1st Problem definition
2nd The most important representatives
3rd Household demand for consumer goods
4th The concept of consumer surplus
5th The supply of goods by a company
6th The aggregation of supply and demand
7th The equilibrium theory of the market
8th The concept of elasticity
9th Short and long-term supply
10th The marginal productivity theory
11th The theory of disutility of labour
12th The exhaustion theorem
8th The concept of elasticity
It is Alfred Marshall's special merit to have developed two instruments of thought in connection with market theory, which have considerably facilitated the analysis of market events. One new thinking instrument is the concept of elasticity, the other the distinction between short-term and long-term reactions. In this section, we want to take a closer look at the concept of elasticity.
Let us consider a diagram with a supply curve and a demand curve. We have seen so far that the question of whether a market is actually heading towards a state of equilibrium depends decisively on the gradient of the two response curves. Now the indication of the gradient for the characterisation of a response curve is a very imperfect instrument. On the one hand, we know that the gradient of a curve always changes when we move along a curve and when this function is non-linear. Although we have worked with linear supply and demand curves in the previous section, we have added that this is only done to simplify the representation, but that in reality almost always non-linear functions must be expected, where the gradient also has different values for different abscissa values.
On the other hand, the mere indication of a gradient provides only imperfect information, since in reality it is much less important how big a reaction is in absolute terms than rather what relative percentages in the reaction must be expected. But it is just these relative changes that are captured by the concept of elasticity.
The concept of elasticity can basically be applied to all economic relations between two variables. With regard to the demand function for goods, the elasticity of demand in relation to the price of this good indicates by how much the demand increases on a percentage basis when the price of this good decreases by one percent (strictly speaking, by an infinitesimal percentage).
If we denote with dX the absolute change in the demanded production quantity and with X the absolute demand quantity, and if dp on the other hand denotes the absolute change in price and p the absolute price, then we understand the elasticity of demand in relation to the price h to be the following expression:
If we now apply this concept of elasticity to the demand function and assume a linear course, we find that the elasticity of demand is different at every point of the demand curve and passes through values from ∞ to 0. Let us first ask for the elasticity value at the intersection of the demand function with the ordinate. At this point the quantity of goods in demand is zero. Therefore, the term of elasticity is divided by zero. Thus, the entire term is infinitely large. Secondly, let us ask for the elasticity value at the intersection with the abscissa. Here the price tends towards zero and thus the entire term becomes zero.
Let us now ask ourselves which is the course of an isoelastic curve with always the same elasticity in all points. Mathematically speaking, a parabola has an isoelastic course:
The concept of elasticity has greatly facilitated the analysis of economic problems. In the second part of this lecture we will learn in detail about applications of this thinking tool in the different special fields. For example, the Marshall-Lerner condition in foreign trade theory shows that a devaluation leads to a reduction of a passive balance of the foreign exchange balance only if the sum of domestic and foreign import elasticities is greater than one. In the wage theory we learn that if the demand curve of the entrepreneurs for labour shows an isoelastic course, the trade unions cannot succeed in achieving higher wages by way of a shortage of labour. In the scope of the Amoroso-Robinson formula, it is shown within the theory of market forms that the marginal revenue only coincides with the selling price if the elasticity of demand tends towards infinity.
9th Short and long-term supply
Alfred Marshall furthermore distinguished between a short-term and a long-term supply curve. This distinction also contributes to a deeper economic analysis.
The short-term supply curve informs about the adjustments of an enterprise to price variations, which are not necessarily considered as long-term from the point of view of the enterprise. At the moment of the increase in orders, it is initially not clear to an entrepreneur in times of economic crisis whether these orders are already initiating an economic upturn or whether they are one-off special orders which cannot be expected to be repeated in the near future.
In view of this uncertainty, it is advisable for an enterprise to take these special orders along, but by no means to immediately align its entire capacity to a larger output. Rather, it might be advisable to try to take on this additional production with the existing machines and also with the existing manpower.
In general, it can be assumed that enterprises do not base their new purchases of machines on the current production status, but rather set up their machine park in such a way that smaller production expansions seem possible at any time.
A temporarily increased production generally also means an increased labour input. Here, too, an enterprise will try to achieve this additional input by overtime of its staff as long as it is not certain whether this increase in orders will continue in the long term.
This applies for several reasons. On the one hand, a rigorous practice of dismissal protection often prevents to lay off manpower again if it turns out that the demand for labour has been overestimated because of some orders. On the other hand, the new hiring of employees entails additional costs for the enterprise in connection with the recruitment and training of newly engaged workers.
In general, the enterprise can find enough employees from its own establishment who are interested in overtime, especially since overtime is paid better than normal working hours. There is also the possibility of compensating for certain temporary additional burdens by allowing employees who work more hours on a short-term basis to be compensated later by way of time accounts.
If an enterprise cannot persuade enough employees to work overtime, it is still possible to hire temporary workers for a while, who can be dismissed again at any time.
If, however, it is certain that the turnover has increased in the long term, it is worthwhile for an enterprise to adjust its production capacity to this increased demand, which means once purchasing new equipment as well as hiring new workers.
Let us now try to capture these different behaviours in two supply curves, one for short-term and one for long-term adjustment to market data.
Let us start with the construction of the short-term supply curve. We had mentioned that short-term, temporary adjustments involve overtime, which is generally rewarded with wage supplements, so that labour costs are likely to rise sharply when production is expanded in the short term.
Similar considerations apply also to other types of costs. If the existing machinery is used at higher rates, this often leads either to higher failure rates or to a reduction in the quality of the products produced. We must assume that the technology and organisation implemented in the enterprise has been set up in such a way that the individual production factors used in the enterprise complement each other optimally. If the use of labour force is increased while the usage of operating resources remains constant, then this leads usually to a certain reduction in efficiency.
Therefore, we like to note that the short-term supply curve should show a relatively strong positive inclination. Let us now ask ourselves what cost development we can expect to see when it comes to increasing the capacity itself in the case of long-term orders.
Initially, higher costs will incur because new workers will have to be recruited and trained and new equipment will have to be purchased. Nevertheless, unit costs are likely to be lower than in the short-term response. On the one hand, there will be no additional labour costs in terms of overtime. On the other hand, modern plants can be built, which usually become more efficient with each new purchase due to permanent technical progress. We would therefore like to point out that the gradient of the long-term supply curve is generally slighter:
Just like the concept of elasticity, the distinction between short-term and long-term supply curves has also supported the further development of the equilibrium theory. We will see in the second part of this lecture, when discussing the Cobweb system, that the equilibrium process is much more complicated than it was initially assumed by neoclassical theory. Thus, it is shown there that the process of adjustment is wavelike and sometimes even leads away from equilibrium, although normal price flexibility as well as normal elasticity of supply and demand are expected. In providing evidence, the fact that supply is constant in the short term and reacts to price increases only in later periods plays a decisive role. In this theorem, it depends on the ratio of supply elasticity to demand elasticity whether the market process takes an explosive or subdued course.
10th The marginal productivity theory
The neoclassical theory developed a market theory which applies to all markets. Our previous research was limited to the problems that occur in goods markets. However, the neoclassic school of economics, especially John Bates Clark, also tried to transfer the general laws developed in the goods markets to the factor markets.
In the same way as the supply of products by entrepreneurs is ultimately determined by the course of marginal costs, Clark proceeds from the thesis that the demand of enterprises can be represented analogous to the goods market in the framework of a marginal analysis, whereby the demand for production factors can be derived from the course of the marginal product function.
In doing so, Clark is taking a completely different path than the marginal utility school. While the representatives of the marginal utility school endeavoured to directly assign the total return of a product to the production factors involved in production, Clark endeavours to prove that the remuneration rates of the production factors are formed in a market and automatically reach their equilibrium where supply and demand for production factors coincide.
This marginal productivity theory was developed in principle for all factor markets but has been used in the literature mainly to explain wage rates. However, it should be remembered that the Old classics already spoke of the law of diminishing returns of the soil, whereby the term marginal revenue representing nothing other than the term marginal product. Furthermore, the marginal product theory was also applied to the capital markets, which were referred to as the law of the diminishing marginal product of an investment.
At the centre of marginal productivity theory is thus - as the name suggests - the concept of the marginal product, which is used synonymously with the older concept of the older marginal returns. Here, a distinction must be made between the physical marginal product and the value of marginal product. The term physical marginal product refers here to physical quantities, i.e. it indicates by how much the physical product increases when a certain factor is increased by one (infinitesimal) unit - assuming all other factors of production remain constant.
The concept of the value product is derived from the concept of the physical marginal product by multiplying this physical marginal product by the price of the produced product. In other words, the value of marginal product indicates by how much the value of production increases when a production factor is increased by one unit.
Now, with the neo-classics we tacitly assume here at the beginning of this development that there is competition on the goods markets, with the consequence that the price of goods is constant and predetermined for the enterprises (assumption of the quantity adjuster). Within the framework of the theory of market forms in the second part of this lecture we will get to know a third concept of the marginal product, the marginal revenue product. Here, it is assumed that the increase in revenue of the monopolist and oligopolist differs more or less from the price of the goods, since at the production of an additional unit, the monopolist achieves the price as additional revenue in the same way as the quantity adjuster, but at the same time the total revenue also decreases partially, because the additional production can only be sold by reducing the price of the goods according to the demand curve for all goods.
The distinction between physical marginal product and value of marginal product has an equivalent in the theory of the supply of goods. There too, when a production function is used, the relationship between physical output and the usage of the various production factors is examined, while the cost function sees the value of the implemented production factors in relation to production quantity.
In the following we will analyse marginal productivity theory with the help of the labour market. Here, three assumptions are made:
Firstly, it is assumed that entrepreneurs compete with each other in goods markets and factor markets and thus take the price of goods and production factors out of the market without trying to influence it.
Secondly, profit maximisation is assumed, i.e. it is assumed that the enterprises will take every possible increase in profit, obviously in compliance with the law.
Third and finally, a production function of the Cobb-Douglas type is assumed with the following two characteristics: If a single production factor is increasingly used, the total product increases, but the marginal product, i.e. the increase in production, decreases as the factor input increases. If, however, all the used production factors are increased while the input ratio remains constant, then the growth in production remains constant, i.e. the law of the constant marginal product applies.
This formulation of the assumptions has now been criticised in particular by Hans Albert, whereby Albert accused the neoclassical period of 'model platonism', according to which this theory is limited to starting from given assumptions that do not need to be further examined and from this alone, by means of logical derivations, to derive the most important statements of marginal productivity theory. For logical reasons, however, no additional information would be gained here; the epistemic value of this theory would not be greater than that of the supposed assumptions, since logical derivations can only ever reveal what is already contained in the assumptions. The realism of these assumptions is not checked here, this task is at best assigned to other knowledge disciplines. However, these disciplines did not even think of taking over the questions of economic theory and seeing themselves as auxiliary sciences.
Despite all the justified criticism of this neoclassical theory of marginal productivity, it can be reformulated relatively easily in such a way that empirically sound assumptions are formulated, which then have to be examined within the framework of national economics itself.
In this case, one starts out from the assumption of intensive competition. Competition cannot be taken for granted, because entrepreneurs find competition very annoying and therefore strive to prevent competition as far as possible through mergers and cartel agreements.
However, whether these efforts are successful depends on the respective regulatory policy of the state. Monopolies generally only arise when the state protects domestic enterprises from foreign competition by imposing customs duties and other import restrictions. The degree of competition in an economy also depends on how intensively the state prevents cartels and company mergers by means of monopoly supervision. Whether competition can indeed be expected is therefore very well a hypothesis of great informative value.
Secondly, it can furthermore be assumed that competition provides strong incentives for entrepreneurs to exploit every possible increase in profits. In a competitive environment, an entrepreneur can hardly afford to settle for a certain level of profit and forego further profit, as in this case he very quickly runs the risk of being driven out of the market by his competitors. In a highly competitive environment, entrepreneurs are faced with an 'all or nothing' decision.
On the other hand, it cannot be taken for granted that competition forces profit-maximising behaviour. Even under competitive conditions, there is a 'lockstep' behaviour: if an entrepreneur starts from the certainty that all his competitors will forego certain profit increases, he does not run the risk of being driven out of the market if he follows this general practice.
Thirdly and finally, it is necessary to test empirically the course of the production functions in practice. It was Cobb and Douglas who, in numerous empirical studies, found that the real production conditions can be represented in the best way by a Cobb-Douglas production function.
In a first step, we now want to derive from these three assumptions (competition, profit maximisation and the Cobb-Douglas production function) the demand curve of the enterprises for labour. A decisive role is played here by the course of the marginal product function as a function of labour input. If the entrepreneur tries to maximise his profit, he will expand an existing demand for labour as long as this step promises him an increase in profit.
If the entrepreneur demands one work unit (one working hour) more than before, under competitive conditions on the labour market, he will incur additional costs amounting to the hourly wage rate. Here, his revenue increases - again assuming that there is competition on the goods markets - by the product of the price obtained multiplied by the physical marginal product. As long as the difference between marginal expenditure (wage rate) and value of marginal product is positive, the profit increases and under the assumptions made, the entrepreneur will therefore take on this extra work. In other words, he will only stop increasing his demand for labour when the growth in profits becomes zero, that is, when marginal expenditure (the wage rate) is just equal to the growth in revenue, the value of marginal product. The equilibrium condition applies:
l: wage rate p: goods price dX/dA: physical marginal product.
Let us illustrate these correlations with the help of a graph, where we draw the labour input calculated in hours on the abscissa and the real wage rate (l/p) as well as the physical marginal product (dX/dA) on the ordinate.
The assumptions about the production function result in a falling course demand for labour. In the literature, a distinction is made here between two different courses of the marginal product function. In general, a course is assumed that is concave regarding the coordinate origin. Here the concave curved function intersects both coordinate axes. At an alternative representation, a convex curvature is assumed, thus e.g. a parabolic curve, in which case the curve approaches the axes asymptotically without intersecting them. In this case it is sometimes assumed that the curve is isoelastic:
Starting from a marginal productivity function, we can now derive the demand curve for labour, which coincides with the marginal productivity curve on the assumptions made. Each alternative demand for labour corresponds to a certain marginal product; the entrepreneur will only exercise this demand if he must pay a wage no higher than the amount of this marginal product. Thus, we obtain a demand curve which assigns to an alternative labour demand the respective wage rates which the entrepreneur is ready to pay at most. Conversely, we can also interpret this resulting demand curve in such a way that it indicates how many working hours are demanded by an enterprise at alternative wage rates.
For the sake of simplicity, we will now again assume a linear curve of the demand for labour. The interaction of supply and demand then affects the level of the wage rate. We want to assume that the supply of labour is also normal in the sense of the neoclassical market theory, i.e. that it has a rising inclination.
The point of intersection of both curves then marks the equilibrium wage rate where supply and demand coincide. If - as shown here - both supply and demand react normally, there is also a tendency towards equilibrium.
Let us assume that for some reason the supply of labour exceeds demand, i.e. there is unemployment. In a normal free market, the wage rate will then decrease, as those employees who are still unemployed will be willing to work at a lower rate than the current rate. As a result of the reduction in wages, demand will increase and supply will decrease, with the result that unemployment will decline, and the market will tend to reduce unemployment by itself.
It must be noted critically that in reality, we generally do not find competition in the labour markets, but rather collective bargaining takes place in almost all sectors, which constitutes a kind of bilateral monopoly in the labour markets. In the second part of this lecture we will deal with this problem in detail in the context of the theory of market forms and collective bargaining models.
11th The theory of disutility of labour
Neoclassical theory has contributed not only to the development of the demand curve for labour, but also to the development of the labour supply function. In this context, the work of Stanley Jevons is particularly noteworthy. Basically, he too assumes a subjective determination of prices; he too derives the demand for goods from the marginal utility that the consumer goods create.
This consideration can now be applied to the supply of the factors of production. The supply of production factors, just like the demand for consumer goods, ultimately results from the subjective decisions of the households.
In the previous chapter we have seen that the system of indifference curves can not only be used to determine the demand for consumer goods, but that it is also possible to derive from such a system the supply of labour as a function of the respective wage rate. We had seen there that when asking whether a household should offer one more hour of work, the loss of utility that results from having one hour less of leisure time is compared with the gain in utility that the household achieves by receiving a higher income due to the increased labour, from which it can then also demand more consumer goods than before, whereby this increased consumption leads to a benefit increase.
Both variables (the loss of utility due to reduced leisure time and the gain in utility due to increased consumption) are compared with each other and the labour supply is expanded as long as the gain in utility is greater than the loss in utility.
Stanley Jevons now chose a slightly different way of determining the labour supply as a function of the wage rate. If the employee chooses to offer one more hour of labour, he or she would be faced with extra work and effort as a result of this gainful employment, which Jevons summarises in the workload that results from this additional work. Jevons now compares this disutility of labour with the increase in utility that can be expected from the extra income resulting from the extra work. Jevons assumes that the household is always able to offset disutility of labour and utility gain.
Just as when applying the laws of marginal utility, the course of the marginal utility of leisure time ultimately determines the labour supply curve, so here with Jevons one can ultimately derive the labour supply curve from the curve of disutility of labour with regard to alternative labour supply.
If one wants to, it is even possible and also makes sense to combine the approaches of marginal disutility of labour and marginal utility of leisure time. An employee who is faced with the decision whether to offer one more hour of work will thus compare the following changes in personal welfare. The fact that he works more causes marginal disutility of labour. The fact that this necessarily means that one hour less leisure time can be used causes an additional reduction in utility. Finally, thirdly, it is important to determine by how much the utility increases because more consumer goods can be consumed due to an additional income.
If we assume with Jevons that the marginal disutility of labour increases with growing economic activity, i.e. that more work not only causes more disutility of labour, but that the increase in disutility of labour, i.e. the marginal disutility of labour, also increases with increasing employment, we obtain a labour supply curve with an increasing course also for the path chosen by Jevons.
Finally, it remains to be examined whether the labour supply in reality is actually determined by the disutility of labour that the employee experiences at his work.
Of course, we can assume that gainful employment almost always causes endeavours and efforts, which can certainly be summarised as disutility of labour. However, it is also important to note that, at least in part, gainful employment also generates pleasure and satisfaction, i.e. the opposite of disutility of labour. Is it necessary to calculate these two psychological factors in order to maintain the welfare associated with gainful employment?
It may also be questionable whether the disutility of labour and work pleasure are in reality included in the wage rate that appears to be justified. At the very least, it can be observed that this question (of the consideration of disutility of labour and work pleasure) is handled differently in different occupational sectors. It can be seen that for engineers employed on oil platforms or pilots of modern jet aircraft, and also for managers with particularly high stress factors, these additional burdens have certainly contributed to the fact that above-average incomes are granted in these professions.
In other occupations, the performance of the individual and the success that his or her activity brings about are much more important in determining the income to be paid. Here, the burdens that this occupation entails are of less interest. Taking these factors into account is likely to be decisive, especially in many academic professions, but also for brokers on the stock exchange or even for top athletes.
12th The exhaustion theorem
Finally, we will deal the exhaustion theorem developed by Philipp Henry Wicksteed and John Bates Clark. In this theorem, an attempt is made to show that if the factors of production are remunerated to their marginal revenue products, then the sum of all factor remunerations is also equal to the total value of production, which is tantamount to saying that in the equilibrium no pure profit is made.
This does not mean, of course, that in a real market economy no profits are reported. There is always room for 'windfall profits', which arise during periods of demand surpluses and which are reflected in temporary profits. It will also have to be borne in mind that in reality entrepreneurs invest capital, land and their own labour into production, and that these services are remunerated in the form of land rents, interest income and entrepreneur's wages, which are often allocated somewhat imprecisely to the entrepreneur's profit.
In the following demonstration we want to start from the simplest conceivable case and assume that merely labour is employed in the production of a good and that interest has accrued on the borrowed capital. It is thus determined by only two factors of production: labour and capital. At the same time, a Cobb-Douglas production function is assumed. This states that:
X: output quantity b: growth coefficient A: labour input K: capital input α: production elasticity in relation to labour
According to the marginal productivity theory developed above, wages (l) are paid in equilibrium with their products of marginal value (p*dx/dA). The wage ratio (λ), the ratio of the wage total (l*A) to the value of the domestic product (p*X) is therefore:
In this expression the term for p can be cancelled:
We now replace the expression for dX/dA by the first derivative of the Cobb-Douglas function:
In the expression on the right side we can replace the term b * Aα-1 * K1-α with b * (Aα-1)/A * K1-α = X/A, thus for equation 2) we can write also:
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Finally, inserted into equation 1b), the following results:
Similarly, it can be shown that the share of interest income in the domestic product corresponds precisely to the elasticity of production in relation to capital, i.e. 1 – α.
Now adding the two shares of the factors of production in the domestic product, the result is:
This means that the sum of the two factors of production used in the production of X is just equal to the domestic product, so that there is no room for gains or losses in the equilibrium.