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Why Marginalism is Wrong


Written in collaboration with Nsplitter AKA Invariance for evilzone.org & revleft.com
Edited to reflect changes desired after original publication on evilzone.org

The original argument in the classical school of economics was that price was set by the cost of production. Translated to modern economics, it means a horizontal or even falling supply curve, so that the market price doesn’t change as the quantity produced rises (and it can actually fall). On the other hand, modern economic theory argues that productivity falls as output rises, so that higher levels of output result in… higher prices. The supply curve, according to economics, therefore slopes upwards; a higher price has to be offered to entice firms to produce a higher output.

Whilst the modern approach is superficially appealing, there are numerous logical errors with it, which means that the classical position is a far more coherent paradigm. Most of this material comes from Debunking Economics by Steve Keen which reiterates Sraffa's 1926 paper 'The Laws of Returns under Competitive Conditions'.

Classical & Neo-Classical Value Paradigms:

Any adequate critique of Marginalism would be incomplete without having first addressed the disparate opinions held by the Classical school and the Neo-Classical school concerning what exactly constitutes 'value', and therefore price. The classical argument, as was mentioned above, favours cost of production as the primary determinant of value, while regarding fluctuations in exchange value or 'price' to be external to the commodity and therefore not reflexive of the true value of the thing itself. This viewpoint challenges the apparent truisms of modern neoclassical thought, seeing as fundamental to the Classical school is the notion that the study of economics starts with hoping to understand the very nature of a commodity, and by analyzing the processes necessary for its production. Conversely, the neoclassical school only acknowledges the commodity once it has entered the marketplace, and as if it had magically appeared on the shelves of stores instead of being the product of a complex process of production.

To disregard the productive process altogether in any kind of value determination is to embrace a reductive approach which relegates the entire study of economics to nothing more than the development of overly-complicated theories of price calculus rather than being the study of value, price and the social relations which underly both the production and consumption of commodities.
 
In short, seeing as neoclassical thought is profoundly limited in what exactly it even hopes to prove, it cannot hope to explain, let alone remedy, the litany of problems and contradictions present in a modern capitalist system.

The Dissent of Factory Owners:

When the modern theory was put to those who do know how factories are designed and managed, they rejected it as ‘the product of the itching imaginations of uninformed and inexperienced arm-chair theorisers’ (Lee, F. (1998) Post Keynesian Price Theory, Cambridge University Press). How could something which seems so intuitive be so unrealistic? The problem, once again, rests on the assumptions made which are in fact contradictory; if one applies for a given industry, then the other one will almost certainly not. More on this later. Economic theory doesn’t apply in the real world, because engineers purposely design factories to avoid the problems that economists believe force production costs to rise; they are built with excess capacity and are designed to work at high efficiency from low to high capacity. Only products which cannot be produced in factories, e.g. oil, may behave the way economists expect. A further problem is that economics takes a completely static approach.

Diminishing Productivity Causes Rising Price:

The economic theory of production argues that capacity constraints play a key role in determining prices, with the cost of production rising as producers try to 'squeeze more and more output' out of a fixed number of machines. This falling productivity translates into a rising price. Therefore, there is a link between ‘marginal productivity’ – the amount produced by the last worker – and ‘marginal cost’ – the cost of producing the last unit. We can represent this in a hypothetical firm:

This table shows an example of how economists expect production to behave. The firm has fixed costs of $250,000 and pays its workers a wage of $1,000. It can sell as many units as it can produce at the market price of $4. With no workers the output is zero. The first worker enables the firm to produce 52 units of output. The marginal product of this worker is the difference between production without her (zero) and the amount the worker produces (52), hence a marginal product of 52.

The marginal cost is the worker's wage divided by the number of units produced. Hence, $1,000 divided by 52 equals approximately $19.20. The average fixed costs of output are 250,000 divided by 52 at approximately $4808. The average total cost is $251,000 divided by 52 or 4827 per unit. That is, a loss of $4823 per unit sold if this was the chosen level of production.

Additional workers allow jobs to be divided up and allows for specialisation, increasing the productivity of the workers. With rising marginal productivity, and therefore falling marginal cost, the firm begins to lose less and less. By the 100th worker the firm is still making a loss but the loss is falling because its marginal cost has fallen below the sale price; the 100th worker adds 398.5 units to output, at a marginal cost of $1000 divided by 398.5, or just $2.50 a unit – which is less than the sale price of $4 per unit, so the firm is making a profit on the increase in output but not only enough to reduce its losses – not enough to ‘go over’ the total costs at that stage (350,000).

The 277th worker has a marginal product of 773.7 at a sale price of $4 bringing in $3090 profit for the firm. Rising marginal productivity continues up until the 400th worker hired. Marginal cost has fallen steeply; $1000 wage divided by 850 additional units or $1.18. Average fixed costs are $250,000 divided by the output of 233,333, that is, about $1.07. After this point, productivity of each new worker ceases to rise. Each new worker adds less to output than the previous worker.

The rationale is that the ratio of workers, the variable factor of production, to the machines, the fixed factor of production, has exceeded an optimal level. Now each worker adds output but at a diminishing rate. That is, diminishing marginal productivity applies. Hence, marginal cost will start to rise. However, profit will continue to rise because even though each additional worker adds less output and therefore brings in less revenue, the revenue from the additional units still exceeds the cost of hiring the worker. Marginal revenue exceeds marginal cost. We can see this with the 500th worker who adds 800.5 units to output. The marginal cost of her output is her wage $1000 divided by 800.5 or $1.25. This is higher than the minimum level reached by the 400th worker at $1.18 but the additional units can all be sold at $4 so the firm still makes a profit from employing that worker.

This ends with the employment of the 747th worker, whose additional product – 249.7 units can only be sold at $998.8 versus the cost of his wage of $1000. Any additional workers would cost more to employ than the amount of additional output they produce could be sold for. The firm will therefore employ 747 workers to maximise its profits at $837,588. At this point, the marginal cost of production equals the marginal revenue from sale, and profit is maximised.  We can plot this graphically:


Labor inputs are on the horizontal axis, and output on the vertical axis. We can see from the graph that the highest marginal product is reached at 400 labour inputs. We can see at point B, 813 labour inputs (workers) that the firm has reached the maximum level of output (but not the maximum level of profit). Output falls after that; additional workers actually reduce output. We can also see point C, 747 workers, the number the firm should employ.

Falling Productivity Means Rising Costs:

The next graph simply swaps the axes around in the previous figure. Pick a level of output on the horizontal axis and the vertical axis tells us how many workers are needed to produce it:

Next, we convert the vertical axis in the second figure from a measure of the number of workers to a measure of variable costs. All we need to do this is multiply the labour input by wages; multiply by $1000. Now that it is in monetary terms we can add other monetary data to it, in particular, the fixed costs of production of $250,000. Now we have a cost curve that shows total costs. We can also add the total revenue the firm earns from selling its product. Since we have assumed that the firm can sell as much as it likes at $4 a unit, this will be a straight line through the origin of the graph with a slope of 4. $4 revenue for each 1 unit sold. The graph will look like the following:

Determining the Point of Maximum Profitability:

The firm's maximum profit will occur where the gap between its straight line revenue function and the curved total cost function is biggest. It happens to be where the slope of the total revenue curve equals the slope of the total cost curve because this results in the biggest gap between total revenue and total cost. This is because when the revenue curve rises more steeply than the cost curve, an additional sale will make the gap bigger still. On the other hand, when the cost curve rises more steeply than the revenue curve, an additional sale will reduce the gap between revenue and costs. Therefore, the biggest gap occurs where the slopes of the two curves are equal. We can see this in the following graph:

Here the additional profit/loss line is added, and we can see that the place where profit is maximised is also where the gap between total revenue and total cost is largest.
We can also figure it out by referring to the slopes of the cost and revenue curves – marginal cost and marginal revenue. The slope of the total revenue curve is simply its price of $4 per unit sold. The slope of the total cost curve is equal to the change in cost divided by the change in output. The difference in total cost from 746 workers to 747 workers is 1,000 and the change in output is 250. Hence, 1000/250 = 4. At point C, with 746 workers employed, the marginal cost is $4, which is equal to the sale price.
The point where the two marginal curves intersect corresponds to the point at which the distance between the total revenue and total cost curves is greatest. A perfectly competitive firm producing a quantity at which marginal costs equals both marginal revenue and price.

To derive the market supply curve, we have to aggregate the supply curves of a multitude of producers. The total market supply curve is derived simply by adding up all the individual marginal cost curves of firms in a competitive market, resulting in an upward sloping supply curve.

Problems:

This account seems superficially appealing. However, as Piero Sraffa pointed out in 1926 it is fundamentally flawed. Sraffa argued that the law of diminishing marginal returns will not in generally apply to an industrial economy. Sraffa argued that the common position would instead be constant marginal returns, and therefore horizontal marginal costs. This gets to the very heart of economic theory, since diminishing marginal returns is used to determine everything in the economic theory of production. The output function determines marginal product, which in turn determines marginal cost. With diminishing marginal productivity, the marginal cost of production eventually rises to equal marginal revenue. Since firms seek to maximise profit and since this equality of rising marginal costs to marginal revenue gives you maximum profit, this determines the level of output.

However, if constant returns are the norm, then the output function instead is a straight line through the origin just like the total revenue line, though with a different slope. If the slope of the revenue is greater than the slope of the cost curve, then after a firm had met its fixed costs it would make a profit from every unit sold. The more units sold, the greater the profit would be. At least in terms of the economic model of production, there would be no limit to the amount a competitive firm would wish to produce, so that economic theory could not explain how firms in a competitive industry decided how much to produce. In fact, according to economic theory, each firm would want to produce an infinite amount! The economists will reply that this is patently absurd, that firms don’t produce an infinite amount of goods therefore Sraffa must be wrong. Sraffa put the opposite case: sure, the economic model of production works in theory if you accept its assumptions. But do those assumptions that economists rely on actually apply in practice? If they can’t, then it will be irrelevant to practice.
Sraffa focused on the economic assumption that there were factors of production which were fixed in the short run and that supply and demand were independent of each other. He argued that these two assumptions could not be fulfilled simultaneously. In circumstances where it was valid to say that some factor of production was fixed in the short run, supply and demand would not be independent, so that every point on the supply curve would be associated with a different demand curve! Conversely, where supply and demand could justifiably be treated as independent, then in general it would be impossible for any factor of production to be fixed. Thus, the marginal cost of production would be constant.

Firstly, Sraffa noted that the classical school of economics had a ‘law of diminishing marginal returns’, however, it was not part of price theory, but a part of the theory of income distribution, restricted to the explanation of rent. The classical argument was that farming would first be done on the best land available, and only when that land was fully utilised would land of a lesser quality be used. This poorer land would produce a lower yield than the better land. Diminishing marginal returns therefore applied, but they occurred because the quality of the land used fell, not because of any relationship between fixed and variable factors of production.

The neoclassical theory of diminishing marginal productivity was based on an inappropriate application of this concept in the context of their model of a competitive economy, where the model assumed that firms were so small relative to the market that they could not influence the price for their commodity, and that factors of production were homogeneous. In the neoclassical model therefore, falling quality of inputs couldn’t explain diminishing marginal productivity. Instead, productivity could only fall because the ratio of variable factors of production to fixed factors exceeded an optimal level. The next question then is when it is valid to regard a factor of production as fixed. Sraffa said that this was a valid assumption only when industries were defined very broadly, but this then contradicted the assumption that supply and demand were independent.
Broad Critique:

If we take the broadest possible definition of an industry, say agriculture, then it is valid to treat factors it uses heavily (e.g. land) as fixed. Since additional land can only be obtained by converting land from other uses (e.g manufacturing) it is difficult to increase that factor in the short run. The ‘agricultural industry’ will therefore suffer from diminishing returns. However, such a broadly defined industry is so big that changes in its output must affect other industries. An attempt to increase agricultural output will affect the price of the chief variable input – labour – as it takes workers away from other industries, and it will also affect the price of the fixed input.

This, however, undermines crucial parts of the model: the assumption that demand for and supply of a commodity are independent, and the proposition that one market can be studied in isolation from all others. If increasing the supply of agriculture changes the relative prices of land and labour, then it will also change the distribution of income. Changing the distribution of income will change the demand curve. There will, therefore, be a different demand curve for every different position along the supply curve for agriculture. This makes it impossible to draw independent demand and supply curves that intersect in one place.

‘…if in the production of a particular commodity a considerable part of a factor is employed, the total amount of which is fixed or can be increased only at a more than proportional cost, a small increase in the production of the commodity will necessitate a more intense utilisation of that factor, and this will affect in the same manner the cost of the commodity in question and the cost of the other commodities into the production of which that factor enters; and since commodities into the production of which a common special factor enters are frequently, to a certain extent, substitutes for one another (for example, various kinds of agricultural produce), the modification in their price will not be without appreciable effects upon demand in the industry concerned.’ (Sraffa 1926).
 

This means that the demand curve for this industry will shift every movement along its supply curve. It is therefore illegitimate to draw independent demand and supply curves since factors that alter supply will also alter demand! Supply and demand will therefore intersect in multiple locations as shown in the following figure. It is therefore, impossible to say which price or quantity will prevail:

Narrow Critique:

What if we use a more realistic, narrow definition of an industry, for example ‘wheat’ rather than agriculture?

It becomes worse for the marginalists, because, in general, diminishing returns are unlikely to exist. This is because the assumption that supply and demand are independent is now reasonable, but the assumption that some factor of production is fixed isn’t! Economists assume that production occurs in a period of time during which it is impossible to vary one factor of production. Sraffa argues that in the real world firms and industries can vary one factor of production fairly easily. This is because additional inputs can be taken from other industries, or garnered from stocks of under-utilised resources. If there is an increased demand for wheat, then rather than farming a given quantity of land more intensely, farmers will convert some land from another crop to wheat. Or they will convert some of their own land which is currently lying fallow to wheat production. Or farmers who currently grow a different crop will convert to wheat.

‘If we next take an industry which employs only a small part of the " constant factor " (which appears more appropriate for the study of the particular equilibrium of a single industry), we find that a (small) increase in its production is generally met much more by drawing " marginal doses ' of the constant factor from other industries than by intensifying its own utilisation of it; thus the increase in cost will be practically negligible, and anyhow it will still operate in a like degree upon all the industries of the group.’ (Sraffa, 1926)
 

Hence, the ratio of one factor of production to any other will remain relatively constant, while the total amount of resources devoted to it will rise. This results in a straight line output function. Since the shape of the total, average and marginal cost curves are entirely a product of the shape of the output curve, a straight line output curve results in constant marginal costs and falling average costs. Hence, costs for a firm are likely to be constant (or even falling) within the normal range of output.Irrational Managers:

Sraffa argues that a firm is likely to produce at maximum productivity right up until the point at which diminishing marginal productivity sets in. Any other patter shows that the firm is behaving irrationally. To use an analogy, suppose you have a franchise to supply ice-creams to a football stadium, and that the franchise lets you determine where patrons are seated. If you have a small crowd one night – say one quarter of capacity – would you spread the patrons around over the whole stadium, so that each patron was surrounded by several empty seats? Of course not. This arrangement would force your staff to walk further to make a sale. Instead, you’d leave much of the ground empty, thus minimising the work your staff had to do. There’s no sense in using ever every last inch of your fixed resource (stadium) if demand is less than capacity.

The same logic applies to a farm of a factory. If a variable input displayed increasing marginal returns at some scale of output, then the sensible thing for the farmer or factory owner to do is leave some of the fixed resource idle, and work the variable input to maximum efficiency on part only of the fixed resource.

Consider a wheat farm of 100 hectres where one worker per hectare produces an output of 1 bushel per hectare, 2 workers per hectare produces 3 bushels, 3 workers per hectare produces 6 bushels, 4 workers per hectare produces 10 bushels, and 5 workers per hectare produces 12 bushels. According to economists, if a farmer had 100 workers he would spread them out 1 per hectare to produce a total of 100 bushels of wheat. But according to Sraffa, the farmed would instead leave 75 hectares of the farm idle, and work 25 hectares with the 100 workers to produce an output of 250 bushels. The farmer that behaves as Sraffa predicts comes out 150 bushels ahead of any farmer who behaves as economics predicts.

Economic theory implies that a farm with 200 workers would spread them over the farm’s 100 hectares to produce an output of 300 bushels. Sraffa says the sensible farmer would instead leave 50 hectares fallow, work the other 50 at 4 workers per hectare and produce an output of 500 bushels. The same pattern continues up until the point at which 400 workers are employed, when finally diminishing marginal productivity sets in. A farm will produce more output by using less than all of the fixed input up until this point. Firms will therefore have straight line marginal cost curves below the level of maximum productivity. If marginal costs are constant, then average cost must be greater than marginal cost, so that any firm which sets price equal to marginal cost is going to make a loss. The economic theory of price-setting can therefore only apply when demand is such that all firms are producing well beyond the point of maximum efficiency. It therefore depends on the economy being in full employment.

Sraffa’s critiques mean that economic theory of production can apply in only the tiny minority of cases that fall between the two circumstances he outlines, and only when those industries are operating beyond their optimum efficiency. Only then such industries will not violate the assumed independence of supply and demand, but they will still have a relatively fixed factor of production and will also experience rising marginal cost. Only a tiny minority of industries are likely to fill these limitations: those that use the vast majority of some input to production where the input itself is not important to the rest of the economy. The majority of industries are instead likely to be better represented by the classical theory, which saw prices as being determines exclusively by costs, while demand set the quantity sold.
‘Reduced within such restricted limits, the supply schedule with variable costs cannot claim to be a general conception applicable to normal industries; it can prove a useful instrument only in regard to such exceptional industries as can reasonably satisfy its conditions. In normal cases the cost of production of commodities produced competitively-as we are not entitled to take into consideration the causes which may make it rise or fall-must be regarded as constant in respect of small variations in the quantity produced.' And so, as a simple way of approaching the problem of competitive value, the old and now obsolete theory which makes it dependent on the cost of production alone appears to hold its ground as the best available.’ (Sraffa, 1926).

If not rising marginal cost, then what?

If rising costs and constant revenue do not determine the output from a single firm or a single industry, what does? Sraffa’s argument is simple: the output of a single firm is constrained by all those factors that are familiar to ordinary businessmen, but that are abstracted away by economic theory. In particular, rising marketing and financing costs, both of which are a product of the difficulty of encouraging consumers to buy the firm’s output rather than a rival’s. These are a product of the fact that, in reality, products are not homogeneous and consumers do have preferences for one firm’s product over another’s. Sraffa mocked the economic belief that the limit to a firm’s output is set by rising costs, and emphasised the importance of finance and marketing in constraining a firm’s size:

‘Business men, who regard themselves as being subject to competitive conditions, would consider absurd the assertion that the limit to their production is to be found in the internal conditions of production in their firm, which do not permit of the production of a greater quantity without an increase in cost. The chief obstacle against which they have to contend when they want gradually to increase their production does not lie in the cost of production-which, indeed, generally favours them in that direction-but in the difficulty of selling the larger quantity of goods without reducing the price, or without having to face increased marketing expenses. This necessity of reducing prices in order to sell a larger quantity of one's own product is only an aspect of the usual descending demand curve, with the difference that instead of concerning the whole of a commodity, whatever its origin, it relates only to the goods produced by a particular firm; and the marketing expenses necessary for the extension of its market are merely costly efforts (in the form of advertising, commercial travellers, facilities to customers, etc.) to increase the willingness of the market to buy from it-that is, to raise that demand curve artificially.’ (Sraffa, 1926)
 

Economists assumes this real world answer away by assuming that products are homogeneous, consumers are indifferent between the outputs of different firms and decide their purchases solely on the basis of price, that there are no transportation costs etc. In such a world no-one needs marketing because consumers already know everything, and only price distinguishes one firm’s output from another. On the contrary, in most industries products are heterogeneous, consumers do not know everything and they consider other aspects of a product apart from price. Further, even where products are homogeneous, transportation costs can act to give a single firm an effective local monopoly. Hence, even the concept of a competitive market, in which all firms are ‘price-takers’ is suspect (I’ll discuss this another time). Instead, most firms will to varying degrees act like monopolists, who according to economic theory face a downward-sloping demand curve.

A firm has a product which fits within a broad category, for example passenger cars which is qualitatively distinguished from its rivals in a fashion that matters to a subset of buyers. The firm attempts to manipulate the demand for its product, but faces prohibitive costs in any attempt to completely eliminate their competitors and thus take over the entire industry. Not only must the firm persuade a different niche market to buy its product – to convince Porsche buyers to buy Volvos for instance, it must also convince investors and banks that the expense of building a factory big enough to produce for both market niches is worth the risk. Therefore, with the difficulty of marketing beyond your product’s niche goes the problem of raising finance:

Thus, the limited credit of many firms, which does not permit any one of them to obtain more than a limited amount of capital at the current rate of interest, is often a direct consequence of its being known that a given firm is unable to increase its sales outside its own particular market without incurring heavy marketing expenses. If it were known that a firm which -is in a position to pr6duce an increased quantity of goods at a lower cost is also in a position to sell them without difficulty at a constant price, such a firm could encounter no obstacle in a free capital market. On the other hand, if a banker, or the owner of land on which a firm proposes to extend its own plant, or any other supplier of the firm's means of production, stands in a privileged position in respect to it, he can certainly exact from it a price higher than the current price-for his supplies, but this possibility will still be a direct consequence of the fact that such a firm, being in its turn in a privileged position in regard to its particular market, also sells its products at prices above cost. What happens in such cases is that a portion of its mono-poly profits are taken away from the firm, not that its cost of production is increased. (Sraffa, 1926).
 

Neoclassical theory cannot be saved by simply adding marketing costs to the cost of production, and thus generating a rising marginal cost curve.
Firstly, marketing is not a cost of production, but a cost of distribution. Secondly it is inconsistent with the underlying economic premise that marginal cost rises because of diminishing marginal productivity. Thirdly, its implausible in the economic context of the theory of the firm. There is no point saving the concept of a rising marginal cost curve by introducing marketing costs since this requires acknowledging that one firm’s product differs from another. If products differ from one firm to another, then products are no longer homogeneous which is an essential assumption of the theory of perfect competition. It is more legitimate to threat marketing cost as a cost of distribution, whose object is to alter the demand faced by an individual firm.

With this critique, the most popular image of economic theory, a falling demand curve and rising supply curve intersecting to jointly determine the equilibrium price is an illusion. Rather than firms producing at the point where marginal cost equals marginal revenue, the marginal revenue of the final unit sold will normally be substantially greater than the marginal cost of producing it, and output will be constrained not by marginal cost but by the cost and difficulty of expanding sales at the expense of sales by competitors.

What are the implications?

These may look like minor points. The supply curve should be horizontal rather than upward sloping; the output of an individual firm isn’t set by the intersection of marginal revenue and marginal cost; and marketing and finance issues, rather than cost of production issues, determine the maximum scale of a firm’s output. What’s the deal?

If marginal returns are constant rather than falling, then the neoclassical explanation of just about everything collapses. For example, the theory of employment and wage determination. The theory asserts that the real wage is equivalent to the marginal product of labour. The argument goes that each employer takes the wage level as given, since with competitive markets no employer can affect the price of his inputs. An employer will employ an additional worker if the amount the worker adds to the output – the worker’s marginal product – exceeds the real wage. The employer stops employing workers once the marginal product of the last one employed has fallen to the same level as the real wage.

Since employment in turn determines output, the real wage determines the level of output. If society desires a higher level of employment and output, then the only way to get this is to reduce the real wage (and the logical limit of this argument is that output will reach its maximum when the real wage equals zero!). The real wage, in turn, is determined by the willingness of workers to work – to forego leisure for income, so that the level of employment is determined by workers alone. This is why Galbraith said that economics can be summed up in the two propositions that the poor don’t work hard enough because they’re paid too much, and the rich don’t work hard enough because they’re not paid enough .

However, if the output to employment relationship is relatively constant than the neoclassical explanation for employment and output determination collapses. With a flat production function the marginal product of labour will be constant and it will never intersect the real wage. The output of the firm then can’t be explained by the cost of employing labour.

Responses:

The general response to Sraffa’s paper was to ignore it. This is the common initial response to 'anomalies' in all sciences, economics being no different.

Where they do address the critique, the neoclassical school argue that Sraffa has failed to understand the concept of the short run. Neoclassical economics defines three concepts of time: the market period, during which no factor of production can be varied, so that supply is fixed and only price can vary, the short run, during which at least one factor of production cannot be varied, so that output can be varied but only at the cost of diminishing returns and the ling run during which all inputs can be varied. Since production occurs in the short run, the remainder of the theory follows logically. Diminishing marginal returns will apply, marginal cost will rise, price and quantity will be jointly determined by supply and demand and the theory of production and distribution remains intact.

Right?

Wrong. It is ironic that economists turn to time to defend their theory when economics ignores time altogether. Far from helping to defend the theory, the proper analysis of time highlights a weakness.

A firm’s revenue and costs clearly vary over time, as well as varying the firm changes its level of output at any one point in time. The economic rule that profit is maximised when cost equals marginal revenue is derived by holding time constant and thus describing revenue and cost as simply a function of the quantity produced. The gap between revenue and cost is widest where marginal cost equals marginal revenue.

But this only applies where ‘time stands still’ – which time never does. The rule tells you how to maximise profit with respect to quantity, but in reality businesses are interested in maximising profit over both time and output. It is possible to consider profit as a function of both time and quantity as opposed to the economic approach of dividing time into artificial segments, by explicitly acknowledging that profit is a function of both time and quantity (which the firm can vary at any point in time, and that will also change and hopefully grow over time). Profit therefore depends both on the amount a firm produces, and the historical time during which it produces.

We can then decompose the change in profit into the contribution due to the change of time, and the contribution due to changes in quantity (which will also change over time), resulting in a formula worded like: change in profit equals chance in profit due to change in time multiplied by the change in time, plus change in profit due to change in quantity multiplied by the change in quantity.

This tells us how big a change in profit will be so if a firm wants to maximise its profit, it wants this number to be as big as possible. Change in profit due to change in quantity is the same thing as ‘marginal revenue minus marginal cost.’ Economic theory argues that profit is maximised when marginal revenue equals marginal cost, so that if you follow the economic profit maximisation rule, you would deliberately set this quantity to zero. Since you get zero when you multiply by any number by zero, following this economic rule sets the second half of the formula (change in profit due to change in quantity multiplied by the change in quantity) to zero.

Therefore economic theory tells us that the change in profit will be maximised when we eliminate the contribution that changes in quantity make to changes in profit. Change in profit is thus reduced simply to the first half of the formula, where changes due to time alone determine the change in profit. But economic theory has given us no advice about how to make change in profit due to change in time as big as possible.

Suddenly advice that previously seemed sensible now looks absurd. Going back to the formula, which is true by definition, and see what it says. If the firm’s output is growing over time, then the change in quantity will be positive. Setting marginal revenue equal to marginal cost means multiplying this positive number by zero – which results in a smaller increase in profit than if marginal revenue exceeds marginal cost. Thus, a careful consideration of time argues that a firm should ensure that its marginal revenue is greater than its marginal cost. The economic rule about how to maximise profit is therefore correct only if the quantity produced never changes.

To use an analogy, suppose you have a formula which describes how much fuel your car uses at any given speed, and you want to work out the most economical speed to drive. What you need to do is work out the lowest rate at which to consumer petrol per unit of distance travelled per second. However, if instead you first work out the most economical speed at which to travel, the answer to this first question will be zero miles per hour! Because at this speed you consume the lowest possible amount of petrol per unit of time, zero. This is an accurate but useless answer, since you’re not interested in staying put. If you want to work out the speed that minimizes petrol consumed but still gets you to your destination, you have to handle both problems simultaneously.

The economic theory of the firm ignores time in the same way that the wrong answer to the ‘most economical speed at which to travel’ question ignores distance. But time is essential to economic behaviour. The economic policy for profit maximisation is derived by following the economic equivalent of finding the cheapest speed at which to travel first, and then multiplying by the distance travelled. By ignoring time in its analysis economic theory with its static emphasis upon maximising profit now ignores the fact that to survive a firm must also grow over time. To grow it must invest and develop new products. If it devotes all its resources to maximizing profit now, then it will not have resources left to devote to investment for new development. What the theory tries to do is work out the ideal level of output of a product for all time. But in the real world there is no such output.

Further, because economists believe that competitive industries set price equal to marginal cost, economists pressure public utilities to price their services at marginal cost. Since the marginal cost of production are normally constant and well below the average costs, this policy will normally result in public utilities making a loss. Which is likely to mean that public utilities are unable to finance investment they need in order to maintain the quality of services over time. Economists then argue that such businesses should be privatised!

Empirical Studies of the 'Law of Diminishing Returns':

In numerous surveys by Andrews, Bishop, Downie, Eiteman, Eiteman and Guthrie, Haines, Hall & Hitch, Lee, Means, Tucker, the ‘Oxford Economic Research Group’ found that 95% of real firms report:

  • 'Marginal revenue/cost' as irrelevant, foreign concepts to business owners.
  • Every extra sale adds to profit
  • Average costs fall with output (high fixed costs, constant or falling variable costs)
  • Prices set by mark-up on average costs.
  • Firms operate well within capacity (not at margin)

In another study, Eiteman & Guthrie 1952 showed managers 8 hypothetical average cost curves:


Graphs 3-5 were typical neoclassical models, number 5 “high at minimum output, … decline gradually to a least-cost point near capacity, after which they rise sharply.” number 6 “high at minimum output, … decline gradually to a least-cost point near capacity, after which they rise slightly" number 7 "high at minimum output, … decline gradually to capacity at which point they are lowest.” (Eiteman & Guthrie 1952: 835)

How were they seen by managers? The following table gives the results:

That is, only 18 out of 336 fit neoclassical vision of diminishing marginal productivity, rising marginal cost. The neoclassical concept of cost curves fits just 5% of companies & products, the other 95% experience constant or falling marginal cost.

The results for firms setting MC to MR:

As Eiteman put it, [engineers design factories]:

"so as to cause the variable factor to be used most efficiently when the plant is operated close to capacity. Under such conditions an average variable cost curve declines steadily until the point of capacity output is reached. A marginal cost curve derived from such an average cost curve lies below the average cost curve at all scales of operation short of capacity, a fact that makes it physically impossible for an enterprise to determine a scale of operations by equating marginal cost and marginal revenues.” (Eiteman, 1947)

 

“The amazing thing is that any sane economist could consider No. 3, No. 4 and No. 5 as representing business thinking. It looks as if some economists, assuming a premise that business is not progressive, are trying to prove the premise by suggesting curves like Nos. 3, 4 & 5”

“Even with the low efficiency and premium pay of overtime work, our unit costs would still decline with increased production since the absorption of fixed expenses would more than offset the added direct expenses incurred.”

Economist Janos Kornai argued that modern capitalism is 'demand constrained' versus the neoclassical idea that the limit of the fixed capital of production affects supply. In a growing economy a new factory must have much more capacity than currently needed. In an uncertain world excess capacity is needed to react to new opportunities. Income distribution limits effective demand. The main problem for firms was not producing with diminishing productivity, but selling what they can produce given constrained effective demand.

Empirical data supports Kornai: even during boom years, US capacity utilisation well below 90%:
To Kornai this wasn't a weakness of capitalism but its strength, the existence of excess capacity vying for the same market, forces innovation. Yet the proponents of capitalism totally ignore it.

In more recent survey work: Over 89 per cent of respondents indicated that ‘marginal’ costs either declined or stayed constant with changes in output (sometimes involving discrete jumps). Finally, only four [of 200] enterprises had both elastic demand curves and increasing marginal costs.” (Downward & Lee 2001, reviewing Blinder)

Fixed costs appear to be more important in the real world than in economic theory.” (Blinder)

Neoclassical economics ignores all the research and all the papers. Anything which does not fit their model is discarded and ignored. And in the end we have a (more realistic) model like this:

which tells us nothing about anything except the failure of marginalism.

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