For economic science, the **Demand-Supply Model** is a fundamental truth, describing the behavior of both consumer and producer in the markets. It would be irresponsible to deny that, yet the model has several serious flaws.

1. We cannot use it to predict future prices and amounts of goods produced and consumed. At best we can see the direction of the changes, which is important, no doubt about it. Yet it is not enough to make the model a tool for practical calculations.

2. It shows only static market situations. We cannot track down the path of the price, while it is moving (as we simply postulate) to the equilibrium point. Because of that, we just ignore the possibility of not reaching the equilibrium (in fluctuations, for example).

3. We are inclined to make an absolute of the point that demand and supply curves intersect. The **Demand-Supply** **Model** looks so universal, so true regardless of market nature (monopolistic markets theory only modifies it, without radical changes).

Yet in the markets with a speculative component it may be not true. From the teaching standpoint, it is critical to formulate the limits of the basic classical model in the very beginning of the economics course to prevent creation of dogmas in the minds of students.

Point 1 is too big a problem to even come close to resolving it. Still, there is no real science without quantitative predictions. Yes, we use extrapolations for that purpose. Unfortunately, they often fail due to misunderstanding of the process they describe (being nowadays extremely sophisticated).

What about points 2 and 3?

Dealing with point 3, I am showing the **Demand-Supply Model** without intersection of curves (except zero point). It is the asset bubble model, presented in my previous posts. It does make sense to show it again in this piece with some simplifications. Here it is.

As I have already explained it, D1 is the demand curve for the boom phase of a bubble, S is the supply curve, and D2 is the demand curve for the bust phase of a bubble.

This picture does not tell us anything about how an asset bubble develops; it shows no dynamics at all. This is where dynamic equations (finite differential equations, to be exact) must step out to show the path of the price, and there is no better way to put the path on a graph than using spider diagram. This way I am dealing with point 2 of my agenda too.

Let us denote:

P(t) – price at moment t, $M,

S(t) – quantity supplied at t, units,

D(t) – quantity demanded at t, units

∆P(t) – change in price at t, $M,

The equation for supply curve S is:

P(t) = S(t) (1)

The equation for demand curve D1 is:

P(t) = 0.5D(t) (2)

The equation for demand curve D2 is:

P(t) = 2D(t) (3)

In my post “Asset Bubble Microeconomics: A Peculiar Demand and Supply Diagram” I assumed (for illustration purposes only) that the price change was equal to the difference between demand and supply. I admit that it is too strong an abstraction. There must be, of course, some elasticity coefficient in this equation, depending on how the price reacts to shortages or surpluses in the markets. So

∆P(t) = k(D(t) – S(t)), (4),

where k is the elasticity coefficient.

Let us take the boom phase first. Transform (4) using (1) and (2), which are the boom phase equations.

What we get is

∆P(t) = k(P(t)/0.5 – P(t)) (5)

Suppose k = 0.2. This strong is the reaction of the price to the difference between supply and demand. Then the equation for the booming price is

∆P(t) = 0.2P(t)

With starting price = 1, the following graph shows price changes until the supposed crash point at approximately double price is reached.

We can see also the spider diagram of the booming price.

Now I am going to show price dynamics after the price crashes at the level=2 and goes subsequently down (the bust phase).

In this case we need to transform (4) using equations (1) and (3), describing the bust phase.

The result is

∆P(t) = k(P(t)/2 – P(t)) (6)

Elasticity coefficient is still k=0.2. Then the equation for price dynamics when the bubble bursts is

∆P(t) = -0.1P(t)

Starting from high point 2, the price goes down as the following graph shows.

The spider diagram on the graph shows the path of the price during the bust.

Both phases of the bubble should have been put on the same graph, of course. I separated them to avoid overloading it with details.

Conclusion: equations and spider diagrams are a big advantage as far as teaching **Demand–Supply Model** (theory) in Economics is concerned.

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