2.1.3. elasticities

We have already discussed about the elasticity of demand, see elasticity of the demand, althought Adam Smith doesn't use the term. However Adam Smith was already aware that a low tax on consumption can yield more than a high tax, because if the tax is passed to the price, something he assumes because due to competition the retailers have no leeway, the effect on amount can exceed the effect on price.

To keep it simple: Let's assume that the price for an apple is 20 cent and for this price 100 apples were sold. If the government know imposes an apple tax of 5 cent the apple would cost 25 cent. The amount of apples however would decrease and only 80 apples were sold. The tax revenue would therfore be 4 dollars. But if the government would impose 10 cent of apple tax only 30 apples were sold and the tax revenue would be 3 dollars. The effect on the amount overcompensates the effect on the price.

Alfred Marhall only mentions the price elasticity, in other words the impact on the amount of a changes in prices.

Beside that we have the income elasticity which describes the impact of a change in the income on the amount. Some branches for example will be the losers of an increase of income. If the income doubles people won't eat the double with the effect that the part of the agrarian sector of the gpd will shrink. (If not compensates, what actually happens, by the use of more and more convenience food. Convenience food and more sophisticated products were able to slow down a bit the general tendency of the last 50 years, however food production on all levels is losing importance. At least in industrialised countries.)

Explicetely Alfred Marshall only mentions the price elasticity. However he mentions as well the rich and poor and that means that implicetely he mentions the income elasticity as well.

The current prices of meat, milk and butter, wool, tobacco, imported fruits, and of ordinary medical attendance, are such that every variation in price makes a great change in the consumption of them by the working classes, and the lower half of the middle classes; but the rich would not much increase their own personal consumption of them however cheaply they were to be had. In other words, the direct demand for these commodities is very elastic on the part of the working and lower middle classes, though not on the part of the rich. But the working class is so numerous that their consumption of such things as are well within their reach is much greater than that of the rich; and therefore the aggregate demand for all things of the kind is very elastic. A little while ago sugar belonged to this group of commodities: but its price in England has now fallen so far as to be low relatively even to the working classes, and the demand for it is therefore not elastic.

Alfred Marshall, Principles of economics, BOOK III, CHAPTER IV, THE ELASTICITY OF WANTS

There is an interesting remark in this paragraph. Alfred Marshall distinguishes two groups, rich and poor. A change of prices for meat, milk, butter, wool, tobacco will have a heavy impact on the amount for one group, the poor. That can be explained by the fact, that they spent almost all their money, at that time, for food. If the price for more "luxury" food increases, they are obliged to buy more bread, potatoe, collards etc. in order to survive. The rich will maintain their consumption of these goods and spent less in trips, vine, luxury clothing etc..

We have therefore two different groups with two different price elasticities. The price elasticity of the poor is very high, very elastic in the word of Alfred Marshall. A small change in the prices for these goods will lead to a strong reduction of the demand. The price elasticity of the rich at the other side is very low, inelastic if we want to use the term used in modern textbooks. A change in prices would lead only to a little change of demand.

Completely inelastic means that the there is no impact on the amount to a change of the price. This is for instance true for drugs. Whatever they cost, the addicts will pay it.

Completely elastic means that only a little change in the price will reduce the demand to zero. This is for instance the case if there exists a perfect substitute. Sugar made of sugar beet will be immediately substituted by sugar made of cane if the prices of sugar made of sugar beet increases.

Alfred Marshall deduces the price elasticity from the marginal utility. The greater the loss of utility per unit with every unit consumed, the less people will be willing to pay for any further unit.

The price elasticity is a an instrument about which we can reflect 10 minutes. (No more. Time is precious, see preliminaries. The time spent in the academic world is definitifly to much. Several hours is to much.)

Depending on the elasticity it is for instance possible to raise the prices. A baker can for instance produce 10 breads for 40 cents. The turnover is then 4 dollars. If at a price for 30 cents he can sell 20 breads, the turnover is 6 euros.

However that doesn't mean that the profits are maximised. It is very plausible that turnover of Volkswagen would increase dramatically if they sell their cars for 5000 dolloars, however they will go bankrupt by doing that.

The profit only increases as long as the marginal turnover is higher than the marginal costs. In other words: As long as the the price of the last unit sold exceeds the variable production costs of this last unit the benefit increases. From the moment on that the variable costs exceeds the price, the profit will diminish. The point where the variable costs per unit equals the price we have reached the benefit maximising price / amount relation. This point is called the point of Cournot.

To illustrate this with an example. We assume that we can sell more if the price decreases, but the costs increases.

Price for the last unit: 10, 9, 6, 3, 2, 1.
Marginal cost of production: 3, 5, 6, 9, 11, 14.

In this case the company would sell three units and 6 would the price at the Cournot point.

This not really complicated relationship is explained in textbooks with a lot of mathematical modeling. However the modell presented in texbooks is too simple to explain reality and therefore irrelevant for the practise. The actually used costing system works with direct costing. The problem with the modell we find in textbooks is that there is only one bloque of fix costs.

Fix costs are costs that have nothing to do with the decision to offer or not a certain product or service. If a company had already bought a specialised machine the decision is already made and therefore irrlevant for the concrete calculation. If the machine cost 1000 dollars and they can make a profit with each unit sold (price - the costs which are related to this decision) of 2 dollars they need to sell 500 units to pay the machine. However if they can only sell 400 the lose money, but at least not as much as in a situation where they sell absolutely nothing. A calculation that includes the fix costs, the machine for 1000 dollars, would therefore misleading. There is no doubt that the company has to cover these costs in the long run, otherwise it goes bankrupt, but if that is not possible, they have to try to minimise the losses.

The problem is, that in reality things are more complicated. We don't have one cost block, but several cost blocks for each group and each kind of product. The decision to offer or not a product or service depends therefore on the cost block related to the decision. BEFORE we decide in GENERAL to offer a product or service the respective fix cost block has to be taken into account, obviously. AFTER this desision is made, we don't have to take it into account any more.

Actually the terms variable costs and fixed costs used in textbooks about microeconomics are misleading. We have to speak about decision relevant costs and decision irrelevant costs.

Alfred Marshal describes the price elasticity without any kind of mathematical modeling and all what we find today in modern textbooks is relegated to the appendix. But he discusses the problem whether it is possible to know exactly the slope of the demand curve (something he denies, see above.)

Alfred Marshall describe la elasticidad del precio de manera meramente verbal, pero se ocupa del problema principal, o sea con la pregunta si es posible de determinarla o que problemas se encontrará al tratar de determinarla. (La modelización matemática la trasladó al apendix de su obra.)

In theory and in practise the elasticity is a concept we can talk about for ten minutes, but not longer. Of course every company calculates with different scenarios, different compinations of price / demand. However no company knows the impact on prices on the demand. If they knew that, they never, absolutely never, would go bankrupt. In the academic world it is easy to paint a function on a piece of paper. Reality is something very different. The basic concept is easy to understand, further mathematical modeling doesn't lead to a deeper insight. It may look more "intelligent", but is a waste of time. It is obvious that all entrepreneur knows that their is a theoretically ideal combination of price and amount sold and the will try to find it. However in practice this is done by experience. Beside that the concept is irrelevant and doesn't play any role when it comes to discuss real world problems.

The price elaticity is due to two completely different phenomenon that should not be confused. In textbook about microeconomics is only mentioned one, see Say's Law. The slope of the demand curve, and therefore the elasticity, can be explained by the decreasing marginal utility. The more is consumed of a product, the less the utilitiy it yields and the less people are willing to pay.

The second phenomenon is completely different. In this case only ONE unit of an item is consumed and the different alternatives are competing with each other. Demand for an item increseases if the relationship utility / price increases.

For mathematical modeling and other funny plays of this kind it doesn't make any difference of course whether the units solds increase if prices decreases is due to the decreasing marginal utility or to the fact the alternatives compete with each other. However it makes a big difference in real live for real companies, because the marketing mix, price / condition policy, distribution policy, product policy, communication policy is completely different in each case. From a practical point of view they have nothing to do with each other.

A new product, for instance a tablet that that competes with a laptop, that competes with other products have to be explained and the advantages have to be underlined. If a company wants to increase the turnover of a product with a decreasing marginal utility, are completely different marketing strategy is needed. The product has not to be explained, but the consumption has to increase increase.

To keep it simple: Introduce tablets into the market is a completely different problem than increasing the demand for milk. For both products we have a price elasticity and we can make the same mathematical modeling for both if we abstract from the real world. But in the real world the problems are very different and more complicated. Mathematical modelings suggest an exactness which is actually pure nonsense.

A demand curve, de condition for calculating the consumer surplus, see cardinal measurement of utility, can only be obtained if we collect data during a long period of time. A company can perhaps "playing" with prices inside a small range or set different prices in different markets, but even that is in general not possible.

The problem is however that during a long period of time everything changes. Even if the prices for a product don't increase at all, it is well possible that people pay more, because their income increases. It is as well possible that other product became less expensive and therefore people can buy more from something else. It is possible as well that people buy more of an item, because their preferences change etc. etc..

It is true, that the change to get bought increases if prices are low. But in most cases this is not due to the decreasing marginal utility. It is much more simple. Products compete with each other and we buy the cheapest one and this is in practise a really relevant information. A company who thinks about offering a poduct will do that only, if it thinks that they can offer the product for a lower price than the competitors for similar products.

The concept of price elastictiy was first introduced by Alfred Marshall. However Alfred Marshall himself was more critiqual about the practical relevance of this concept. The demand curve establishs a relationship between two effects without mentioning the causes of these effects. In practice the price is ONE parameter that determines the demand, but not even the most important one. Spending several hours in analysing with a lot of functions and equations an irrelevant relationship and abstracting completely from the relevant ones is stupid.

It is generally argued that this simplification allows to focus on the central problems. The truth is, that the central problems are obscured by the modell and that modeling narrows the perspective.

In the long run, to give another example, things become cheaper not because the prices fall, but because the income raises. It is cristal clear, otherwise the economy wouldn't grow and the promise of the market economy would fail, that in the long run people can buy more with their income, but that has little to do with the price elasticity.

The price elasticity can be mentioned in a textbook. But is 10 percent of the pages is dedicated to this topic, then it is definitely too much.

It is indeed true that the marshallian cross of the supply and demand curve allows some insights. It is for instance a handy way to show that only in equilibrium, where the consumer surplus and the producer surplus are maximised the general welfare reaches its maximum. It is as well a handy way to show who benefits and who pays if the price is fixed above (or below) the equilibrium price, see cardinal measurement of utility. It is however important to see that this type of analysis takes into account only some aspects and that the whole picture is more complicated.

Let's see what the master himself thinks about the topic.

The above difficulties are fundamental: but there are others which do not lie deeper than the more or less inevitable faults of our statistical returns. We desire to obtain, if possible, a series of prices at which different amounts of a commodity can find purchasers during a given time in a market. A perfect market is a district, small or large, in which there are many buyers and many sellers all so keenly on the alert and so well acquainted with one another's affairs that the price of a commodity is always practically the same for the whole of the district. But independently of the fact that those who buy for their own consumption, and not for the purposes of trade, are not always on the look out for every change in the market, there is no means of ascertaining exactly what prices are paid in many transactions. Again, the geographical limits of a market are seldom clearly drawn, except when they are marked out by the sea or by custom-house barriers; and no country has accurate statistics of commodities produced in it for home consumption. Again, there is generally some ambiguity even in such statistics as are to be had. They commonly show goods as entered for consumption as soon as they pass into the hands of dealers; and consequently an increase of dealers' stocks cannot easily be distinguished from an increase of consumption. But the two are governed by different causes. A rise of prices tends to check consumption; but if the rise is expected to continue, it will probably, as has already been noticed, lead dealers to increase their stocks. Next it is difficult to insure that the commodities referred to are always of the same quality. After a dry summer what wheat there is, is exceptionally good; and the prices for the next harvest year appear to be higher than they really are. It is possible to make allowance for this, particularly now that dry Californian wheat affords a standard. But it is almost impossible to allow properly for the changes in quality of many kinds of manufactured goods. This difficulty occurs even in the case of such a thing as tea: the substitution in recent years of the stronger Indian tea for the weaker Chinese tea has made the real increase of consumption greater than that which is shown by the statistics.

Alfred Marshall, Principles of Economics, BOOK III, CHAPTER IV, THE ELASTICITY OF WANTS

Economics is really a strange kind of science.If asked, the vaste majority of the economists would answer that they obtained their "economics laws", something they are fond of, by distilling from empirical data the laws that explain these empirical data. However this is not what actually happens in microeconomics. Microeconomics is more a mathematical modeling of an insight got by pure "intuition" and the insight we get from mathematical modeling is not deeper than the one we get by pure "intuition", but the pure intuition has the big advantage, that is doesn't narrow the perspective.

If we want to be precise, the marshallian cross is even wrong. The marshallian cross assumes a relationship between amount and cost, the higher the cost, the more supply and between the amount and price, the lower the price the bigger the amount. Demand and supply are therefore considered as two completely different issues. The cause are the costs and the result the supply, in case of the supply curve and the price is the cause and the amount the result, in case of the demand curve.

Actually the relationships are more complicated. The costs for instance can decrease if the DEMAND increases. If only 100 people have a mobile these 100 people have to pay the whole infrastructure. In this case every mobil would cost several hundred millons of dollar. If hundred of millons of people have a smartphone, the part of the fix costs that every mobil has to bear are minimal. The marshallian cross suggests that the cost of production has nothing to do with the demand. That's not true at all.

[Economists will argue that the supply curve represents an aggregation of marginal costs and that the fix costs don't play any role in this case. However this is only true in the short run. In the long run a company must cover ALL costs. Companies who don't cover all their costs will disappear in the long run. In the long run fix costs are part of the prices.]

The cross assumes that less companies will be able to produce the product and more people will buy it if the price decreases. This is obviously wrong. Most products become CHEAPER if the demand increases, because most product, especially consumer durables, have heavy fix costs. Cars, television, computers, refrigerators, any kind of electronic devises, etc. etc. has become CHEAPER in the last fifty years while the demand has increased drastically. What actually happens is the exact opposite of what the marshallian cross suggests.

[Something Alfred Marshall was well aware of. He distinguishes cleary between the short run, where the relationships suggested by the marshallian cross are more or less true and the long run, where these relationships are not true at all.]

The fact that the costs depend on the DEMAND can't be demonstrated by this modell. Even worse: The modell obscures the real relationships.

Beside all these problems there is the problem we already discussed in the chapter cardinal measurement of utility. A large demand for a product, for instance smartphones, will attract other producers and the existent producers will quickly gain in efficiency. Only in the short run, where the production structure doesn't change an increase in demand will lead to higher prices and only in the short run there will be a consumer surplus, cardinal measurement of utility.

The marshallian cross, the best known low of all "economics laws", we find that in any textbooks at least one hundred times in different situations, describes ONE possible relationship, but not even the most typical one. We can even say in practise the exact opposite is much more typical. In the long run prices DECREASE with an increase of demand.

That the prices increases if the demand increase given that only high prices will induce more producers to produce the good is plausible in the short run and very plausible in the case of resources which are scarce by nature. The supply of precious stones for instance can't be increased infenitively. If the demand increases, only those demander who are willing to pay more than others will get one. The amount will remain the same and the prices increase.

We can observe as well that prices raise if the supply needs some time to adapt itself. That happens for instance in the housing sector. If the demand for housing increases suddenly it will take some time until new housings are constructed. (Sometimes due to a lack of land they are even constructed never.)

Beside that the idea, that the prices raise if demand increases is completely incompatible with a market economy or, in other words, the market economy would lose its justification. The justification of a market economy is that in the long run people are better off, because in the long run a market economy leads to a higher efficiency. If a market economy led only to higher prices if the demand increases, it is a bad kind of economic order. A market economy can only be justified if the real prices, the prices in relationship to the income, decreases in the long run.

The mathematical modeling, the simplified version of the marshallian cross we find in textbooks about microeconmis, is actually based on an incorrect "intuition" experienced in some special situations. People buy a good when it is cheaper than competing goods. In some cases, the most prominent example for that is food, because due to the decreasing marginal utilitity they are only willing to buy more if the prices decreases. In some special situations the supply is actually limited. In this case the some demanders has to be kicked out throug higher prices. These special situations are then taken for typical, although they are an exception.

Another explanation could be that people are more away of this effects, because a raise of prices due to this effects is more noticeable than the decrease of prices over the years.

If we take the most basic "economic law" of economics, the marshallian cross, we can say that mathematical and graphical modeling does exactly the opposite what it pretends to do. It is said that mathematical / graphical modeling leads to a more precise thinking and allows a deeper insight. The opposite is true. In mathematical / graphical modeling people get completely lost. They concentrate so much on the modell, that they lose any contact to reality.

We have already seen in the chapter about David Ricardo that a lot of "economic laws" taken for enternally and universally valid showed up to be very instable. The "law" of supply and demand seems to be the next candidate for an "economic law" that becomes obsolet.

The famous marshallian cross based on the ceteris paribus clause, in other words, on the assumption that nothing changes. If nothing changes, what is actually true in the short run, prices has to raise if demand increases. (If we put a side the problem with the fix costs mentioned before. This is another problem.) If the productive structure doesn't change the costs will raise if the production increases. Extra wages are to pay for overtime, the machines don't work at their optimal state, raw materials become more expensive and so on. The slope of the supply curve suggests that there are some companies more efficient than others. All of that is true in the short run. In the long run however competition will bring down prices again. The more efficient companies will be copied. It this were not true, a market economy couldn't held its promises. If prices increases if the demand increase, people are never be better off.

We have to distinguish therefore very clearly between a short run analysis and a long run analysis. We will see later on, when discussing about Léon Walras, that it is a fatal error that leads to absurd results not to distinguish between these two scenarios.

In other words the price elasticity makes only sense inside a certain period and even then it is known, if ever, inside a small range of amount on a certain geographic market.

It is a general believe that the neoclassical theory is the opponent of marxism. That can be doubted. There is a big difference in the content, obviously, but the methodological approach is very similar and that is more important than the content. Both of them make heavy use of hypothetical examples and draw all their conclusions from these hypothetical examples. Both focus on certain issues and abstract from the more relevant once. The question is not really whether this theories or ideologies are wrong or wright. The question is whether the problems discussed are relevant and this is not the case.

Neoliberalism, or the austrian school, is often confused with neoclassical theory, although they have little to do with each other. Neoclassical theory adresses at least the right problems, although they give the wrong answers. There is indeed a problem with the control of governmental activities at all levels, see preliminaries. The error of neoliberalism is the assumptions that the market mechanisms are the only way to steer an economy, but due to the fact that this mechanisms very often lead to unwanted results, we need other mechanisms, for instance transparency. Videos like Milton Friedman, free to choose reach a great public, because they address a real problem and if the keynesian theory is misunderstood, and in public debate as well as in the academic sphere we find a lot of misleading ideas about keynesian theory, the risk that the government will attract more and more resources actually exists. See the booklet downloadable from the startsite of this website.

It is important to distinguish clearly between the neoclassical theory and neoliberalism which has little to do with John Stuart Mill, the founder of liberalism. If we mix up everything with everything we get finally to the situation that we have different terms for the same thing and nobody has a clear understanding what the mean.

Neoliberalism puts a strong emphasis on the dynamic of economies and the need for coordination. The ceteris paribus clause of the neoclassical theory in the simplified version we find in textbooks, assumes with the ceteris paribus clause that nothing changes. If nothing changes, the need for coordination mechanisms is very small. Once the optimal state achieved, it remains there until the Last Judgement.

To illustrate it with an example: The producer surplus is not a static size. It lasts only until the other producers achieve the same efficiency. To calculate it is mathematically nonsense, because it is flow variable, a period of time is needed, and not a size of stock as suggested in textbook about economics, and distracts from the real problems.

Abstracting from the dynamic of economies can lead to complete erroneous results. Léon Walras for instance assumes for a long time that is the price only that balances supply and demand and there is no change in the amount. This is true for a market where producst are only changed, but not produced. This is a static view of the economy. The dynamic part, the production side, is ignored. He got traped in his mathematical modeling, that narrowed his perspective.

The case of Alfred Marshall is different. Alfred Marshall, the founder of almost all the concepts we find nowadays in textbooks aobut economics is different. He distinguishs clearly between a short run analysis and a long run analysis, see equilibrium in the long run and in the short run.

The marshallian cross is a static modell. If we want to be exact, the supply curve is an aggregation of the individuel marginal costs curve, in other words, the fix costs are not included. In the long run the equilibrium price can as well be a price where the companies minimise only their losses, but don't earn anything. If they bought a special machine because they expected a higher turnover and can't sell this machine because they would only get the scrap value, they can do nothing but minimize their losses. Something that won't work obviously in the long run.

In the long run the fix costs can't be ignored. All the concepts based on this model, half of we find in textbooks, assumes that fix costs doesn't exist. In other words, all the funny exercises we find in textbooks abstracts completely from the real world and it can be argued that this simplification helps to understand better some issues of the real world.

We cannot even say that the funny exercises of moving the supply curve to the right when there is a subsidy or to the left, if there are taxes are right. What we actually see in this case is an increase or decrease of the gross margin. But if the gross margin falls beyond what is needed to cover the fix costs, much more companies will disappear than what is showed by the model.

What does that actually means? That means that all the funny things we find in modern textbooks, consumer surplus, producer surplus, price elasticity, income elasticity, pareto optimum, equilibrium price, marginal utility, marginal cost curve, etc. etc. can be reduced. Twenty hours is enough, no need to dedicate a whole semester to that. The time saved can be spent to discuss about relevant issues and if the economists have nothing to say about the real problems, it is much better to dissolve the economic faculties, "think tanks", "research institutes" etc.. The tax payer would save an enormous amount of money that can be used better otherwise, see prelimaries.

All these problems can't be imputed to Alfred Marshall himself. He warned extensively about using modells in a mechanical way. It would be a big progress if the academic studies would be based on the original work and not on the copies.

return to the top of the page ...

2.1.3. elasticities

Price / income elasticity