by Filip Palda
We need not be mathematicians to understand what economists are up to when finding out how to maximize the value of a function. How much product a firm should make to maximize profits is among the first lessons economists learn.
Profit is the “maximand” and output is the variable whose “optimal level” we seek in order to maximize profits. If the firm can sell more for a gain that exceeds the cost of producing it, then the firm should increase output. It would be nice to continue on this path but then the problem would have no solution. The firm would keep increasing its output indefinitely while profits tended towards infinity.
The maximizing problem has a solution when the components of profit start changing with each increase in output. Costs are seldom the same for each unit produced. Usually one sees the cost per unit increasing as output increases. Increasing unit costs drive the solution to the maximizing problem. The solution is to increase output until the price of the very last unit produced, the “marginal revenue” comes vanishingly close to the steadily rising cost of providing that extra unit, the “marginal cost”. “Marginal” is an economic jargon word meaning “extra” or “additional”. Profits reach a maximum when marginal revenues equal marginal cost.
Maximizing the returns from pressure: opening move
NOW WE CAN get a notion of what is going on in Becker’s pressure functions. Predators want to maximize money extracted from victims less the cost of doing so. To do this the predator adjusts the amount to invest in the components of her pressure function, such as mobilizing her members to political action.Victims have symmetric objectives. They want to minimize the money they lose and the deadweight loss from the frustration of having to limit their use of cabs less the cost of defending themselves. They too must invest to mobilize their members to beat back the efforts of their oppressors. So how does maximization work here? In the case of Uber, cab owners make an opening gambit. They take political expenditures by riders to be fixed, or “given”. That is, they assume no reaction. This is just an assumption Becker makes to get his model going. He modifies it to allow for interest groups to anticipate what their rivals will do, but this does not change the core of his analysis.
Cab owners keep increasing their expenditures on mobilizing themselves for political action until the increasing cost of getting themselves to push even harder for non-competitive premiums just equals the extra or “marginal” gains these extra premiums deliver. The calculation of these marginal gains is based on the cab owners’ knowledge of market conditions. Economists call these conditions supply and demand and the equilibrium price and quantity to which they settle.
This is a first indication of how Becker’s model blends market conditions and political calculations by a fusion of precise mathematical sub-functions that encapsulate how money is transformed into power and how non-competitive premiums emerge from demand and supply conditions.
Reaction to being preyed upon: countermove
UBER WILL REACT to the opening gambit of cab owners by first calculating how much damage is done to riders, both actual and potential, from the increased political activity of cab owners.
This damage will be greater than the gain to cab owners because of the existence of deadweight loss. But Uber faces a greater cost of organizing riders because their interests are more diffuse than those of owners. Is it possible that these costs inhibit Uber from reacting to cab owners?
Now comes that part that should have been told at the start of this story but would have made no sense to readers if exposed then. The story started by hiding the fact that both groups were already in some stable equilibrium relation to each other. While this is a bit of a cheat, the story cannot be told in any other way without diving into the mathematics. The existence of a previous equilibrium means that Uber had gone through a maximizing process where it kept increasing political expenditures until the increasing costs of political activity exceeded the non-competitive premiums and deadweight losses kept at bay from predators. Then something changed for cab owners, perhaps in their pressure function, to make it attractive to “re-optimize” by increasing their political expenditures. That “something” which changed could be a new friend highly placed in city hall, or rising demand for cab services. Whatever the reasons for the cab owners’ initial thrust, Uber would then react because its marginal costs of organizing had not changed but the benefits from fighting cab owners had increased. Higher takings by cab owners threaten even greater losses to Uber customers. The threat of greater losses increases the gains to Uber of increasing its efforts to beat back newly proposed non-competitive premiums by cab owners. The prospect of increased gain from political activity galvanizes Uber to go through the same process as cab owners. Uber increases spending until the marginal costs once again rise to the level of the marginal gains of political activity.
The story does not end here because it is based on the “Cournot assumption” that neither party believes the other party will react to it. Cab owners all make this assumption and all are surprised by Uber’s counter-thrust. So they go back to the drawing board and calculate a new optimal level of political spending, to which Uber then reacts, to which owners react, until either of two things happen. Either both opponents react increasingly violently to each other until political spending continues to balloon without end, or both settle, in ever smaller steps of political reaction to a stable equilibrium. In the first scenario this “game” between opponents is said not to have a solution. In the second scenario the game has a solution in which both opponents see their political spending increase and then stop. Becker believed in the likelihood of the second outcome because of a curious fact about deadweight losses popularized by a mysterious but hugely influential figure in economics named Arnold Harberger.
Non-linearity and equilibrium
HARBERGER DISCOVERED THAT in a demand and supply situation, distortions to equilibrium brought about by artificial price hikes, taxes, and even subsidies, created at first a small deadweight loss, that is, a thwarted or unrealized opportunity for mutually benefiting exchange. Each similar, or “marginal”, rise in the distortion created an ever increasing concomitant rise in deadweight loss. Put technically, linear increases in taxes created non-linear increases in deadweight loss.
The non-linearity of any sort of cost should not come as a surprise. When you press harder on the pedal the resulting increase to the speed at which a car is driven leads to ever increasing fuel consumption per unit of extra speed. Non-linearity is a barrier to the expansion of almost all forces in nature.
Becker was the first to understand that the non-linearity of deadweight loss was an important, though not determining factor in the establishment of political equilibrium. If the rise in deadweight loss grows with every increase in tax, then a tax hike will increase the “pain per unit of tax” or conversely the gain from reducing taxes by a unit. In other words, the return to victims from investing in self-defence increases as predators increasingly attempt to grab their wealth. Increasing predation provokes a greater than proportional outrage in the victims. With mounting fury, they redouble their efforts to repulse their oppressors.
Equilibrium comes about as two opposing incentives tug equally at each other. The incentive to mobilize a group to political action is blunted by the rising extra, or “marginal”, costs of mobilization. Both predators and prey share this debilitation. What they do not share is the direction in which marginal deadweight losses influence the returns from investing in mobilization. Ballooning deadweight losses raise the returns to prey from investing in their own defence. As prey invest in political influence, predators see their returns from political activity diminish.
Equilibrium comes about when the increasing costs of mobilization catch up to prey and the decreasing returns from extra predation fall to the level of the costs of extra predation. If the costs of mobilization decrease with rising expenses on political activity the picture gets murky and equilibrium depends on some fancy sounding maths that basically
state that equilibrium will be attained provided that diminishing costs of mobilization do not overtake rising marginal deadweight losses.
In this arid academic description of humans throwing rocks at each other, Becker glimpsed a bizarre possibility. It seems that rising deadweight loss might give predators an incentive to blunt the harm to victims from their attacks. Becker put it this way “Political policies that raise efficiency are more likely to be adopted than policies that lower efficiency.”
On the surface the comment seems to say that Becker believed politics would evolve towards efficiency. We must go below the surface of this sentence to grasp its nuance. For this is the central claim of Chicago political economy. It divides the field from public choice and may drive members of this school to acknowledge that free markets and coercive governments are working towards the same end. Before we can digest this thought an interlude is called for.
A quick summary
LET US CATCH our breath by reviewing briefly the main ideas behind Becker’s model of political equilibrium. Until Becker, deadweight loss had occupied a respectable but quiet corner of economics. It was used mainly in the cost-benefit analysis of road and damn construction. Economists were happy to leave deadweight loss in this niche. It did not seem to have any behavioral implications. It was an epiphenomenon of market interactions and government interventions. Its link to social accounting was obscure. No one could conceive of its connection to political behavior. It was the collateral damage from taxation and that was about all you wanted to know on the topic.
Becker thought differently. He saw deadweight loss as the interface between economics and politics. Through that interface he could unite the two fields. His trick for uniting economics and politics was to assume that ultimately the distribution of all resources in society rests upon the threat of violence. All resources in society were up for grabs between rival interest groups. Yes, there was a private market in which people worked together to produced items of value. But on top of this market, government operated by force. The interest group that pushed the hardest was essentially hiring government muscle to back up its play to extract, or extort, rival interest groups. While this assumption might seem simplistic, even gross, it helps to read again the words of the British historian cited earlier in this book. In The Mask of Command he writes “But, remote though the battlefield is from the marketplace and the court of law, its pre-existence, or the potentiality of recourse to it, underlie all assumptions citizens make about the order of things as they find them. Force … provides the ultimate constraint by which all settled societies protect themselves against the enemies of order, within and without (pages 311-312)”.
The jostle in politics over resources inevitably drains and damages the resource being contested. The deadweight loss that results from tax battles in politics perturbs the market. It represents an upset to the social accounts between people peacefully trading with each other. This upset feeds back into the political world in the form of protests by people who resent paying taxes to subsidize predatory interest groups.
Thus there is a tussle between the creation of value, which takes place in the cooperative setting of the market, and the theft of value, which takes place on the adversarial stage of politics.The tussle between predation and market resistance might go on indefinitely. It might settle into a fixed level of expenditure on political activity by both sides with the concomitant fixed, or equilibrium level of government taxes and transfers.
The endpoint depends on how groups react to each other’s behavior.With this quick summary we can now return to asking why Becker thought politics would tend to efficiency and we can examine some historical examples supporting this claim. Though it is beyond the scope of this book, Becker’s model also contains insights for competition among lower organisms.
Efficiency of politics
IN STATING THAT “Political policies that raise efficiency are more likely to be adopted than policies that lower efficiency” Becker sowed confusion. He would have done better to qualify this sentence by adding ceteris paribus. All other things held constant. These “other things” can overwhelm and negate the efficiency Becker spied sprouting amid conflict between interest groups. He understood this but chose to focus on the one force which no one in economics and politics had noticed nor bothered to assign a role in the theory of power. That force was deadweight loss.
Recall that deadweight loss provokes needless ire in its victims and brings no pleasure to their oppressors. It puts oppressors at a disadvantage. Think of why pick pocketing is almost absent in the US. Individuals from this class of thief pocket the cash and discard the wallet. The thief may gain a hundred dollars. The victim loses a hundred dollars. She also losses documents and financial plastic that can takes weeks of effort to replace. These efforts divert her from living a productive life. They benefit no one. They are a deadweight loss. Due to the asymmetry of gains and losses, outraged victims may thus have a greater incentive to put pressure on the police and politicians than pickpockets have incentive in trying to find new ways of lifting wallets. Deadweight loss may also explain the near total disappearance of mugging in the US. As citizens grow more educated, the value of their “human capital” rises. Mugging is a psychologically and physically violent undertaking. Muggers may cause hundreds of thousands of dollars of damage to the victim’s human capital in return for the paltry gain of petty cash. This may explain why muggers are an endangered species, whereas white collar crime flourishes. Confidence tricksters do minimal physical damage to their victims. They specialize in transferring money from victims to predators with minimal deadweight loss.
The above examples are in the spirit of Becker but stray from his formal analysis. They are not easily quantified in a demand and supply model. But they illustrate why predators find advantage in minimizing harm to their victims. This seemingly benevolent incentive may explain the evolution of taxation.
Becker’s model applied to history
BEFORE THE 19TH century taxation in Western countries was a rough business. Governments had not yet developed the bureaucratic expertise to correctly assess the income of its citizenry. Most economic activity could only be taxed by the coarsest of methods. To raise the revenue for their armies, governments allowed their soldiers to be billeted with the population. Peasants frequently revolted against what in effect was a virulent parasitic host of soldiers defining their own revenues through extortion and violence. As civil servants became more expert in identifying regular and non-destructive means of revenue, governments could afford to build barracks in which to effectively imprison their soldiery until they were needed in battle. Deadweight losses of taxation fell. Rebellions of citizens decreased in frequency.
Despite improved methods of detecting income, taxation remained limited to a few obvious sources, such as imports of fine goods and alcohol. Poor citizens hid their money. Rich citizens bribed their way out of paying.
The problem with taxing a narrow base of riches is that the deadweight losses rise at an increasing rate. To keep deadweight losses down and raise more money one must spread the burden over a wide base. Oarspeople driving on a boat understand this phenomenon on a physical level. If one oarsperson reduces her effort the slack must be taken up by others. But the physics of effort is such that for every extra equivalent amount of slack, each remaining rower must expend energy at an increasing rate. As rowers withdraw under the strain, the cooperative effort of moving the boat can collapse. Similarly, governments that rely on narrow sources of revenue face a point of taxation beyond which they risk destroying their base of ratepayers. Thus taxation in Western countries never could exceed roughly ten percent of national income. High deadweight losses from taxation limited governments’ fiscal expansion.
Taxation however is not the only means by which government can control revenues. Regulations are a clumsier means of raising money, because they simultaneously entail its expenditure. Despite this shortcoming, if regulations can extract money resources
from victims on a broad base they may entail lower deadweight losses than if government taxed and spent the money towards the same end. An example can be found in the minimum wage. Sources of revenue are easily identified: employers of low-skilled labor. By forcing salaries to a level above the market wage, minimum wages take revenue from employers and transfer it to employees. This is a simultaneous tax and transfer of money. The deadweight loss comes from the jobs that the higher wage destroys. According to Becker’s analysis, the minimum wage may remain the most efficient and thus popular means of redistributing money if the alternative means of achieving this goal through taxation and spending on the poor provokes higher deadweight losses.
The minimum wage gradually lost its importance as a supplement to income after the second world war. Governments discovered the financial miracle of income withholding. Combined with advances in computer technology, data storage and retrieval, and the emergence of a competent and hard to corrupt corps of tax officials, governments were able to spread income taxes over an enormous base and so reduce the deadweight loss per dollar of tax revenue. The reduction in the collateral damage from taxation led to the decline of redistribution of income by regulatory means and the rise of overt fiscal policies of taxing some to enrich others with direct cash transfers.