# Free Market Prices Between Supply and Demand

## An Engineer's Perspective

When looking for the mechanism that controls prices, you might run across a scheme similar to the diagram seen to the right. It shows the price in the middle between supply and demand. The arrows expain the interaction: High prices reduce demand, and a high demand drives the price up. This is symbolized by the minus and plus signs near the arrow tips. In addition, high prices increase supply, and a large supply drives the price back down. The vertical double bars symbolize a delay, indicating that the effect does not take place instantaneously but rather takes some time to take effect. I would like to examine these relationships a bit more closely, using more formal methods derived from feedback control theory.

### What is a feedback control?

Everybody is surrounded by feedback systems in everyday's life. I will pick a very simple system to explain the fundamental mechanisms and some terminology. Let us assume a room or a house in a wintry landscape that needs to be heated. There is a permanent loss of energy through gaps, through doors, windows, and even through the insulation. With this energy loss (the disturbance), the room cools down if you don't heat.

The room has a temperature sensor and a thermostat. You can control the thermostat setting and adjust the desired temperature. This is called the setpoint. When you subtract your actual room temperature from your setpoint, you obtain the control deviation - this is an indication how much you have to heat in order to reach your desired (setpoint) temperature. Finally, you have a heater system. Let us assume that the heater's output power is proportional to the control deviation, meaning that the heater applies more power when the room is quite cold than when the room has almost reached the desired temperature. The activity of the heater is called the corrective action. Simply turning on the heater would not be a good idea. The heater would introduce heat to the room, and temperature would simply rise uncontrollably. We need to be smarter than that: we will use the thermostat and temperature sensor to create a closed feedback loop. The feedback loop is capable of stabilizing the temperature. Take a look at the diagram above. The room temperature is the controlled variable, and the task of the control system is to keep the controlled variable as close to the setpoint as possible. This implies that the control deviation is close to zero. If somebody opens the door and some heat escapes (disturbance), the sensor will register a lower temperature than desired. In other words, the difference between setpoint and actual temperature (the control deviation) is positive and the heater gets turned on automatically to produce a corrective action. The room temperature rises, and the control deviation drops back to zero until equilibrium is reached again. Clearly, the feedback loop is able to stabilize the controlled variable.

One more consideration: The room temperature does not rise instantaneously. Rather, it takes several minutes of heating for the room temperature to rise. There is a delay. In technical terms, the room integrates the heating power. We can simulate this process to see how the control system reacts to a disturbance. In this graph, we assume that somebody opened the door at 60 seconds. The room temperature drops from 21°C (the desired temperature) to 14°C. Instantly, the control deviation rises, and the corrective action (heat) increases proportionally. Slowly, the room temperature rises with the applied heat, the control deviation drops back to zero, the heater reduces its power, and eventually, the room reaches its equilibrium point again.

Now what does this have to do with markets and prices?

### The feedback model of the free market

Imagine some item that you frequently buy. All of a sudden, the price increases. It is very likely that you buy less of it, or you stop buying it altogether. In addition, you may well assume that other people think like you. We can see a first relationship between price and demand: An increased price reduces the demand. This is probably an instant reaction - demand drops without much of a delay. This causes a problem, however: manufacturers and vendors have the item in stock, and the want to sell off the stock. So they need to lower the price again to increase demand. These considerations give us a first idea of a price-stabilizing feedback loop. A diagram analogous to the room temperature control is seen above. The fact that a the demand of the customers decreases when the price increases, establishes a negative feedback loop. This negative feedback stabilizes the price.

Of course, this scheme is incomplete. The customer is only one side of the coin. There is also the vendor - and the manufacturer. A vendor who has to lower prices sells at reduced margin and may lose interest in selling the product. The same applies to the manufacturer. Conversely, if a product sells at a higher price, vendors get more interested in selling it. More manufacturers will take up production, or production capacity will be increased. We therefore observe: increased prices increase the supply. However, it usually takes some time until manufacturers increase production or even build a new plant. We observe a delay, similar to the delay in the room with the heating system.

Increased supply has two effects on the market. First, pressure increases to sell the product, and prices will be reduced. We observe: a high supply level lowers prices. Second, the marked may saturate. If there is a constantly high supply of a product, the customers lose interest in buying the product, and demand decreases. Here, we find yet another negative, and therefore stabilizing, feedback branch.

Now we can attempt to sketch a simplified feedback diagram of the market system that balances supply and demand through the price. Let us change the symbols slightly. Let a square symbolize a proportional function (i.e., an instantaneous reaction), and a square with a bar at the input symbolize a function with a delay (such as the heated room in the initial example). Interestingly, the controlled variable is the price. The double feedback loop stabilizes the price. This does not mean (as we will see further below) that the price is always the same; it just means that the price finds an equilibrium value, and that strong disturbances have a small effect on the price in the long run. Another interesting observation is the control deviation - in this model, the control deviation is the stock, i.e., the difference between supply and demand. A feedback system tries to keep the control deviation close to zero. This is intuituvely correct in our model. If the stock is negative, we are facing empty shelves. People don't get what they need. On the other hand, a large stock means that resources are stored unused. Economic capacity is bound uselessly. The economic optimum is in the middle when demand meets supply. Let us check if this diagram reflects our observations. An increased price and increased market saturation reduce the demand, reflected by the negative signs at the top right summation point. Demand subtracted from supply accounts for items not sold - stock - as modeled by the summation point to the left. Finally, an increased price entices manufacturers to incease production. Other effects play a role, however, such as the production costs. High production costs make a product less attractive to manufacturers. In fact, the difference between price and production costs is the profitability of a product - the sole reason for a manufacturer to produce an item. Here, we may have arrived at one of the most interesting observations. Manufacturers and vendors would naturally attempt to increase their profits. However, the negative (stabilizing) feedback mechanism of the free market guarantees that manufacturers cannot arbitrarily dictate the prices. Price - and with it the profit - is stabilized and varies within the tight constraints of a stable feedback system. Profit is constrained by the customer, and in a correctly functioning free market no manufacturer can achieve excessive profits.

It should be clear that this is a simplified model, yet it reflects the stabilizing effect of the feedback mechanism. A more comprehensive model could, for example, consider the effect of increased demand on production costs. Costs of commodities, even of labor, are parts of feedback loops themselves.

We can now use the model to observe the reaction of the market to disturbances. Let us first consider a sudden increase in demand (arrow), for example by a fashion wave or some emergency needs. As the demand spontaneously increases, supply falls short and prices go up. However, production picks up soon, and the balance of supply and demand is re-established. Prices return to their original level. The green line in the lower diagram represents the manufacturing output (supply), which, following increased demand, stays at a higher level to maintain the equilibrium.

The next example involves a sudden increase in production costs. Such an increase may be caused by the introduction of minimum wages (increase in labor costs), increase in commodity taxes or import custom duties, or - to name a topical example - by the introduction of CO2 certificates. The consequence of increased production costs is two-fold. In the short run, the manufacturers will try to increase prices. Because of the feedback system in which the manufacturer works, room for price increases is limited. Consequently, production will fall short with a subsequent long-term price increase. Either way, prices achieve an equilibrium, stabilized by the feedback control system, but in this case at a higher level. The consumer (that is you) pays the higher price.

The feedback model represents a correctly functioning free market. This is an important limitation since there are plenty of market distortions. For example monopolies and oligopolies, cartels, unions, government intervention. Generally anything that breaks one of the feedback paths removes the mechanism for price stabilization, and the consumer will either suffer a shortage or bear overly high prices.

### The market model of government-supplied commodities

The worst distortion of the market occurs when the government intervenes and offers a commodity paid for by fees and taxes. An exaggerated example to illustrate the point: the government decides that bread is essential and offers it for everybody free of charge. Production costs are covered by increasing taxes. What will happen? Demand for zero-cost bread will go through the roof, and the shelves will empty with lightning speed. The government can react by rationing the bread or by mandating higher production. In no case, however, will there be any control over the production costs. The taxpayer does not know how much he pays for the bread because the direct link between demand, supply, and price is severed. There is, in fact, no incentive to offer the bread at the minimum possible price to remain competitive. The "free" bread will be scarce and overpaid through taxes.

Let us attempt to model a market system for a government-provided commodity. Clearly, the government dictates the price which it collects as a fee. The fee determines demand in the same manner as in the free-market feedback system: a low fee increases demand. Whoever supplies the product or service earns part of the fee (minus bureaucratic overhead) but has production costs. We may safely assume that the fees do not cover production costs, otherwise the government could just let the market regulate the product without intervention. Consequently, the difference between fee and production costs is covered by the public treasury - the taxpayer. Most importantly, the government-mandated fee (the price) is no longer the controlled variable. What the diagram reveals is a feedforward system. No feedback path that would act in a stabilizing manner exists any more. The system is extremely sensitive towards any disturbance such as a change in production costs or a sudden change in demand. If demand goes up for whatever reason, supply will not be able to follow because of its inherent delay, and the product will be in short supply. At least as bad is the lack of control for the production side. There is no mechanism to keep production or administration costs at bay, and there is no mechanism that controls the price because the taxpayer has no control over how taxes are being used.

Such a model is well-suited to explain why control of government-offered commodities must fail. Only massive and costly bureaucratic efforts can keep this system within bounds. Tax money must be used to cover all costs. Therefore, from an engineer's perspective, through the application of the principles of feedback control, it becomes clear why Gerald Ford said:

Remember that a government big enough to give you everything you want is also big enough to take away everything you have.

### It becomes clear why only a lean government can function.

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