider the short run, where the amount of capital is fixed.

As shown in Lecture week 47, consumers who take prices as given put the rate at which they are able to exchange one beer for pizza on the market (given by pb/pz, the slope of the budget line) equal to the rate at which they are willing to exchange one beer for pizza (given by the slope of the indifference curve).

At the same time, in perfect competition, beer producers put pb = SMCb (the short-run marginal cost of producing an extra beer) and pizza producers put pz = SMCz (the short-run marginal cost of producing an extra pizza). We have seen in Lecture week 48 that in the short run, MCb = wb/MPLb, and that MCz = wz/MPLz (where wb is wage when working for a beer producer, and wz is the wage when working for a pizza producer; MPLb is the marginal product of an extra unit of labour in the beer production process, and MPLb is the marginal product of an extra unit of labour in the pizza production process).

Note now that it must be the case that wb = wz. With perfect mobility of factors of production (including labour), no firm can offer a higher wage than the other. It follows that MCb/MCz = MPLz/MPLb. The expression MPLz/MPLb is a measure for the amount of extra pizza that can be produced when one beer less is produced (where an appropriate amount of labour is then moved from the beer market to the labour market), and is referred to as the marginal rate of transformation.

Given that marginal cost is equal to price, and given that pb/pz is equal to the marginal rate of substitution, it follows that the marginal rate of transformation is equal to the marginal rate of substitution. Thus, the rate at which the production side of the economy is able to swap beers for pizza is the rate at which the consumption side of the economy is willing to swap beers for pizza.

It can now be seen that this implies that all the potential for mutually beneficial exchanges between consumers and firms have been exploited. Suppose that consumers are willing to swap 1 beer for 1 pizza, but that firms are able to swap 1 beer for 2 pizzas. Then by making 2 more pizzas and 1 beer less, firms can make consumers better off without hurting themselves. Next assume that consumers are willing to swap 1 beer for 1 pizza, but that firms are able to swap 1 beer for half a pizza. Then by making half a pizza less and 1 more beer, the consumer can be made better off, without the firms being hurt.pSR

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Fiona

Evelyn

p*

q*

q

p

demand

supply

Total welfare

600

500

400

300

200

100

Monthly rent

Student rooms

1

2

3

4

5

6

Abe

Ben

Cathy

Dave

Edie

Frank

Agatha

Bertha

Cecile

Deirdre

Fiona

Evelyn

CS

PS

Tax

revenuee

Deadweight

loss

pd

q*

q

p

demand

supply

ps

t

CS

PS

T

deadweight loss

pd

q*

yachts

Price of yachts

demand

supply

ps

t

PS

Tax revenue

T

supply

CS

deadweight loss

pd

q*

fuel

Price of fuel

demand

supply

ps

t

CS

PS

T

supply

Other goods

A

B

D

C

Beer

600

500

400

300

200

100

Monthly rent

Student rooms

1

2

3

4

5

6

Abe

Ben

Cathy

Dave

Edie

Frank

Agatha

Bertha

Cecile

Deirdre

Fiona

Evelyn

Price ceiling

Excess demand

PS

CS

Deadweight

loss

pwater

pdiamonds

water

diamonds

PAGE 19

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