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.

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.

Demand and supply are possibly the two most fundamental concepts used in economics. The concept of market is usually defined as a number of buyers and sellers of a given good or service that are willing to negotiate in order to exchange those goods. We will first explain them separately and then jointly to show their interaction.

Demand:

Demand is the global market value that expresses the purchasing intentions of consumers. The demand curve shows the quantity of a specific product that individuals or society are willing to buy according to its price and their income. This curve shows an inverse relationship between price and quantity demanded giving it a downward slope. The reason why this happens is known as the law of demand: ceteris paribus, and considering ordinary goods, the higher the price the lower the quantity demanded, and vice versa.

We can start by analysing demand from a purely microeconomic point of view: a single individual, let’s say her name is Joan. Joan’s demand for, let’s say, books, is such as shown in the adjacent graph. If the price of a book is $35 or more, Joan won’t demand any (point a), given her preferences (basically, she would rather spend her money on something else). However, if the price of books goes down to $30, she will want to buy one (point b). If it decreases to $20, Joan will buy two books (point c), and so on. By joining all the points (a-h), we’ll get Joan’s demand curve. It’s worth mentioning that, for simplicity’s sake (though violating monotonicity), we consider that the demand curve ends at the axes.

From a macroeconomic point of view, the demand curve is just the aggregation of all demand curves from all buyers in a particular market. Let’s say the market for books has only two buyers: Joan and her classmate Edward. The horizontal sum of Joan and Edward’s demand curves will give us the market demand: 

Supply:

On the other side, supply is the set of offers made in the market for the sale of goods and services. The supply curve records the location of the points corresponding to the amount offered for a particular good or service at the different prices. This curve shows a direct relationship between price and quantity supplied, giving it an upward slope. The reason why this happens is known as the law of supply: ceteris paribus, and considering ordinary goods, the higher the price the higher the quantity supplied, and vice versa.

Let’s see how the supply curve can be built, starting with an individual’s offer, let’s say his name is Robert. Robert is willing to supply books for $10 or more, this is, Robert won’t supply any books for $5 (point a). However, if the price of books goes up to $10, he will be willing to sell one book (point b). If it increases to $15, Robert will sell two books (point c), and so on. By joining all the points (a-g), we’ll get Robert’s supply curve. Notice that the supply curve goes up and seems not to have limits, an assumption made for simplicity’s sake. Of course Robert will have troubles to supply more than a certain amount of books, but let’s keep it simple and not think about the upper end of the supply curve.

Again, the market’s supply curve is just the aggregation of all supply curves from all sellers in a particular market. Let’s say the market for books has only two sellers: Robert and the librarian next door, Gregory. The horizontal sum of Robert and Gregory’s supply curves will give us the market supply:

Equilibrium and market clearing:

The demand and supply curves define the market clearing, that is, where the demand of the products meets its supply. At this point we have what is known as, an equilibrium point, with its corresponding price and quantity of equilibrium.

It is possible for disequilibrium to occur when the amount demanded does not equal the amount supplied. There are a series of scenarios in which this can happen. In situations in which the quantity demanded is higher than the quantity supplied, the market is suffering from an excess demand. When the opposite occurs we will be talking about an excess supply. Prices will have to gradually adjust through different market mechanisms until the equilibrium price is met.

Movements vs. shifts:

When analysing demand and supply and their respective curves, it is important to distinguish between two aspects: movements along curves and shifts in curves.

A movement refers to a change in either the demand or supply curve, which occurs when a change in the quantity is caused by a change in price and vice versa. An increase in the price of a good or service would cause a movement along its demand curve, decreasing the amount demanded. In the case of supply curves, as we previously saw, an increase in price would also increase quantity. It’s important to understand that movement along the curves does never actually change the equilibrium point, as movements along the curves do not affect it. In the adjacent figure we can see a price increase (let’s say, because an increase of VAT), which causes a movement along the demand curve.

Sometimes the market suffers from changes due to a displacement (shift) of the demand and/or the supply curve. This shift in curves will always result in a new market equilibrium. When a shift occurs, the curve moves, meaning that for each price there will be a new different quantity being demanded or offered. This curve shifts can occur in two directions, upwards and downwards, or if preferred, rightwards and leftwards. Depending in what curve we are considering one is equal to another one.

Demand curves may shift for multiple reasons, for example, an increase in the consumers’ level of income would increase the aggregate demand of a normal good for each price, and hence shift the demand curve to the right (left figure). Other examples would include changes in the price of competitors (substitute goods), changes in complementary goods, tastes, expectations, number of buyers, seasonality, etc.  Supply curve shifts may be also motivated by a variety of different reasons, such as input prices: an increase on the price of paper would shift the supply curve to the left, since the same quantity would be sold at a higher price (right figure). Other variables that can shift the supply curve include technological progress, expectations, number of sellers, etc.

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:

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.

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.

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.