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May 8

Multiproduct monopoly

Multiproduct monopolies are those monopolistic firms that sell, at least, more than one product. The firm will have to take into account how a change in the price of one of its products affects the demand of the rest of them, especially when they are complementary or substitutive goods. The magnitude of the cross elasticity of demand will be of great importance as it will measure this effect. The multiproduct monopoly will maximise its profits as:

It is noteworthy to comment the different effects that an increase in price of one product will have in the rest of the products depending if they are substitute or complementary goods. For substitute goods the loss of demand in the market when prices are raised will be balanced by the increase of demand of the other good as consumers will just switch to the other product. However, for complementary goods the loss of demand will be amplified in the other market. To understand this second effect let’s think of petrol and cars. When price of petrol increases, demand for cars will be negatively affected as their overall cost will be increased.

Multiproduct monopolies can set prices to each of its products either jointly, or by division, each division setting the price for the product it sells. If the goods are substitutes, and each division sets the price, prices will be low, since each firm has an incentive to lower the price and steal some sales from other divisions, thus behaving as oligopolists. This is commonly known as cannibalization. Therefore, a multiproduct monopoly producing substitute goods must set its prices jointly.

If the multiproduct monopoly sells goods that are perfect complements, it must take into account the necessity of setting the right price in order to sell both products. When each division sets these products’ prices separately, these divisions will have an incentive to increase the price, acting as a regular monopoly, which will increase the total price of both products. If set jointly, the price of each product will be lower, but total profits will be higher. Therefore, for both complementary and substitute goods the multiproduct monopoly should set its prices jointly.

May 8

Lope Gallego

Multiplant monopoly

A multiplant monopoly is given in monopolistic firms that have their production divided into more than one production plant, each one having its own cost structure. Different cost stuctures give place to different marginal costs and hence each production plant will have to choose the individual production output level following the maximising principle. For a monopoly with two plants, we have

where x₁ and x₂ are the same product, but produced at different plants. This multiplant monopoly will maximise its profits when

where MR is the marginal revenue and MC is the marginal cost in each plant.

The multiplant monopolist will need to decide whether to produce in both plants or just in one plant. This decision depends on each plant’s marginal costs. If it has increasing marginal costs, the multiplant monopoly will produce in either plant, taking into account the marginal total cost of both firms. If there are decreasing marginal costs, it will produce only in one plant, the one with the steepest marginal cost curve, provided it has equal or lower fixed costs than the other plant.
If marginal costs are constant and equal in both plants, the multiplant monopolist can produce in either plant, as long as capacity allows it (see figure below). If demand can be reached with only one plant, the others must be shut down.

If marginal costs are constant but different in each plant, production should take place only in the plant with lowest marginal costs, as long as maximum capacity is not reached. When this maximum capacity is reached, production will be moved to the other plant, as shown in the figure below.

May 6

Lope Gallego

Cobweb model

Cobweb models explain irregular fluctuations in prices and quantities that may appear in some markets. The key issue in these models is time, since the way in which expectations of prices adapt determines the fluctuations in prices and quantities. Cobweb models have been analysed by economists such as Ronald H. Coase, Wassily Leontief or Nicholas Kaldor. It was in Kaldor’s paper on the subject, “A Classificatory Note on the Determinateness of Equilibrium”, 1934, where the analysis of these models became of great interest, and where the phenomenon took the name of Cobweb theorem. Four years later, in 1938, economist Mordecai Ezekiel wrote the paper “The Cobweb Theorem”, which gave the phenomenon and its particular diagrams popularity.

Cobweb models are easily explained using the example used by Kaldor in 1934: agricultural markets. Let’s say weather conditions aren’t optimal during a year, which causes the quantity supplied of a certain crop to be quite small (Q_t, see figure below, first diagram). This excessive demand, or shortage, causes prices to be unusually high (P_t). When farmers realise how high prices are, they’ll plant more in order to supply more the following year. However, supply is so high the following year (Q_t+1) that prices decrease to meet consumers’ demand (P_t+1). Since prices are low, farmers decide to lower their supply the following year (Q_t+2), resulting in high prices again (P_t+2). This process will go on until an equilibrium is reached after a few fluctuations. This unique equilibrium is reached because in this first scenario, the elasticity of the demand curve, in absolute terms, is higher than the elasticity of the supply curve, which implies a convergent fluctuation.

The second diagram shows that a continuous fluctuation between two equilibriums will take place when both elasticities are equal to each other. The third diagram shows a divergent fluctuation, given by the fact that the demand curve is steeper than the supply curve. Even though these three diagrams show very different results, the example explained above can result in any of these scenarios, depending on each curve’s elasticity.

There is another possible scenario, which is given by changes in the steepness of curves: if near the point where the supply and demand curves cross demand is steeper than supply, but when we move far away from this point the supply curve gets steeper than the demand curve, we get a cobweb as the one in the figure below. At first, prices and quantities act as in a divergent fluctuation. However, as supply gets steeper than demand, a limit cycle may be reached, turning this divergent fluctuation into a continuous fluctuation.

May 3

Lope Gallego

Comparative statics

Comparative statics is a method used to analyse the result of changes in a model’s exogenous parameters by comparing the resulting equilibrium to the original one. However, this analysing method limits itself to comparing equilibriums, not analysing the reasons for the new equilibrium or the adjustment process. The use of comparative statics is of special interest for microeconomics when studying changes in demand and supply of a single market or a firm’s cost variation. It can also be used for macroeconomic purposes when studying changes in monetary or fiscal policies.

The use of comparative statics is as old as economics, and can be traced back to David Hume in 1752, when he studied how the increases in the stock of gold affected the prices in the economy. However, its use was formalized in the 20^th century by John Hicks in his book “Value and Capital”, 1939, and Paul Samuelson in his book “Foundations of Economic Analysis”, 1947.

May 2

Lope Gallego

Taxes

Governments will choose to implement taxes to either individuals or firms in order to increase its revenue. When considering taxes to firms, it must be noted that these taxes will increase the price of goods being produced and sold, which translates into a welfare loss. However, a distinction between the loss in consumer and producer surplus must be made. The impact on both surpluses depends on the period analysed.

Short and long run analysis:

In the short run, both consumers and producers will suffer from the tax imposed. A new tax increases the price of goods. Let’s say this tax is imposed to firms, which increase their prices in order to cover their losses. In this case, as shown in the adjacent figure, supply will shift to the left, decreasing the quantity being produced, which increases its prices since demand remains unchanged: the new equilibrium price will be p_D (if the tax was to be imposed to consumers, there would be a shift in demand instead). A corresponds to the amount of the tax paid by consumers, while B is the amount paid by producers. Only consumers actually pay more, but producers are getting less out of the sale. The loss in consumer and producer surplus will depend on the elasticity of the demand curve, as shown in the figures below. The lower the elasticity in absolute terms (left figure), the higher the loss in consumer surplus, and the lower in producer surplus. Higher elasticity (right figure) will have the opposite effect.

In the long run, since the supply curve is completely elastic, the new tax will reduce only consumer surplus. Producer surplus will remain equal to zero, since there are no profits to be made.

Welfare analysis and government’s revenue:

Governments usually increase taxes to increase their revenue, which they use to relocate wealth and increase social welfare. The adjacent figure shows the effects of imposing a new tax on a good. P₀ was the price before the tax was imposed, p_D is the price consumers pay and p_S the price producers receive. Consumer surplus is reduced by B and E, producer surplus decreases by C and F, while government increases its revenue from zero to B and C. Consumers and producers lose B+E+C+F and the tax revenue is B+C, which determines the deadweight loss, the reduction in total surplus: E+F. The deadweight loss depends on the elasticity of both the supply and demand curves: the higher the elasticity in absolute terms, the larger the deadweight loss.

Also, depending on the size of a tax, the tax revenue may be bigger or smaller. In the following figure we see how as the tax increases, the deadweight loss (grey) increases too.

However, the tax revenue (green) will first increase, and then will start to shrink. This relationship is known as the Laffer curve, shown in the figure below (being t the tax size and T the tax revenue). The Laffer curve might seem as an incredibly useful tool for government intervention. However, it has been widely criticized, mainly because empirical evidence to support it is rarely found, and because even if the relationship was accurate, it’s quite hard to know at which point of the curve a country actually is.

Taxing firms:

There are three main possible ways the government can impose taxes on firms: lump-sum tax, tax on profits and tax on output.

Lump-Sum Tax:

A certain amount of money has to be paid by the firm over a period of time. This kind of tax represents an increase in fixed costs and they consequently treat it as one. It holds the entry of firms in the market as it acts as an entry barrier, and will force some inefficient firms out of the market.

Tax on Profits:

Firms have to pay the government a percentage of their profits. This kind of tax is also considered a fixed cost. Sometimes the application this tax will cause profits to be negative, thus forcing some firms to exit the market.

The effects on total quantity sold and the quantity produced by a given firm of both lump-sum taxes and taxes on profits can be analysed with the following figure:

Tax on Output (or output tax):

In this case, firms pay a certain amount for each unit of output produced. As it has a direct relationship with the output level it is considered an increase in variable costs. The least efficient firms will be forced to exit the market.

The effects on total quantity sold and the quantity produced by a given firm of an output tax can be analysed with the following figure:

May 1

Lope Gallego

Market clearing

Market clearing occurs in those market situations in which the amount demanded by consumers equals the amount supplied by firms. In market clearing the equilibrium point has its corresponding equilibrium quantity and an equilibrium price. Economic science has developed several adjustment models to reach this stable point. Léon Walras’ and Alfred Marshall’s models are those mostly studied.

Léon Walras’ model is based on price as the force that motivates the adjustment process towards equilibrium. In moments of an excessive demand, prices will rise and against an insufficient demand a decrease in price will take place. The process of tâtonnement or “groping” will happen until the equilibrium price is reached and then transactions will begin to take place.

On the contrary, Alfred Marshall’s model considers that adjustment occurs via quantity. If the demand price is lower than that of supply, the quantity will decrease. The available quantity will be sold at the different prices that consumers are willing to pay for, until the actual equilibrium is reached.

The walrasian approach makes sense when prices are easily observed (a market with perfect information) and modified, being auctions of almost any kind a good example. When prices can hardly be modified (let’s say, because of adjustment costs such as menu costs), and when it’s easier to modify quantities (when there are excessive inventories), the marshallian approach is more reliable.

Apr 30

Lope Gallego

Cost variation

Firms’ cost structures will change over time, even when the quantity produced is kept constant. The price of an essential input for the production or the cost of rent may inevitably change. New costs will modify a firm’s equilibrium quantity and price. Once the differences between fixed and variable, and average and marginal costs are understood, it’s interesting to use comparative statics in order to see how new, higher costs may vary the firm’s cost structure, as well as the market structure as a whole. This analysis must be done in the long term, since long run cost analysis considers changes in both variable and fixed costs, and allows the entry and exit of firms to and from the market.

Fixed costs

If fixed costs increase but the initial market equilibrium is still maintained on the point in which average costs used to be at its lowest (A), the firm will incur in losses. Increases in fixed costs automatically imply an increase in average total cost. If a firm has an increase in its costs, it can easily result in losses that will cause it to exit the market, and thus motivate a contraction on supply. This contraction will cause an increase in price that eventually will result in a decrease in the demand for the product. Since there is a shift in demand to the left, less total quantity will be sold. However, because some firms exit the market, quantity produced by remaining firms will increase. It must be noted that the lowest possible supply level (X) remains unchanged because variable costs remain unchanged.

Variable costs

When variable costs increase, they cause an upward shift in the marginal and average cost curves. The market production costs will increase causing a contraction in supply, and thus firms exiting the market. Remaining firms will keep producing the same quantity of goods. Note that here the lowest possible supply level (X) changes because variable costs increase.

Variable costs

Apr 29

Lope Gallego

Long run supply curve

Cost analysis in the long run is quite different from short run cost analysis. Period analysis tells us that in the long run all factors are variable; this flexibility of factors will consequently be reflected in the long-run cost curves. This long-run curve will be formed by different period short-run curves and will serve as an envelope for all of them. Isoquants are used to compare the short-run periods with the long-run one. At each period we have a combination of labour and capital such that the firm will choose to minimise costs at each output level. The curve that joins the points of tangency between different isocost lines and isoquants is known as the expansion path.

One of the key features of the long-run is the possibility of firms entering and/or exiting the market. Economic profits will attract new entries to the market while economic losses will throw firms out of it. This process will occur whenever profits are different to 0. The equilibrium price will be influenced by the number of firms in the market, decreasing as the number of firms increases. Let’s say we start at E₁, where the firm we consider has profits equal to area A. It is able to supply products from point X onwards, due to its minimum efficiency requirements. Since there are profits, other firms will be attracted and will enter the market. Due to a new firm entering the market, market supply will shift to the right, since there are now more firms supplying the same goods. This increase in supply will force prices down to p₂. The firm we’re analysing still has profits at this point, but these profits decreased because of the new firm entering the market. Let’s say another firm enters the market, pushing again market supply to the right. This has the same effects, but this third firm has pushed marginal costs to its minimum, as well as average costs. Now, the three firms (including the one we’re analysing) supply such a quantity at such a price that there are no profits, nor losses, which will mean this market has reached its equilibrium, with no firms entering or exiting it.

Once this market equilibrium is reached, one might ask: what happens if there is an increase in demand? First, this will shift market demand to D’, increasing prices because supply (for the moment) is given. This increase in prices allows for profits to be made, at point 1. However, as seen before, these profits will attract new firms, which will force supply to the right (S’), going to an equilibrium such as E₂, where our firm will produce the exact same initial quantity (point 2).

The long-run market equilibrium is conformed of successive short-run equilibrium points. The supply curve in the long run will be totally elastic as a result of the flexibility derived from the factors of production and the free entry and exit of firms (imagine the firm-entry process portrayed before a few more times). In the long run, market demand will only affect the number of firms but not to the quantity produced by each of these firms. Therefore we can assume that the equilibrium in the long run is the point where profits are maximised (although each firm achieves zero economic profit), there are no firms entries nor exits and there is market clearance.

Apr 26

Lope Gallego

Short run supply curve

Short run cost analysis would not be properly taught without the inclusion of demand and supply curves and their correct understanding, specially how its shifts may affect firms’ cost functions. The total supply of the industry is the aggregate of the supply of all the individual firms.

The amount that is produced by each individual firm is subject to its optimal level of production. We must consider that the optimum production level of a firm is that in which marginal revenue (price) equals marginal cost, as long as it also covers its average variable costs. If this is not the case the firm will not achieve its highest level of profit and could even be incurring in losses.

It is common that input prices vary over time, causing firms to have to make adjustments. In order to optimise, firms will have to constantly adapt their production to the changes in their marginal costs. If a firm fails to adequate its production to the new marginal costs, there will be a loss in profits.

The equilibrium point between the aggregate demand of a product and its aggregate supply will be subject to variations if one of them suffers a change, and thus producing a new equilibrium price and quantity. These shifts may come from either the demand or the supply side. Let’s analyse thoroughly what happens to quantity sold by a given firm when there is a shift in either the demand or the supply curve.

Examples of shifts in demand include changes in income or changes in the price of the substitute goods. It must be noted that the aggregate supply curve starts at X, and not before, because a lower quantity would get producers to incur in losses. Also, notice that we assume firms are getting at least some profits (area A) because in the short term only labour is variable, which means that there are no firms entering this market, even though profits exist. Let’s say there is an increase of consumers’ income, which would increase the aggregate quantity demanded at a given price, thus shifting the demand curve to the right (D’ would be our new demand curve). Because there are no changes affecting the supply curve, the new equilibrium would be E₁, which means more quantity sold by each firm, as well as an increase in total quantity sold (Q₁). Since the cost functions of each firm are the same, each firm would be selling more quantity at a higher price (p₁), which would increase their profits (from area A to area B). To sum up, in the short term, an increase in demand would increase each firm’s profits by the area B-A, which would depend on both the marginal and average total cost, as well as the increase on quantity.

Shifts in the supply curve are caused by changes in outputs’ prices, technological innovations and changes in the number of firms in the industry. The last two cases, however, are not associated to the short-run. So let’s say there is a drop in the price of an input, used by all firms during their production process. This would decrease marginal costs and therefore average variable and total costs, which shifts each curve downwards (left, in red). Since the supply curve we consider is the aggregate of all firms’ supply, the aggregated supply curve also shifts downwards. Note that, since there are now lower marginal and average costs, the lowest point of the supply curve drops to X’. The new equilibrium would be E₂, with a decreased price of p₂. The new profits of each firm, C, is determined by both the new quantity produced and the drop in marginal and average costs. Even though in this case profits increase, profits can either increase or decrease. To sum up, in the short term, a reduction of inputs’ prices shifts the supply curve to the right and decreases market prices, but has undetermined effects on each firm’s profits.

Apr 25

Lope Gallego

Surplus

Surplus in economics refers to the profits (in terms of money or welfare) an individual or group of individuals is capable of extracting from the correct functioning of markets. Welfare economics analyses these surpluses in order to determine whether a market structure is socially optimal. From a microeconomic point of view, we can differentiate between consumer and producer surplus, which jointly form what is known as total or economic surplus, also known as total welfare. Let’s analyse them separately.

Consumer surplus:

Consumer surplus is quite easy to understand, since it’s the difference between how much someone is willing to pay for a given quantity of goods, an how much they actually pay. In this case, the demand curve is given by the willingness to pay of consumers, how much they will pay for a good.

Let’s consider the market for books, and that we have three potential customers: Arthur, Bertil and Carl. Arthur is willing to pay less than $25 for a book, Bertil would pay less than $20 and Carl would pay less than $15. If price is set at $25, no one buys books. When the price drops to $20, Arthur buys a book, and Arthur’s consumer surplus corresponds to area A. Note that this area equals $5, being this the difference between how much he was willing to pay ($25) and how much he actually pays ($20). If the price drops again, this time to $15, Bertil buys a book. In this case, Bertil’s consumer surplus corresponds to area B. It must be noted that, since the price of a book dropped even more, Arthur’s consumer surplus increased by A’. Both B and A’ equal $5. The same happens when Carl buys a book when price drops to $10. Consumer surplus, understood as the sum of all individual consumer surpluses, corresponds to area A+A’+A’’+B+B’+C.

When we repeat this process with a far greater number of buyers, we get a nice, straight demand curve. Now, let’s say the price for a given good is set at p₀. In that case, consumer surplus is area CS. When price drops to p₁, quantity sold increases. On the one hand, there is an increase on the consumer surplus of initial consumers, being this equal to area CS’. On the other hand, new consumers are willing to buy, being their consumer surplus nCS.

Producer surplus:

This is the exact opposite concept, since in this case we examine the market from the producers’ point of view. Producer surplus is the difference between the price the producer is paid and the cost of production.

Let’s consider again the market for books, now from the perspective of three producers: David, Edward and Frank. The supply curve corresponds to each producer’s costs of production, being $2 for David, $4 for Edward and $8 for Frank. If the price is lower than $2, no one will supply books since they’ll incur in losses. Now, if the price increases to $4, David sells a book, since he’ll be able to make a profit from the sale. This profit corresponds to D, his producer surplus. If the price increases to $8, Edward will also sell a book, having a producer surplus of E. In this case, David’s producer surplus will increase by $4 (area D’). The same will happen when the price gets over $8, let’s say $10. Producer surplus, understood as the sum of all individual producer surpluses, corresponds to area D+D’+D’’+E+E’+F.

When we repeat this process with more sellers, we get a straight supply curve. Now, let’s say the price for a given good is set at p₀. In that case, producer surplus is area PS. When price increases to p₁, quantity sold increases. On the one hand, there is an increase on the producer surplus of initial producers, being this equal to area PS’. On the other hand, new producers are willing to sell, being their producer surplus nPS.

Total welfare:

Total welfare, also known as economic or total surplus, is equal to the sum of both consumer and producer surpluses. It can be understood as the surplus of society, since both consumers and producers are getting something from the exchanges taking place in the market.

The analysis of economic surplus is used to determine the total loss of welfare when comparing a perfectly competitive market to other market structures, such as monopolies or oligopolies. It is also used to analyse the impact of the implementation of new taxes.