2nd The thesis that profit taxes cannot be passed along
3rd Carl Föhl: The criticism of progressive income taxation
4th Criticism of Föhl's thesis
In this chapter we will deal with the problem of profit taxes. Within the framework of neoclassical doctrine, the thesis was advanced for a long time that, apart from the so-called head taxes, profit taxes are the only taxes that cannot be passed on.
As is well known, within the framework of financial theory we differentiate between taxpayers and ultimate taxpayers. The term taxpayer refers to those persons who have to pay a tax to the state. With the term “ultimate taxpayerer”, on the other hand, the question is posed as to which persons actually ultimately have to bear this tax burden in the sense of a reduction in their income and assets.
One of the basic statements of financial theory is that taxes in general can be passed on to other persons to a greater or lesser extent, so that the taxpayer does not always coincide with the ultimate taxpayer. Passing-on processes take place in the market, namely in the way that taxes represent costs for the economic agents and that enterprises in particular attempt to pass through costs to the sales price. With the production and supply of goods, entrepreneurs pursue the goal of generating profits, but this only succeeds if the revenues of the enterprises exceed the costs incurred in production, and this in turn presupposes that the costs incurred by the enterprises are passed along to the selling price.
Of course, it is not primarily the entrepreneur's intention that determines whether taxes are passed on; the market must also create the possibilities to realise this intention. First of all, it must be assumed that every increase in the sales price leads to a reduction in demand and thus possibly also in revenue, so that the increase in unit profit is at least partly compensated for by the fact that the entrepreneur can sell fewer goods precisely due to this price increase. And this means that the partial increase in profit associated with the price increase is in turn reversed by the fact that the quantity of goods sold decreases precisely due to the price increase. However, since profit results from the product of price multiplied by quantity, it is only very imperfectly successful to pass on the taxes in full to the price.
We even have to expect that under certain conditions the decrease in the demanded quantity will be higher than the price increase with the consequence that in this case the attempt to pass on the tax will even lead to an additional burden for the entrepreneur. However, taxes can also be passed on back again.
Just as a supplier may be able to increase his sales price and thus pass on the tax to the buyer, it must be expected that an entrepreneur may also be able to pass on a tax back to the suppliers of the raw materials or semi-finished products he demands. In fact, an entrepreneur succeeds in passing back on such a tax by wringing a reduction of the purchase price from the supplier of these raw materials and semi-finished products.
Now, we can assume that the lawmaker does indeed to some extent expect that taxes will be more or less passed on to the market partners. There are taxes - and above all the general turnover tax: value added tax is one of these types of taxes - where the lawmaker certainly intend that it is not the taxpayer, the entrepreneur, who has to pay these taxes, but that these taxes are to be paid in full by the buyer of these goods.
However, in the case of other taxes - and this includes especially income taxes - the legislator wants to target the taxpayer himself. If, for example, within the framework of the general income tax, the tax rate increases with the level of income, this is mainly because it is assumed that the loss of benefit resulting from a certain tax sum is lower for the person with a higher income than for the recipient with a lower income; the tax progression is thus associated with the intention that the higher earner also has to pay a higher tax sum. However, this intention presupposes that the taxpayer in this case also coincides with the ultimate tax payer and that therefore no passing on of taxes takes place.
However, experience shows that the question of whether and to what extent taxes are actually passed on does not primarily depend on the intention of the legislator when introducing a tax, but solely on the respective market conditions. Whether and to what extent taxes are actually passed on depends, on the one hand, on the will to pass on taxes and, on the other hand, on the power of the person passing on the taxes to actually pass them on.
An entrepreneur who sets up his production to maximise his profit will always try to pass on tax burdens whenever possible. However, we have seen above that intense competition can force entrepreneurs to seize all possible profit increases, because if they forego possible profit increases, they run the risk that their customers will migrate to the competition and that they will eventually face bankruptcy.
We had also seen that, although for a monopolist this pressure does not exist, he does not run the risk of having to declare bankruptcy if he does not make use of all possibilities of an increase in profit. Nevertheless, it can be assumed that most monopolists will try to pass on the taxes, they have the power to do so and, as is well known, power tempts them to exercise this power, to maintain and expand their power, power simply tempts them to abuse it.
But what determines the extent to which an entrepreneur has the power to pass on taxes? Taxes can always be passed on to consumers if consumers have no possibility of substituting their demand with other goods, so-called substitute goods. Without the possibility to switch to substitute goods, the consumer must - perhaps grudgingly - accept the price increase associated with the pass-on, even though it causes him a loss of utility.
This power of the entrepreneur and the corresponding powerlessness of the buyer can now be determined on the basis of the relationship between the elasticity of supply and demand with regard to price. In general, the lower the price elasticity of demand or the higher the price elasticity of supply, the greater the power of the entrepreneur. In the case of goods that are essential to life, such as salt, but for which there is hardly any substitute, the price elasticity of demand is close to zero. Conversely, the entrepreneur has an extremely small price elasticity if - as in the case of fresh fruit, for example - he is forced to sell the goods by the end of the day, otherwise they will be spoiled and no longer have any value.
How large these price elasticities actually are, however, depends in turn on whether an entrepreneur has a supply monopoly or is in competition with other enterprises. If an entrepreneur can determine that the tax burden affects every competitor and that therefore competitors will also strive to pass on the tax burden through price increases, an entrepreneur can also afford to pass on this tax burden through price increases without having to fear that he will lose customers to the competition due to this price increase. The competing entrepreneurs then also increase their prices, but the migration of customers to the competition only occurs if the prices of the existing suppliers increase in comparison to the prices of the competitors. It is therefore only the price relations and not the absolute price level that determine whether or to what extent taxes can actually be passed on.
So far, we have explained the question of the possibility of passing on the tax burden by means of the attempt of the suppliers to pass it on to the demanders. Of course, these considerations also apply mutatis mutandis to the attempt to pass on the tax burden. As already mentioned, an entrepreneur can also pass on the tax burden by succeeding in his capacity as a buyer of raw materials, semi-finished products or labour in forcing down the price towards the supplier of these services. Also here, the possibility of passing on the tax depends on the relationship between the price elasticities of supply and demand.
What is the role of a profit tax in this context? Neoclassical finance theory came to the conclusion that profit taxes, as the only tax apart from poll taxes, cannot be passed on at all, so that the legislator can be sure that entrepreneurs have no possibility of passing on this tax burden. We will take a critical look at this thesis in the following section. First, however, a few words on the thesis that poll taxes cannot be passed along.
One always speaks of poll taxes when the tax amount is levied independently of the economic data of the taxpayer, e.g. when every citizen is taxed regardless of how high his income and assets are or how great his need for certain goods is: the demanded tax amount is the same for every citizen.
But why does the taxpayer not succeed in passing on the tax burden to others with poll taxes just as well as with sales taxes, for example? The reason why head taxes cannot be passed on is that the amount of the head tax is not linked to a specific economic activity. Therefore, one cannot avoid tax liability by avoiding the activities that trigger tax liability.
Of course, in this case the taxpayer also carries out certain economic activities and the taxpayer can also try to pass on the tax burden to other economic persons with whom he trades. However, in this case, he can no longer be sure that his competitors are equally attempting to pass on the tax burden on the same products.
A taxpayer has the possibility to react in very different markets. It can be very advantageous for a taxpayer X to precisely not reduce the supply of goods on the same markets as his competitor in order to entice away his competitor's customers in this manner. This means that when trying to raise the prices of certain goods, the entrepreneur acting in this way must always fear that his competitor will not follow and that his own customers will therefore switch to the competition. In this case, it is no longer possible to pass on the tax burden to the other market partners.
We can assume that real poll taxes are hardly ever levied in highly developed economies any more, the injustice associated with this is too great, and the principle of equal tax sacrifice is massively violated. In ancient times, however, the levying of poll taxes was a popular means for conquerors to collect poll taxes from the subjugated population, as this type of tax was the easiest for the conquerors to collect.
2nd The thesis that profit taxes cannot be passed along
The justification for the neoclassical thesis that profit taxes cannot be passed on at all was as follows: In free markets, taxes can only be passed on to the price of goods to the extent that entrepreneurs reduce the supply of goods due to the introduction or increase of taxes. If the supply of goods becomes scarce, the willingness of consumers to accept price increases rises in accordance with the demand curve for the increase of goods.
The entrepreneur reaches his maximum profit just when the marginal profit becomes zero. In this case, an expansion of production does not lead to an increase in profit, since it is assumed that the increase in revenue (marginal revenue) is only as high as the increase in costs (the so-called marginal costs). The marginal profit (the increase in the profit total) therefore falls to zero.
The marginal profit is therefore not taxed either. If an entrepreneur does not achieve an increase in profit compared to the previous situation, no additional tax burden will arise, even if the tax rate remains the same. Consequently, after the introduction or increase of profit taxation, the entrepreneur reaches his maximum profit with the previously realised production quantity.
The entrepreneur thus has no interest in restricting production, but only in this case could prices be raised and thus a passing-on of the profit tax be realised. Although the profit tax reduces the net profit, the entrepreneur has no incentive to cut production. The increases in the tax burden caused by the levying of the tax cannot be absorbed (passed on) by reducing supply and for this reason the demanders are willing to accept a higher price.
Let us try to illustrate these relationships with a diagram. We plot the price p on the ordinate and the quantity of goods x on the abscissa. First, we draw a normal (blue) demand curve. This assigns to every conceivable price a certain quantity of goods in demand. Here, demand is normal, i.e. price increases lead to a decrease in demand. For the sake of simplicity, we assume that the demand curve is linear. In reality, the demand curve is curved, but the results of our model are not affected by this simplification.
Next, we plot the (red) supply curve on our diagram. We assume a normal course for it as well, which means that rising prices also lead to rising supply. For reasons of simplification, the supply curve is also linear, although also here, a curved course must generally be expected due to the law of diminishing returns, but also here our conclusions are not affected by this simplification.
The intersection of the two curves marks on the one hand the price at which supply and demand coincide, i.e. the market is cleared and which is also headed for by itself in functioning markets. On the other hand, however, it is precisely at this quantity that the supplier reaches his maximum profit. The supply curve results from the course of the marginal cost curve. At the same time, the demand curve indicates the revenue growth (marginal revenue) that the supplier can expect. At the intersection of the two curves, marginal costs and marginal revenue correspond to each other; this means that the expansion of supply would lead to marginal costs being higher than marginal revenue and would thus have to result in a loss of profit. The supplier thus also reaches his maximum profit at the point of intersection of the supply and demand curves.
In our model we now introduce a taxation of the entrepreneur's profit, again assuming a percentage profit tax for the sake of simplicity. The tax sum is thus always a certain percentage of the gross profit sum.
We now want to consider profit taxation in our model by plotting the course of the gross profit and net profit totals in our diagram. We want to start from the supply quantity zero. At this point, profit is of course also zero, since profits only arise if the entrepreneur also sells his goods. Because of the assumed course of the supply and demand curve, the profit and thus also the tax sum is large, since the marginal revenue is high according to the course of the demand curve with low supply quantities and at the same time the marginal costs are low here.
Now, if supply increases, marginal revenue is assumed to decrease, but marginal costs increase at the same time. Both changes lead to a reduction in the gross profit sum and thus also in the tax sum that is to be paid. This is equivalent to the fact that the profit increase of the last unit of goods offered (the so-called marginal profit) decreases. As long as the point of intersection of the two curves has not yet been reached, the gross profit total increases - the revenue increases are assumed to be higher than the cost increases - but the increase in profit growth decreases with the expansion of the supply of goods.
Thus. the gross profit curve, which assigns a certain gross profit sum to each supply, initially shows an increasing course, reaches its peak precisely at the point of intersection of the supply and demand curve, and then falls again in absolute terms as the quantity of goods expands. This means that the entrepreneur achieves his maximum profit precisely at the intersection of supply and demand. And if we assume that the entrepreneur always tries to offer the quantity of goods that brings him the maximum profit, then the entrepreneur will also try to aim for this profit-maximising supply quantity.
Let us now try to plot the course of the net profit sum in our model. Since we have assumed a percentage profit taxation, i.e. the tax sum follows the course of the gross profit sum, the curve of the net profit sum also shows a similar course as the curve of the gross profit sum: Where the gross profit is zero, there is no net profit; if the gross profit increases, the net profit also increases; the maximum of the net profit is reached exactly at the supply quantity at which the gross profit also reaches its maximum. If the entrepreneur were to increase his supply above the equilibrium quantity, the net profit sum would thus also be reduced. The net profit is only assumed to be lower than the gross profit, but otherwise follows the course of the gross profit.
Now we have to assume that the thesis that entrepreneurs try to maximise their profit refers to the net profit and not to the gross profit. The benefit that the entrepreneur derives from his profit does not depend on the amount of the gross profit, but on the net profit. If we now consider this assumption, then the entrepreneur will only change his offer when introducing or increasing the profit tax if by this correction his net profit in turn increases. According to the assumption, the introduction or increase of the profit tax means indeed a reduction of the remaining net profit. Of course, the entrepreneur will usually try to compensate for this reduction in net profit by passing on the profit tax to the consumers and thus raising the sales price by the amount of the profit tax.
We have already shown above that a price increase only leads to the desired success, i.e. makes it possible to pass on the profit tax, if the entrepreneur reduces his supply. We have assumed that price increases lead to a decline in demand and that this in turn means that the increase in unit profit in the case of a price increase is always more or less compensated by the fact that the quantity demanded declines at the same time due to the increased price. A price increase therefore only leads to the desired increase in profit (and thus also enables tax to be passed on) if the partial profit increase due to the increase in unit profit is higher than the partial profit reduction due to the decrease in the quantity of goods sold.
A look at our diagram shows that the introduction of a profit tax or the increase of the profit tax rate leads to a decrease in the net profit sum, but that the quantity of goods at which the entrepreneur achieves the highest possible net profit has not changed. If, however, the entrepreneur still achieves his maximum profit with the previous supply quantity and therefore does not change the supply, there is also no possibility for the entrepreneur to increase the price and thus to pass on the tax to the demanders. However, this conclusion is tantamount to the thesis that taxes on profits can therefore not be passed on to the price of goods.
For the same reasons, however, the attempt to pass on the profit tax to the suppliers of production factors or semi-finished products does not succeed. The demand for production factors or semi-finished products is only derived from the planned supply; the entrepreneur needs these factors to produce the supply. And if he does not change his supply because of the profit tax, there is also no change in the demand for production factors. And here again, the price of these production factors could only be reduced by the entrepreneurs reducing their demand for production factors.
3rd Carl Föhl: The criticism of progressive income taxation
C. Föhl came to the conclusion that, contrary to the conclusions of neoclassical finance theory, profit taxes can be passed on by 100% to the price of goods. Carl Föhl justified this counter-thesis with the fact that the state uses the additional revenue from profit taxation to purchase goods, so that the revenue of the entrepreneur would also increase by the amount of the profit tax. The net profit would initially decrease by the amount of the profit tax, but would then increase again by this amount due to the increase in revenue. The net income thus remained unchanged. This statement is tantamount to the thesis that profit taxes can be passed on by 100%.
Of course, these theses only apply to the entirety of entrepreneurs. It cannot be assumed that each individual entrepreneur will remain unaffected by these transactions; an individual entrepreneur must certainly fear that the demanded profit tax sum will be higher than the additional revenue induced by the additional expenditure of the state. The state will not distribute this additional expenditure evenly across the entire economy and this means that on balance there will be winners and losers from these state measures.
Let's take an example: The net profit of the entire business community has just amounted to 100 billion. So far, no special profit tax has been levied. The state now decides to introduce a 10% profit tax on gross profits. This means that in addition to the previous tax burden in connection with sales taxes, enterprises will have to pay 10 billion to the tax authorities. And in a first step, this actually has the effect of reducing the net profit total to 90 billion. However, since the state is assumed to spend this additional revenue in full, in a second step the revenues of entrepreneurs rise, namely because they earn 10 billion more due to the purchases of state. Thus, in the second step, the net profit increases partially by exactly this amount of 10 billion. Overall, the net profit for the entire business community has not changed in the long run.
Carl Föhl thus comes to the conclusion that profit tax is by no means one of the few taxes that cannot be passed on by enterprises to consumers. On the contrary, it is to be expected that profit tax is one of the few taxes that in general can be passed on by 100%. It is therefore not possible to burden entrepreneurs in their entirety by way of profit taxation.
From a macroeconomic point of view, however, the taxation of corporate profits would have a fatal effect. Precisely because of the ability to pass on a profit tax, it was the introduction of this type of tax that led to an increase in revenues and thus also in gross profits. It is true that net profits did not increase as a result of these transactions, but therefore the inflation rate increased accordingly.
Nevertheless, the rapid increase in gross profits caused by profit taxation has created the impression that the profits of entrepreneurs are increasing at the expense of the rest of the population. And since in normal times it cannot be assumed that the real domestic product can be increased to the same extent as nominal government spending, this increase in revenues is ultimately reflected in an increase in the inflation rate. Thus, at the end of the day, the state has brought about the conditions in the first place that it actually wants to tackle with profit taxation.
It is much more reasonable to renounce the special (i.e. additional) taxation of profits. The total sum of net profits was in fact determined macroeconomically. It corresponds to the difference between the value sum of demand and the cost sum of supply. If this were to increase, the profits of the enterprises would automatically increase in their entirety. The attempt to skim off this additional profit by means of taxation would not succeed, since to the same extent as the enterprises have to pay additional taxes, their revenue would also be increased.
As long as the state does not succeed in reducing the surplus demand, nothing will change in the sum of profits, since it is precisely this surplus demand that is responsible for the sum of profits.
4th Criticism of Föhl's thesis
Criticism of Föhl's thesis was not lacking for long. Hardly any other scientific article in the period after the Second World War has received so much attention and also criticism. This criticism was directed against the tacit assumptions of Föhl's model. In his first article on the subject, Föhl had tacitly assumed that profit taxation had no influence on investment and savings behaviour. In this case, effective demand would increase:
by the amount of government expenditure. The increase in profit (dG) would correspond to the increase in revenue from profit tax (dTGew).
If one furthermore assumes that the real domestic product is not affected by profit taxation, the increase in revenue is reflected in price increases and these in turn in increases in gross profit. However, it is questionable whether the willingness of entrepreneurs to invest remains unaffected by profit taxation. If the propensity to invest decreases, this means that the additional revenue of the enterprises no longer corresponds to the profit taxation sum, but is lower by the amount by which the investment decreases. With the investment, however, the profit total (gross as well as net) also decreases. The demand now changes as follows:
Let us illustrate these considerations with a macroeconomic diagram. On the ordinate, we enter the macroeconomic sum of savings and investment, while on the abscissa we read off the domestic product (nominal).
First, we enter in this diagram the investment sum before the introduction or increase of profit taxation. According to the assumption, it was autonomous, i.e. it would not change with an increase in the domestic product. This assumption is reflected in our diagram by the fact that the investment line runs parallel to the abscissa.
Next, we consider the saving function, which indicates that as national income grows, the savings amount increases; for the sake of simplicity, we assume a linear dependence, which is equivalent to the propensity to save and the savings rate being constant, i.e. not increasing with growing income. The point of intersection between the two curves Y0 marks the equilibrium before the introduction of profit taxation.
Due to the taxation of profits, firstly, in addition to the savings amount, the additional tax revenues are now initially discontinued (before these amounts are spent). The curve of the discontinuation of purchasing power thus shifts upwards by the amount of the additional tax.
Secondly, the profit taxation leads to the fact that the curve of overall demand is shifted upwards by the amount of the additional government expenditure (Gst). Since tax revenues are assumed to be fully spent (= assumption of a balanced state budget), the curve of total autonomous demand (I + Gst) rises by the amount of the additional tax revenues (T).
The point of intersection between the curves of autonomous demand and the discontinuation of purchasing power thus shifts to Y1, thus increases according to the assumption, and the increase in revenues predicted by Föhl then occurs, and with them the increase in the gross profit sum, exactly by the amount of the additional tax revenues. In the final result, the sum of net profits remains constant, so the profit tax could be passed on 100% to the consumers under these assumptions.
The main criticism of Föhl's theses is that Föhl did not examine how the introduction or increase of the profit tax affects the other determinants of the net profit sum; in particular, he neglected the fact that the other demand flows may change as a result of taxation.
Föhl's conclusions were only reached because it was tacitly assumed that the introduction of profit taxation had no influence on the investment level and the propensity to save. Above all, the validity of the assumption of a constant investment rate was now questioned in the criticism of Föhl's theses. From an individual economic point of view, it may well be justified that an individual entrepreneur does not change his investment plans if his profit expectations remain unchanged despite profit taxation.
However, Föhl only comes to the conclusion that the overall economic profit sum remains unaffected by profit taxation calculated in net terms. Since it cannot be assumed that the state spends the additional revenue generated by profit taxation exactly on the enterprises that have paid the tax and to the same extent, it must be expected that some of the entrepreneurs will generate less additional revenue, just as some of the entrepreneurs will generate more additional revenue than they have to pay in additional taxes.
But this means that the assumption that the willingness of entrepreneurs to invest will remain unaffected by profit taxation becomes questionable. Especially since it is unclear at the beginning of this process how the additional government spending will be distributed among the individual enterprises; it must be feared that profit expectations and with them the willingness to invest will decline due to profit taxation. It is sufficient here for entrepreneurs to wait and let a certain amount of time pass before they commit to their original investment plans. First of all, the amount of investment decreases due to this waiting period, and this time lapse already leads to a reduction in the total profit, and this reduction can then also lead to a sustained downward correction of profit expectations.
In our diagram, these changes have the effect that the investment sum and with it the curve of autonomous demand declines. However, this shifts the equilibrium point. The autonomous demand curve now intersects the curve of purchasing power discontinuations at a domestic product Y2, which lies between the original national income Y0 and the income Y1.
For our question about the possibilities of passing on a profit tax, these results mean that a certain part of the profit tax can be passed on, but that contrary to Carl Föhl's conclusions, complete passing on does not succeed, so that entrepreneurs can very well be additionally burdened due to the taxation of their profits. Thus, the thesis of the neoclassical finance theory that profit taxes cannot be passed on at all, in contrast to almost all other types of taxes (turnover and income taxes), remains wrong.
On the other side, however, it is not correct that profit taxes can be passed on completely. Basically, profit tax has lost its special role: Like any other tax, it must be expected that part of the tax burden can be passed on and that the extent of these possible pass-ons depends crucially on the other market data (such as profit expectations).
A first possible reason for a reduction of the investment sum in connection with profit taxation can be seen in Keynes' assumption that the investment volume does not depend so much on the current profit sum but on the long-term profit expectations, but these would deteriorate quite considerably due to profit taxation.
There is a second possible reason for a decline in the amount of investment. The assumption that the investment volume is determined autonomously is certainly questionable. One can at best assume that the extent of investment is not directly dependent on the level of domestic product and/or gross profit sum. In a diagram in which the volume of investment is seen as a function of the domestic product (national income), one can then assume that the volume of investment is considered autonomous in relation to the domestic product and therefore runs parallel to the abscissa. If one of the variables on which the investment volume depends actually then changes, this change in investment behaviour is taken into account by treating the investment line (which is constant in relation to the domestic product) as a data change that triggers a shift in this investment line.
Let us suppose that we could assume that the willingness to invest is a direct function of the expected net profit and would increase with growing profit expectations. In this case, a distinction must be made between whether a change in the amount of investment occurs due to a movement along the investment function or due to a shift in the function. Only then, when the investment function shifts downwards, does the case occur that no 100% passing-on of profit taxes is possible. Temporary changes in profit, which occur through movement on given and unchanged functions, would then not influence the final result. Only if at least one of the relevant curves itself does change, then the intersection of these curves shift and only in this case does the economy head for a new equilibrium point with a changed profit level.
Such a downward shift of the investment function could now be expected if investment decisions depend on the level of net profits. In an equilibrium model, macroeconomic variables such as S and I always refer to market prices (gross profits). Since the gap between gross and net profits increases by exactly the amount of the profit tax increase when the profit tax is introduced/increased, also the investment function shifts in relation to gross profits even if the behaviour with regard to net profits remains unchanged.
Whether Föhl's thesis that taxes on profits can be passed along by 100% has to be modified depends not only on possible influences of a profit tax on investment behaviour, but additionally on possible influences on the propensity to consume. Thus, we also have to ask ourselves whether changes in savings and consumption also result from a tax on profits? The Haavelmo theorem can be used to answer this question. The Haavelmo theorem examines the question of how an increase in government spending (GST) affects the national product (Y) when the increase in government spending is fully financed with taxes. Haavelmo has tried to prove that in this case (increase in expenditure with simultaneous financing of this additional expenditure through additional tax revenue) the domestic product increases by the amount of the increase in expenditure (d GST), so that the income multiplier is one.
The Föhl's tax paradox deals with the question of whether taxes on profits can be passed on and whether this defeats the intended redistribution to the detriment of profit recipients. This is precisely what Föhl's paradox asserts. While in Haavelmoo's theorem it is primarily government expenditure that increases and this policy requires an increase in the tax bill; in Föhl's paradox it is primarily the profit tax bill that is increased, which results in an increase in government expenditure. Both cases have in common that government expenditure and the tax sum increase by the same amount.
Let us again try to illustrate this possible influence of profit taxation on the consumption function and thus also on the savings function with the help of our diagram. We assume here that savings are directly dependent on the level of private disposable income. Since in our diagram savings are considered as a function of domestic product and thus of gross incomes, every change in taxation (and thus also in profit taxation) changes the position of the savings function, assuming otherwise unchanged savings behaviour. Every increase in taxation increases the gap between gross incomes, which is plotted on the abscissa in this diagram, and net income (private disposable income), on which savings behaviour is assumed to depend. Thus, even without a change in savings behaviour (in the relationship between savings sum and net income), a diagram describing the relationship between savings sum and gross income will show an increase in the tax sum and thus a shift in the savings function.
In what way does the increase in the tax sum shift the saving function S = f(EB)? Let us take a numerical example. If the tax sum is increased e.g. by 100, then the savings sum for an income of 1000 just corresponds to a gross income of 900 (1000-100) without taxation. Since savings behaviour is assumed to depend on net income, the savings sum at an income of 1000 is thus exactly equal to the amount that households would have saved at an income of 900 without a tax increase. This means, however, that a tax increase triggers a shift of the saving function to the right by the amount of the tax increase.
Our diagram thus shows: The starting point is the equilibrium at Y0. Due to profit taxation, the curve of autonomous demand is shifted upwards by the amount of additional tax revenue. We neglect here the possible influence of taxation on investment behaviour. At the same time, the savings function (as a function of gross income) shifts to the right by the amount of the additional tax sum. These two shifts of the relevant functions lead to a new equilibrium, which just results in an increase in domestic product (gross income) by the amount of the increase in the tax sum. The Haavelmoo theorem still applies here.
It is precisely these connections that Föhl addresses in his reply to the criticism and considers how the introduction of a profit tax affects the course of the functions of effective demand. If only the savings function were to shift in the sense mentioned, one would indeed arrive at the same results as Föhl in his first contribution. With regard to the changes in savings behaviour, the criticism is thus directed less at the result than at the way it is viewed, and this criticism is defused by Föhl's second contribution. However, the fact remains that taxation reduces profit expectations, that in this way the volume of investment is reduced and that precisely for this reason the entire tax burden cannot be passed on to consumers as a general rule.