2.1.2. cardinal measurement of utility

Cardinal measurement of utility means that the utility is measured with cardinal numbers, that means in practise with money. Cardinal measurement is opposed to ordinal measurement, where a bundle of goods is exchanged between two persons.

If two persons has two goods, for instance chocolate and apples and they change chocolate for apples and apples for chocolate we don't know the utility they lose respectively by exchanging chocolate for appels and appels for chocolate nor the utility they gain by exchanging, but we know that one of them prefers chocolate and the other apples, otherwise they wouldn't change. Every person has therefore an individual subsitution rate. This is called ordinal measurement of utility.

The concepts of Alfred Marshall for instance the consumer surplus, is based on a cardinal measurement of utility and the concepts of Vilfredo Pareto are based on an ordinal measurement of utility.

If someone pays one dollar for an icecream the utility of this icecream is worth for him one dollar, that is obvious, otherwise he would have bought something else. If we regard only this person, the cardinal measurement of utility is not a big problem. If someone buys icecream for one dollar instead of buying chocolate for one dollar he prefers icecream to chocalate. That may change after having eaten the icecream because of the decreasing marginal utility, but at the moment he buys icecream it's like that. Nothing complicated until know.

The problem with the cardinal measurement of utility start if we compare two people or if we aggregate the utility of several people. If two persons buy a smartphone for 300 dollars, we can't say that the utility is the same for both. If someone earns 10 000 dollars a month 300 dollars is just nothing and the smartphone doesn't yield much utility in order to be bought, because the 300 dollars already have little utility. But for a person who earn 500 dollars a month 300 dollars is a lot of money and the smartphone must yield a lot of utility in order to be bought. An interpersonal comparison is therefore not possible with the cardinal measurement of utility. From this point of view the consumer surplus is a problematical concept, because it is an aggregation of the utility abstracting from the personal situation of the people.

To put it simple. Measured in money, and the consumer surplus is a measurement in money, our two persons above get 600 dollars of utility. A unity of money is equal to a unity of utility. But if for the richman the utility is only 30 and for the poor 500, the total utility would be 530.

[We don't say that this is a very relevant practical problem, but it is strange that we find in any textbook several methods to calculate the consumer surplus, the aim is to demonstrate that economics is a very exact science. But if the basic concept is already inexact, there is no need to make exact calculations. What Alfred Marshall himself, by the way, didn't do.]

It is often argued that the falling course of the demand curve is due to the decreasing marginal utilitiy. The more we consume of something, the less we appreciate it and the less we are willing to pay. In this logic the price we are willing to pay is a direct consequence of the utility an item yields us. This is actually true at a microeconomic level where only a single marketplayer is considered.

This is no longer true, for the same reasons already mentioned in relationship to the consumer surplus, if we add the single demand curves. If person A buys 3 units of an item for 4 dollars each and person B 2 units of an item for 4 dollars we can say, obviously, that the demand is 6 if the price is 4 dollars. But we can't say that this corresponds to a certain amount of utility units, because the utility that A gets from one unit of this item is not necessarily the same that the utility B gets from this item. The logic we find in many textbook about micrcoeconomics is wrong.

[What is obviously not a big problem. It's a pure theoretical discussion, without any practical relevance. However, as already said, it is mad to pretend exactness through mathematical modeling if the assumptions made are already very inexact.]

The second problem with the description of the falling demand curve we find in textbooks is more serious. The falling course of the demand curve can only be explained by the decreasing marginal utility if people consume several units of an item. But from most commodities we consume only one unit, one car, one refrigerator, one television etc.. In this case the falling demand curve can't be explained by the decrease of marginal utilitiy, but by the competition between the different choices, see Say's Law. Obviously in this case as well it is not possible to aggregate the individula demand curve, if we assume that the price reflects the individual appreciation of an item.

If we want to be exact we shouldn't talk about the decrease of marginal utilitity, but of the exprected decrease of marginal utility or, in the case that only one unit of a commodity is consumed, of expected utility. If the actual utility is bigger than what we expected it is even possible, that the prices increase with consumption, because people learn to appreciate a product.

[This is, to take an extreme example, the case with drugs. The "utility" increases with consumption and the more one consumes, the more money he spent for it.]

From a purely practical point of view only the cardinal measurement of utility is relevant. The ordinal measurement of utility of the Vilfredo Pareto can be measured only in hypothetical situations, through the substitution rate that describes the substitution of one product for another.

The cardinal measurement allows for instance to give in insight on the loss of consumer surplus due to governmental interventions like customer duties, taxes etc.. Due to the fact that a relationship between prices and utility doesn't exist, see above, we can't really "calculate" the losses, but we can see that there is one. For a more detailed discussion see above.

The most famous application for the cardinal measurement of utility is the consumer surplus. At least in ideal circumstances there is only one market price for a certain commodity, that's the price everybody has to pay if he wants to obtain this commodity. However some people would pay more, if they were obliged to pay more. Therefore they get a consumer surplus. Their preferences for this product is higher than what is actually revealed by the price they pay for it. The difference between the price they would pay if they were obliged to pay and the price they actually pay is there individual consumer surplus. If we aggregate all the consumper surplus, we get the consumer surplus of all the buyers of this commodity, although, see above, this is not very accurate, because money itself is follows the law of the decreasing marginal utility. The more someone has of it, the less utility yields the last unit.

Similar for the supply side, with the big difference that at the supply side we have objective data. Given a certain demand, there is a certain supply necessary in order to satisfy this demand, in other words, all the suppliers able to produce the commodity at the market price, can produce it. The last supplier, the less efficient which is still able to produce the commodity at the market price, is called the marginal supplier and all the others, which can produce the commodity at a lower price, get a producer surplus. This is actually a rent. They get this producer surplus without any extra effort. If for instance the demand and therefore the market price increases, the producer surplus increases as well automatically.

The producer surplus is actually the result of the same mecanism as the rent of David Ricardo, although David Ricardo that only land yields a rent. The markt price for food depends on the demand for food, but the costs of production of food on the fertility and the distance of the land. The more infertil and the more far away the land, the higher the production costs. Land near by and fertil gets therefore a consumer rent.

The fact that David Ricardo applies this concept to the production of food and land is due to the fact that for any other production factor, capital and labour in his case, he assumed that it will flow immediately to the most profitable use, in other words, that there are no differences in efficiency and the cost of production. Wages and profits are the same everywhere. In this case, obviously there are no producer surplus or rent.

In the long run this is even true and still more true under the assumption of neoclassical theory. If we assume full information, differences in efficieny and cost of production will be soon disappear. A problem Alfred Marshall, in contrast to modern textbooks, was well aware of.

Due to the fact that the supply curve is based on costs, we can even aggregate the individual marginal cost curves to an aggegate marginal cost curve.

Actually it is better to interpete the consumer rent as savings. Lets say we have little Ana, little Luisa and little Tom. In their young lives they had already the time to find out what the like and what they don't like. Let's say that the market price for a bar of choclate is two dollars, but Ana would have paid 3.50 dollars, Luisa 3.20 dollars and Tom just the market price, 3 dollars. They actually paid 9 dollars, but would have paid 9.70 dollars. Therefore they saved 70 cent. This is the consumer surplus. Perhaps the 20 cent that Luisa saved have more value for Luisa than the 70 cents that saved Ana, that's something we don't know, but in any case they saved 70 cent.

Alfred Marshall in any case defines the consumer rent as a plus of satisfaction.

We have already seen that the price which a person pays for a thing can never exceed, and seldom comes up to that which he would be willing to pay rather than go without it: so that the satisfaction which he gets from its purchase generally exceeds that which he gives up in paying away its price; and he thus derives from the purchase a surplus of satisfaction. The excess of the price which he would be willing to pay rather than go without the thing, over that which he actually does pay, is the economic measure of this surplus satisfaction. It may be called consumer's surplus.

Alfred Marshall, Principles of Economics, BOOK III, CHAPTER VI, VALUE AND UTILITY

The concept of the consumer / producer surplus is used most of all to explain the effects of taxes. Let's take the example above, Ana, Luisa and Tom to analyse what would happen if the government imposes an anti - caries tax, a tax imposed on all kind of sweets, that would have the effect that the price for a bar of choclate would increase by 20 cent.

In this case Tom wouldn't buy it anymore and would use his three dollars to pay potatoe chips, which for an unknown reason the government believes to be heathier. Luisa and Ana would still buy it, but Luisa would get no consumer surplus at all and the consumer surplus of Ana would be reduced to 30 cent, because she is actually disposed to pay 3.50 dollars. In total the consumer surplus would be reduced to 30 cent.

However this concept can be critisized.

[Remark: If someone really wants to know what Alfred Marshall actually said, has to read the original. Any kind of summarize, including this one, is a simplification. Part of the problems mentioned here were already discussed by Alfred Marshall himself. For instance he already was aware of the fact, that the exact course of the demand curve is always unknown, with the result that the consumer surplus can never really be determined.]

  1. Due to the fact that we don't really believe in the practical utility of microeconomic concepts the critique could be neglected. The exact slope of the demand curve is never known and it can be questioned whether it makes sense to spent a lot of time in analysing equilibriums, although more mathematical modeling is possible if only view things change, that's why microeconomics focuses on the analysing of equilibriums of any kind. In a relatively short period the structure of the demand can change completely. Only fourty years ago germans for instance spent most of their money in food and clothes, nowadays the expenditure for food are almost irrelevant and would be even more irrelevant, if people woudn't buy more and more instant meals or food very near to consumption and clothes has fallen so much in price, that nobody nowadays takes the trouble to repair it. The demand curve is not a very interesting issue and doesn't play any role in public discussions and contributes nothing to the debate about real problems. The interesting issue are the long term changes in the production structures.
  2. It is obvious that the consumer surplus is reduced by taxes on consumption. The question is whether this is a very interesting issues, if we take into account that an income tax reduces consumption as well. A tax on consumption and an income tax has, at least in theory, different impacts. The later one reduces, at least in theory, savings, but is fairer because it is possible to take into account the personal situation of the taxpayer. If a liter of milk is taxed with 20 cents, everybody pays 20 cent, regardless if he earns 10000 dollars a months or 1000. The attention payed to the loss of consumer surplus by governmental intervention seems to be more motivated by the possibility to use mathematic modeling than by the relevance of this phenomenon. It is unclear what this analysis wants to tell us. Should taxes on consumption always be avoided?

    Beside that the concept is misleading. In our example with Ana, Luisa and Tom the consumer surplus is reduced by 30 cent, but this 30 cent are not lost. The goverment will spent them and this spending will increase the utility of the society. The concept of the consumer rent suggests that there is a loss. This is in general only the case, if the government spents the increase of the tax revenue in a less efficient way than the individuals would have done. Another problem is that the aim of some consumer tax is a change of the allocation. This for instance is true in the case of our ficticious anti-caries tax. In this case the argument that there is a loss of consumer surplus is not convincing, because this loss is intended.
  3. The consumer rent is a concept that is generally used to analyse taxes, customer duties, governmental subsidies, governmental imposed mininum or maximal prices. Howerver most of these taxes, for instance the added value tax, is imposed on all products. A partial analysis of the impact of the added value tax on one product doesn't make therefore a lot of sense. If this tax is eliminated people had 19 percent, for instance, more in their pocket. However it is completely unclear what they would do with that money. In order to prognostic what they would do with this money, the demand curve has to be known. This is not the case. We can't assume, as the modell suggests, that people would by more of the product we are analysing. It is much more probable, that they would by something else or even save this money.
  4. The consumer surplus is an analysis based on the analysis of the market of one product. The author would say, that this is a misleading concept. If the government imposes for instance a tax on tobacco there is a loss of producer and consumer surplus for the very simple fact, that people will consume less of this product. If someone had paid for instance 4 dollars for a paquet of cigarettes that gives him the utility of worth 4,50 dollars, he would have obtained a consumer surplus of 50 cent. If the price of a paquete of cigarettes increase to 4.60 dollars due to the tax on tobacco he wouldn't buy it and loses therefore its consumer surplus. But if he buys for his 4 dollars a choclate bar withe a utilitiy worth 4.40 dollars (the price he would have paid if he was obliged to pay) he loses only 10 cent. The isolated analysis overestimates the effects.

Despite the problems mentioned before, as an exercise we can analyse a real world problem with the concepto of the consumer and producer rent.

To understand the following discussion some things should be known. The analysis refers to the taxi market in Germany. In order to follow the discussion it is necessary to know that the taxi price in Germany is fixed. One pays a certain amount of money for kilometer and this price is fixed by the taxi cooperation where all taxis are compulsory a member. This means, that if you want to take a taxi in Germany you can make a special agreement with the taxi driver, something that very often would benefit both, but that is not allowed. This price is above the market price, otherwise it wouldn't be necessary. In other words, it reduces the demand, because at this high price a lot of people prefer to use the bicycle, public transport or their own car.

A price above the market price has two effects. The first effect is, that some taxidrivers earn nothing, because they don't get customers at this price. The second effect is, that those who get customers, earn more.

In other words: The actual realised taxi rides are more profitable, but there are less than it would be the case with market prices.

Posible some wonders why it is not posible that the price for any taxi ride can be negotiated between the taxi driver and the customer. The argument put forward is that in this case we would get an endless bargaining at the taxi rank. The problem with this argumentation is, that this argument could be put forward in any sector of the economy.

The author of this lines has worked as a taxi driver to finance his studies and therefore he knows that there is a big tendency, especially if it is a long ride, to negotiate price. That is not legal, but highly attractive for both, the taxidriver and the customer. For a long trip the fixed price would be so high, that nobody would take a taxi.

If we want to know if a price above the equilibrium price is bad or good we have to add and substract a little bit. It is to assume that taxi cooperation fixes a price that is similar to the monopol price. Being the costs per km always the same no matter how many km are realised, we can say for the sake of simplicty that it maximises the turnover. Simplifying. What the monopolist loses because some people don't by its product is more than compensated by the higher earnings of the units he sells at a higher price.

What should be understood is this. The equilibrium price maximises the consumer and the producer surplus. This is obvious. If it were interesting to sell something below the equilibrium price, the supplier would have done it and if it were interesting to buy something above the equilibrium price, the consumer would have bought it. Both of them bought and sold until both of them got a profit and stoped at the moment, were for the one or the other it was not interesting any more.

A price above the equilibrium price has several effects. It reduces the consumer surplus as well as the producer surplus, because those who buy don't buy something or sell somenting, don't get it. That's obvious.

The second effect is, that the consumers pay more, the consumer surplus is therefore reduced in favour of the producer surplus.

(To put is simple: Let's say that the equilibrium price is 3 dollars and at this price 10 units can be sold. The turnover is therefore 30 dollars. Let's say now that the supplier can reduce the supply, for lack of competition for instance, and that he can sell 6 units at a price of 6 dollars. Then the turnover is 36 dollars. However the difference between 3 dollars and 6 dollars is paid by the consumer, who would has to pay less in a situation of competition.)

From that we can deduce that the sum of the consumer surplus and the producer surplus shrinkens if the price is above the equilibrium price. The first effect, less units bought and sold, reduces it and the second effect, the increase of the producer rent at charge of the consumer rent is a zero-sum game.

It is equally sure that the consumer surplus will be reduced. The case of the producer surplus is a little bit more complicated. While the increase of the producer surplus that is at charge of the consumer surplus is bigger than the loss due to the reduced units sold, the total effect for the producer surplus i positive. But it is chrystal clear that beyond a certain point, for example if the price is so high that he sells nothing, the losses are greater than the gains.

To keep it short: Monopolies maximise the producer surplus and not the common wealth and therefore they are forbidden.

We can therefore distinguish, in our example with the taxi market, the following effects.

a/ +(Increase of the producer surplus if the price is above the equilibrium price)

b/ - (Loss of producer surplus in comparison to the equilibrium price because there are less rides)
c/ - (Loss of consumer surplus in comparison to equilibrium price because the prices are higher)
d/ - (Loss of consumer surplus because there are less rides)
= Difference between the maximum of welfare in a situation of equilibrium price and a price above equilibrium

Let's analyse what that means. (At the end we will geht to a solution. A polypol structure with a monopol price doesn't work. That leads to a situation, where the taxi drivers, not the OWNER of the taxis get a very low wage per hour.)

If the taxi cooperation sets a price above the equilibrium price the consumper surplus is exactly reduced by the amount the producer surplus increases. If the price is 20 cent per km above the equilibrium price, the consumers pay 20 cent more and the taxis earn 20 cent more.

In other words: What is gained in a/ is lost in c/. Concerning this effect the total welfare, the sum of consumer surplus and producer surplus don't change.

Concerning the second effect, fewer demand for taxi rides and therefore less realised taxi rides both loses. Some consumers would have taken a taxi even at a higher price than the equilibrium price, if not higher than 20 cent, and some producers would have been willing to accept them, both would have had therefore a surplus. This consumer and producer surplus is definitely lost. b/ as well as d/ are therefore negative.

It is therefore absolutely sure that welfare, the sum of consumer and producer surplus will decrease. The only thing that can happen is that a/ increases more than b/ decreases. This will happen until a certain point, until the monopol price is reached.

An increase in prices above the equilibrium price increases the producer surplus if this effect is not compensates by a decrease of the taxi rides. If this is the case and how much the price can increase until that happens depend on the elasticity of the demand. If the demand is for instance completely inelastic, in other words if there is no reaction on the amount of units solds / taxi rides, this if for instance the case for drugs, the producer surplus increases proportionally to the increase of prices, because b/ es cero.

If in contrary the demand is completely elastic, in other word a small increase of prices leads to a reduction of demand to cero, this can happen for instance if their is an identical substitue, sugar from sugar beet <=> sugar cane, the producer rent is cero because /a is going to be cero. He will not be able to reduce the consumer rent, because doing so, he would sell nothing.

We have to assume that the taxi cooperation will try to put a monopol price, in other words, they will maximise the producer surplus /a and /a is bigger than b/. The increase of the producer surplus at charge of the consumer surplus exceeds the loss of producer surplus due to the fact that they lose part of their customers.

In case that the price fixed by the taxi cooperation is very high, nobody will take a taxi. We would have this situation. (A theoretical situation obviously. It will never do that.)

a/ In theory the producer surplus would be very high, but unfortenately nobody uses a taxi any more at that price. This producer surplus is therefore cero.

b/ An increase in prices almost always reduces demand. But prohibitive price, a price so hight that nobody buys the product, reduces the demand to cero. This loss is therefore very big.
c/ In this case we can't really say that the producer surplus is decreased at the expense of the consumer surplus because there is none.
d/ In this case there will be a big loss due to the fact that the demand decreases, because the demand simply cero.

El precio de equilibrio es por lo tanto un precio optima en el sentido de Pareto. No es posible de mejorar la situación de un grupo (el de los productores) sin empeorar la situación del otro grupo (el de los consumidores).

What we have to understand now is this. The taxi cooperation will try to maximise the producer surplus. They will try therefore to set a price which in textbooks about microeconomics is called the monopol price. The question therefore is if the price it fixes is really the monopol price. However we have to distinguish between the interests of the TAXI-DRIVER and the interests of the OWNER OF THE TAXIS.

The second thing we have to know is that in general the taxi drivers, at least in Germany, are paid normally with a percentage of the turnover. That means, that the owner of the taxis has always an interest to have the taxi on the road, even if earns very little. The alternative is not earning nothing at all. At a certain price the cake, the total turnover, has a certain size and only the taxis that are on the road get part of it, even if the taxi - driver earns almost nothing.

We have therefore a strange kind of situation. A normal monopoly would set a monopol price, but would as well reduce the amount of unit sold. But in this case, we have a monopol price but the supply remains the same. In other words, there are always to much taxis on the road. 80 percent of the time taxis are just waiting for customers.

The first question that arises is therefore this one. Does it make any sense to have a polypol market it the prices are fixed? If the demand can be satisfied in 20 percent of the time, the taxi drivers and the owner would earn the same amount of money if the government would run that business as it is the case with the public transport. Taxi drivers would then work as employees and would get a fix wage, working only 20 percent of the time they work right now.

Obviously the market would be closed than, it would not be possible to start working as a taxi driver at any time, but this openess of the market is actually paid by a heavy increase of the working hours.

The second solution is to go back to the natural state. Polypol prices in a polypol market. This would be a price, where the taxi drivers earn at least a living working only 8 hours a day. Due to the always existent unemployment rate, the competition between the taxi drivers is so high, that under the present situation they don't earn more than that. That will perhaps not change in a polypol situation with free prices. But it woudn't become worser either, because the limit is already reached.

However the prices would be lower and therefore more people could afford to take a taxi. The consumer surplus would therefore increase. Perhaps the situation of the taxi drivers wouldn't increase, but the society as a whole would be better off.

The third question is whether the price fixed by the taxi cooperation is really the monopol price, the price that maximises the producer surplus at charge of the consumer surplus or if it is to high.

Nobody knows really if the turnover wouldn't increase if they lower the price, that's is the first problem. The second problem is, that nobody knows if the costs per paid km wouldn't decrease. Right know only fifty percent of the km of a taxi are actually with a customer on board and paid. The other fifty percent the taxi is empty, because he only goes back to a taxi rank. If that can be improved, because more people take a taxi, this relationship can be improved.

Due to the fact that prices are fixed arbitrarily in almost all european countries and probably in all developed countries, we cannot know what would be the "right" price. We can only say that with the nowadays system the taxi owners have only one possibility to improve their situation. Increase the amout of taxis they have on the road by buying more licenses, they need a license from the taxi cooperation in order to run a taxi, one for each taxi, and hiring more taxi drivers who are only paid with a a percentage of the turnover. If the price is fixed, the turnover is fixed as well. At a certain price, there is a certain demand.

The nowadays system is convenient for the owner of the taxi and for the tax office, because it is easy to control. There is a stable relationship between the amount of km and the turnover, but the system is illogical. This systems leads to a situation in which much more taxis are in the roads that are actually needed to satisfy the demand that corresponds to that price. It would be more intelligent, if the prices are fixed, to organise the taxis as the public transport. The taxi drivers are paid a fix wage and we would only have the amount of taxis on th road that are actually needed, given a certain price. The "cake" could be distributed following the actual percentages of licenses, but actually there is no need to that. The concentration of taxi licences on a single company doesn't have any positive impact on public wealth and it not the result of better performance.

The actual system create jobs, even only low paid once. The owner of the taxis has an interest to get their taxis on the road 24 hours a day. If the amount of taxis on the road is limited to what is actually needed, we need less taxi drivers. But for the taxi drivers this is a zero sum game. The new taxi drivers are paid by the taxi drivers already working. The benefit for the society is that they have to pay less for social transfers, but that is not would we could call an intelligent solution. An intelligent solution would be to create profitable jobs.

There are arguments in favour of organizing the taxi business as a polypol market, but that prices has to be free and the taxi owners has to act as real entrepreneurs, otherwise they can't compete with services like ueber. Even if we admit that private cars don't have the same insurance as taxis, a problem that can be easily resolved, ueber proves that there is higher demand for taxi services, but only at a lower price and that means, that the capacity utilization rate must be higher, in other words less km with no customer on board.

In theory taxis would be able to improve their performance by offering more specialised services. For intance bring several people to work and back home at a fix price per month. If they succed in gathering some people, they can offer that at a low price (for each customer).

They can offer "touristic tours" through a city, if they train their taxi drivers or if they found the right people.

There must be more flexibility in the negotiating of prices. There must be a decreasing price structure if the amount of km increases. (Something that would even be possible with the existing system. The taximeter only has to be reprogrammed and it should be possible to make a calculation of the prices bevor the ride.)

Not only ueber is a problem for the taxis, but car sharing as well. The more people participate in this system, there it is probable that people can find a car at the place they are. They can drive themselves.

Taxis has actually some advantages. They have more possibilities to equip their cars with the most advanced environmental technology.

There are a lot of arguments against free prices, but none of them is really conving. The argument that free prices leads to a destructive competition is the less convincing, because that argument could be forward everywhere, see homo oeconomicus homo oeconomicus.

It is to assume that the offer of different services would be bigger if the taxi owner would act as real entrepreneur.

Another argument put forward very often is that free prices would lead to "bargaining" at the taxi stands. There are a lot of different ways to resolve this problem. The price fixed by the taxi cooperation could be for instance the standard price. If the customer or the taxi driver are not willing to bargain, they can take this price. If they do, they can bargain. The problem is not the taxi cooperation sets a price above the equilibrium price, the problem is, that this price is compulsory.

The tax office would have a real problem. Right now they have a possibility to calculate the profit, because there is a more or less stable relationship between the km and the costs and turnover. This wouldn't be the case, if prices are free. However this problem exists in a lot of branches.

Fixed prices ABOVE the equilibrium prices we find very seldom in real live. The taxi branche is an exception. If we find them, for instance in the agrarian sector, we have strange kind of effects. We can have the effect that the supply is bigger as it should be for satisfying the given demand at that price, as is in the taxi branche, or that the government must subsidise this branch, as in the case of the agrarian sector.

The problems of the agrarian sector, a relevant problem in Europe, can't be resolved with a governmental fixed price above the equilibrium price for butter, milk, wheat, vine, sugar etc.. The long term effects are devastating. It would be better to buy the sugar at the cheapeast price possible on the world market, for instance in Cuba, instead of imposing a customer duty on sugar from countries outside the European Union. The more money they have, the more they can buy and the easier it is for them to obtain technology. The problem is not only that the european consumers pay more and the european tax payer subsideses this kind of policy, the problem is as well that these countries can buy less. A country like Germany with a large current account surplus should do everything in order to get exports paid with imports and not with debts.

Another problem with fixed prices is that they are lead to intransparent huge bureaucracies. Without protection of sugar farmers in europe would change from sugar to biofuels. But if the prices give the wrong signals, they don't have an incentive to do that. Beside that it becomes more and more complicated to understand what is going on.

Without any customer duties on more elaborated products of choclate and cacao we would see the results. Now we have to make a research in order to find out how more elaborated products of choclate and cacao are taxed and what is the impact of this taxation. Obviously the really interesting data are not availible because bureaucracies never have a real interest to publish them.

The same type of analysis as used in the example with the taxis can be applied to customer duties, taxes on consumption in general (the value added tax), taxes on a specific consumption (tobacco, alcohol), minimum prices (above the equilibrium price), maximal prices (under the equilibrium price). We found hundred of examples of this kind in any textbook about economics.

Concerning b/ and d/ there is never a big difference. If the prices are under the equilibrium price, there is a loss of producer surplus, because if prices are low, there will be less producers. If the prices are above the equilibrium level, there will be a loss of consumer surplus, because some consumer won't consume at all this product.

However there is a big difference, depending on the measure taken by the government, ninimum price, maximal price, tax, subsidises, concerning a/ and c/. If the price is fixed above the equilibrium price, or a monopol fixes it above the equilibrium price the producer surplus will increase at charge of the consumer surplus.

In the case of a tax on consumption or a customer duty the situation is different. Concerning a/ and d/ there is obviously no difference to the example before. If there is no demand, there is no offer and in this case the consumer surplus is lost, the producer surplus is lost and the a tax on zero is zero. But there is a difference concerning a/ and b/. Only the consumer who would have paid more than the price + taxes get a rent. Their rent is the difference between the price they would be willing to pay and the new price (old price + taxes). The rest of the consumer rent goes to the pocket of the government.

The case of the producer surplus is similar. A part of this rent, b/, is lost, because the amount of units sold is reduced. Beside that only the producers who would had sold already at a price inferior to the new price less the taxes get a producer surplus, but from that producer surplus is taken away by taxes. (taxes = units sold * taxes on each unit)

The reduction of the consumer and producer surplus is presented in textbook as a loss of wealth, what is obviously not true. Nor for a/, nor for b/, nor for c/ and not for d/.

Concerning d/, the "loss" to the fact that consumers don't by the product anymore it is not true, becaus they spent the money otherwise. With alternative use is yields less utility, otherwise they had spent it this way, but we can't say that it yields no utility at all. Concerning b/, the units not produced, we can assume that the company will produce something different. Likely less profitable, otherwise they would had produced it before, but we can't they that it yield no profit. Beside that their costs are reduced.

Concerning a/ we have a division. A part of the producer surplus goes to the government. It is not lost, it is simply used in another way. For the c/ the same thing is true. This money is not lost, it is just used otherwise.

If we want to be precise the effects on the consumer surplus / producer surplus is more a question of redistribution than losses. Concerning d/, the loss of consumer surplus because the demand decreases is actually hard to calculate based on an isolated examination. We should know what is the next best alternative of consumption. Concerning c/ it is either a redistribution from the consumer to the producer or from the consumer to the goverment. Taxes on tobacco reduces the consumer surplus, that's obvious, but the government will do something with that money. If governmental expenditures yields a greater utility, welfare can even increase. The message we find in any textbooks on microeconomics, that the loss of consumer surplus is a loss of welfare, is obviously wrong and based on an isolated examination.

A tax on luxury goods can even improve the welfare. If for instance expensive vines, vines which are bought only because they are expensive and not because they yield a greater utility, because the people don't notice the difference were taxed, the goverment could spent this money for instance in the training of refugees, to take a relevant example in 2015. That would yield more utility than the expensive vine, which yields an utility only because it is expensive.

Fixed maximal prices we have for instance as well in a lot of european countries in the housing market. In Germany for instance the rent can't exceed very much the rent to be paid for the appartments in the neighboorhood. It is often said, that this makes it less profitable to construct new houses and therefore the demand will always exceed the supply.

This is obviously wrong and we illustrate by this example that an isolated analysis based on the consumer and producer surplus leads to erroneous conclusions. We should have these concepts in mind, but we shouldn't trust them blindly. An analysis based on the consumer and producer surplus is only part of the picture, but not the full picture.

The most radical critique is keynesian one. Central banks can flood the market with money, they do that actually today, in 2015. The European Central Bank injects EVERY MONTH until 60 billions of euros in the market. This can lead to a drastic reduction of the interest rates, with the effect that almost any investment can be realised, especially if the repayement period of the loans is very long. In this case the investors won't find more attractive investments and will invest in the construction of houses because they have no alternatives. For a more detailed discussion see the booklet downloadable from the startsite of this website.

Beside that for the housing market exists different kinds of subsidises, mostly possible deductions from the income leading to lower tax to pay.

The most prominent example for a minimal price is the labour market. In most of the industrialised countries the wage companies has to pay can't be lower than a fixed minimum. It is argued that this would lead to unemployment, if this fixed minimum wage is higher than the marginal revenue of labour. This is actually true, but there are two problems.

The first problem is that marginal revenue doesn't mean anything. It is obvious that employers won't pay a wage above the marginal revenue. They won't employ someone, to keep it simple, if they pay more than what they earn. That means that if the marginal revenue is below the subsistence level, these people die and dead people, that's obvious, are not unemployed, see David Ricardo. In this logic unemployement is impossible.

However David Ricardo assumes that due to competition the workmen are so powerless, that they can't demand a higher wage. In other words, the "capitalists" could pay more, but they don't want to pay more and for David Ricardo paying them more would be bad, because then the population would increase and the capital disposable for investments would decrease. [We don't discuss here again that the whole logic is wrong, because for investments money is needed, not capital, see interest rates.]

It is logical that the "capitalists" never pay more than the marginal revenue, but it is hard to see why they can't pay less. If the supply of workmen exceeds largely the demand, they will pay less. Neoclassical theory assumes that the wages will fall until everybody is employed. They assume that for a certain product, for instance bread, there is an infinitive demand if only the prices for this product, and therefore the wages paid to the workmen who produce this product, are low enough. The theory behind is that only the supply determinates the value of something and not the demand. We won't discuss this topic here again and the reader is referred to Determination of prices exclusively by the supply side. There is no need to discuss that issue. It is obvious that there are companies who can pay more, but don't want.

If the demand for a certain service is fix, for instance cleaning work in hotels, and the amount of people applying for this job very big, the employers will pay as less as possible. The neoclassical logic that more windows will be cleaned if wages are low is not valid in this case. The demand for this service is limited. In the neoclassical logic the wages will decrease and therefore the price for cleaning windos. The demand for this service will increase until all the windows cleaner are employed. The problem is, that we don't have such an amount of windows.

The neoclassical argument is, that the windows cleaner can then become ingenieurs and the same game starts again. They suppose, that anybody can do any job, without any kind of delay due to training. If that would be our world, we would live in the best of all worlds, in paradise. Unfortunately this is not the world we live in. (Perhaps at a price of 10 cent for each window cleaned it would be true, but then workmen would starve. The neoclassical logic would be right, but only because dead workmen are not unemployed. Neoclassical logic is somehow trivial.)

The minimal wage is never analysed with the concept of the consumer and producer surplus. If we do it, we have to understand, that the producers are the people who OFFER WORK in other words THE WORKMEN (NOT the employers). The demander of work are the COMPANIES (and NOT the workmen).

If the government, or the labour unions, fix a minimal wage, it must be above the equilibrium wage, otherwise it wouldn't have any effect.

A minimal wage fixed by the gouvernment would have the following effects. (If we put aside all the arguments put forward before.)

a/ +(Increase of the producer surplus, the surplus of the workman, because the wage is higher than equilibrium wage.)

b/ - (Loss of producer surplus, because less workmen will be employed)
c/ - (Loss of consumer surplus because the companies has to pay more than the equilibrium price for their workmen)
d/ - (Loss of consumer surplus because some companies will stop employing workmen)
= Difference in welfare in comparison to the equilibrium wage

If we follow the neoclassical logic, something we have no intention to do, the result is negativ. The positive effect of a/ is completely eliminated by the negativ impact on c/ and d/ and d/ are definitely lost.

Actually with this modell we get to the same results as what is shown by the neoclassical modell of the labour market and the errors are the same.

Even if we assume that there are never structural problems, that the productive resources can adapt themselves without any delay to changes in market structures, thats how the labour market is imagined in the neoclassical theory, the logic is strange. It is assumed that the workermen have to left the markets where the demand is limited. (Otherwise the whole logic doesn't make any sense.)

However it is hard to see why it should not be possible to raise the wage in this sector at the expense of the profits. The amount of workmen needed wouldn't decrease. There is a certain demand, therefore a certain amount of workmen needed. The wage paid can't be higher than the marginal revenue of labour, that's obvious. But even if we assume, that labour can be substituted by capital, we can't assume that it can be less than the marginal revenue of labour.

To illustrate that with an example: Garbage collection is without any doubt are very necessary work to be done, although not very qualified. Given a certain technology we have a certain relationship between labour and capital (machines etc.) that can't, at least in the short run, be changed. The demand is therefore given, and the amount of workmen as well. There will be no more garbage collection only because wages are low and garbage collection can be offered at a lower price. The amount of work needed is therefore fixed. As long as the garbage collection company is profitable, they can pay higher wages. In this case b/ and d/ will be cero and a/ will increase at the expense of c/ if the government fixes a minimal wage.

Only in the case that there are several garbage collection companies that competes with each other through the price, what is actually in this business not the case, wages will fall in benefits of the customers who demand this service. Worker unions however can stop this kind of competition through wages by fixing an overall valid minimal wage. That doesn't mean necessarily that the consumer has to pay the bill. Part of the bill will be paid by the employers.

However it is thinkable that the labour unions are interested in forming a monopoly. This is for instance very concretly the case in Berlin. There is public run garbage collection company and a private one. The private one pays lower wages than the public company and with the support of the trade unions the public one is in favour to reserve certain services, garbage collection of private households, for the public run company. Something similar happens with services like public transport, especially the railroad company. For a long time it was not allowed to install bus lines parallel to existing railroad lines.

Keynes refuted the neoclassical theory by somehow sophisticated arguments, but accepted the basic assumptions. (He says that worker unions only bargain on the nominal wage, but not on the real wage, which depends on the prices set by the company.) If we don't accept the neoclassical framework, it can be assumed that higher wages are paid at the expense of the profits.

In the neoclassical logic high profits allows more investments. In the keynesian logic this argument is not valid any more, see interest rate.

Let's repeat again the neoclassical framework concerning the labour market and than discuss the choices of labour unions under these (false) assumptions. The neoclassical framework assumes that labour is completely flexible and floods in the best use. Under these assumptions employers will employ workmen until the marginal revenue of labour corresponds to the wage. The lower the wage, the cheaper production, the higher the demand. That means, that unemployement is impossible. If there is unemployment, wages will decrease, that allows a cheaper production and for if the products are cheaper, demand increases. The equilibrium wage is the wage with no unemployment.

If the labour unions fix a price above the equilibrium price we have a loss of welfare in b/ and d/ and a redistribution to a/ from c/.

The question is therefore what labour unions maximise. Do the maximise the amount of workmen or the amount of the total wages? The more labour can be substituted by machines, the more important becomes this problem.

They can make a policy that allows 10 workmen to work for 6 dollars (60 euros) or a policy that allows 8 workmen to work for 8 dollars (64 dollars.) Beside that there is the problem, that companies compete at an international level. If foreign workmen work for 5 dollars, more workmen will lose their jobs.

However all these arguments are only true, if the neoclassical logic is true, what is not the case. If the demand is fix and the workforce needed to satisfy this demand is fix as well, wages can increase at the expense of the profits. In a situation like that the "capitalists" won't employ people until the wage corresponds to the marginal revenue of labour. They will employ simply as much people as they need to satisfy the demand. The argument that high wages leads to unemployment is not valid in this case, because the amount of workforce is fixed.

When it comes to discuss real world problems the discussion is even more complicated than that. In the center of the debate about minimal wages is the question whether minimal wages leads to unemployment or not. If a minimal wage leads to situation where small business, hairdresser, butcher, baker, retail shops etc.. have to abandon the rent will not immediately decrease. However in the long run rents will be lower, because the only alternative is to leave it unused. Part of the increase of wages will therefore be paid by the houseowners.

The neoclassical theory assumes that the price for the different productive factors depends on their respective marginal revenue and refutes that they are the mere result of power being the most abundant factors, in comparison to the demand, the most powerless. We have seen that in certain situations, that can be reversed.

If we abandon the two central assumptions of the classical theory, the first that the lower the price, the bigger the demand and the second, that work is completely flexible, the picture is more complicated.

If the demand is fixed due to fact that it is constant by "nature", as in the case of garbage collection, or due to the fact that the price is fixed, as in the case of the taxi branche, the wage level will have no impact on the amount of workers needed if it doesn't exceed the marginal revenue of labour.

In this case a minimal wage will be determinated by power and not by the marginal revenue of labour. In other words the wage can never exceed the marginal revenue of labour, but if we abandon the irrealistic assumption of the neoclassical theory, it can very well be below.

In some countries, for instance in Germany, wages beneath the subsistence level are subsidised. In other words, the workman get an aid until his wage + aid reaches the subsistence level. This seems a good measure at first glance. The government has to pay only let's say 500 euros instead of 1200 euros, because at least part of the income derived from a productive activity. What we see however in practise is different. Employers will count with that aid, pay less and the competitors will be obliged to do the same. Without this aid perhaps the products and services would be more expensive and the consumer of these products and services would pay the bill instead of the taxpayer.

A minimal wage is therefore the better solution, because it impedes this kind of competition.

The author actually believes that all these discussion leads nowhere. The solution is lowering the interest rates until they cover only the administration costs of the banks, whereby it is necessary that the banks become more effizient, and the risk. There is no need to pay money for money, because money is not a productive factor and it is not scarce. The money paid for money could be paid for the wages. For a more detailed discussion see the booklet downloadable from the startsite of this website.

If we want to be precise the demand curve describes the utility in money and abstracts from the individual circumstances. Therefore we can't aggregate it.

The price will measure the marginal utility of the commodity to each purchaser individually: we cannot speak of price as measuring marginal utility in general, because the wants and circumstances of different people are different.

Alfred Marshall, Principles of Economics, BOOK III, CHAPTER III, GRADATIONS OF CONSUMERS' DEMAND

In order to understand that we have to understand how the demand curve is deduced in textbooks about microeconomics. (We put the other problems already mentioned, the fact that only one unit is consumed and therefore the decreasing slope has to be explained by the competition between the different alternative, aside, see above.)

If someone spends on dollar to buy a banana it is obvious that the banana yield him the correpondent utilitiy, otherwise he would have bought something else, for instance an orange.

But if we have to persons and both of them spend one dollar for a banana we can't add these two utilities, because the the circumstances of these two persons can be different. It is will possible that the first person bought a banana in order to survive, the second person bought it to feed his monkey. Money is not an objective way to measure utility, because the utility of money itself depends on the amount we have. If we want to be exact, the explanation we found in textbooks about microeconomics are simply wrong.

The opposite, the supply curve is different. The macroeconomic supply curve is the aggregation of the microeconomic marginal costs curve at costs are objective data. The microeconomic costs curve can indeed be aggregrated.

But if we come back to earth the proble is not so relevant as we might expect. If we have a group A that buys an item for 4 dollars and another group B that buys an item for three dollars it is well possible that in group B there is someone to whom the the product yields a greater utilitiy, although he pays less, than in group A, because his income is different. But if we take the total group, there is big chance that in average the groups are homogeneous.

In large markets, where rich and poor, old and young, men and women, persons of all varieties of tastes, temperaments and occupations are mingled together, the peculiarities in the wants of individuals will compensate one another in a comparatively regular gradation of total demand. Every fall, however slight in the price of a commodity in general use, will, other things being equal, increase the total sales of it; just as an unhealthy autumn increases the mortality of a large town, though many persons are uninjured by it. And therefore if we had the requisite knowledge, we could make a list of prices at which each amount of it could find purchasers in a given place during, say, a year.

Alfred Marshall, Principles of Economics, BOOK III, CHAPTER III, GRADATIONS OF CONSUMERS' DEMAND

It can be questioned if the results of an analysis based on the consumer / producer surplus can't be obtained by a more "intuitive" way and if another kind of analysis doesn't allow to get more quickly a more complete picture of the situation.

It can even be asked, if this kind of modeling doesn't lead to a narrowing of the perspective. (A risk that always exists with any kind of modeling.)

The analysis based on the consumer / producer surplus abstracts from any kind of secondary effects and leads therefore to an overestimation of the welfare losses of minimal prices, maximal prices, subsidise, taxes etc.. What we find in textbooks on microeconomics are always hypothetical examples, the typical questions are "Analyse the effect of a price above the equilibrium price", "Analyse the effect of a subsidy", "Analyse the effect of a proportional use tax" and so on. The answer to be given shouldn't exceed the narrow limits of the modell. That is the opposite what should be done in practise.

We can show for instance with the consumer and producer surplus that welfare decreases if a tax is imposed on tobacco. That is obvious. The argument is however not very convincing if the reduction of the consumption of tobacco is the aim of this tax.

Similar absurd results we get if we analyse the labour market with this intrument. We get to the result, that a minimum wage leads to a reduction of welfare. This is however a strange kind of result, if the free market leads to a situation where the wages paid are not high enough to earn a living and social transfers are needed. (Beside the other arguments already put forward.)

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Analysis of minimal / maximal prices, customer duties, taxes, subsidies on public welfare

The cardinal measurement of utility evaluates the utility in money. This is not completely correct, because the utility of money depends on personal circunstances, but statistically the differences are balanced.

At the equilibrium the sum of the producer surplus and the consumer surplus is maximesed.

The producer surplus is based on objective data and can be aggregated.

An isolated analysis of the rents neglects relevant aspects and individual circumstances.

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