The AMM model should be one of the biggest innovations in the current bull market and the currency market.

AMM, Automated Market Maker market maker model. It means that in the transaction, both parties to the transaction calculate the results according to the model and automatically complete the transaction.

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Graphical AMM

right branch of hyperbola

In the swap exchange, there is one of the most basic models, which is the AMM (Automatic Market Maker Model):

X*Y=m (m is a constant).

This is junior high school mathematics, hyperbolic model. Of course, the AMM transaction model is the right branch of the hyperbola. After all, the number of coins in its transaction pool is positive. Each point on the curve represents the quantity of A and B in the trading pool of the group A and B.

Asymptote:

The X-axis and Y-axis are the two asymptotes of the hyperbola, respectively. The so-called asymptote is that this curve can approach infinitely, but can never intersect with .

When the point moves to the right on this curve, it corresponds to the fact that the number of A in the trading pool is increasing and the number of B is decreasing. The curves can be very close to the x-axis but never intersect, which means the number of B's ​​in the pool can never go to zero.

In the same way, the point moves upward along the curve, which corresponds to more B and less A, and the curve will approach the Y axis infinitely, but never intersect. This means that the number of A's in the pool can never become zero.

Slope:

The slope of the curve at point P: draw the tangent of the curve through point P, and the tangent of the angle between the tangent and the X-axis. That is, the ratio of B' to A' on the graph.

The ratio of B' to A' is exactly the ratio of B to A in the fund pool at point P.

The practical significance of the slope is that it reflects the ratio of the decrease of B to the increase of A at point P, or the ratio of the increase of B to the decrease of A, that is, the exchange ratio between A and B, that is The exchange rate between A and B, that is, the price.

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demand curve

This seemingly simple model is not a model that anyone came up with. Its shape is actually consistent with the demand curve. Search the Internet to find the curve, there are two kinds. One is straight and the other is curved (I'm not driving).

Tilt down and right:

Whether straight or curved, demand curves slope downward to the right. The demand curve response is the combination of people's demand for two goods. Sloping down to the right means that when the demand for one good increases, the demand for another good decreases.

The curve of the AMM model has the same reason. In a transaction pool of two currencies, if the quantity of one currency increases, the quantity of the other currency will decrease. Of course, this sounds nonsense, but let's move on.

The diminishing marginal rate of substitution:

In a straight-line demand curve, the rates of substitution for the two goods are constant. From point O to point P, from P to Q, B decreases, A increases, and the substitution rate of B and A remains unchanged. Because the slope of the demand curve has not changed.

In reality, if you are a boy. Let you play the game for 2 hours less, and then let you have a lobster, if you agree. Then let you play the game for 2 hours less and give you a lobster the next day, would you still be happy? If it goes on for a long time, it will save you from playing games for 2 hours a day, and a lobster may not satisfy you. On day 2, day 3, day 4, you may have to eat more lobsters to agree to play two hours less. This is the diminishing marginal rate of substitution.

And the curved demand curve can reflect this.

From point P1 to point P2, and from Q1 to Q2, the demand for B falls equally, while the demand for Q increases significantly differently. A's demand increases less from P1 to P2, and A's demand increases more from Q1 to Q2.

This is the diminishing marginal substitution effect. As demand for B decreases, demand for B needs to be replaced with more demand for A.

The same is true for the two coins in the AMM transaction model. When the user uses A to exchange for B, A in the transaction pool increases and B decreases, that is, the point moves down and to the right on the curve.

We can see that the slope of the curve decreases as the point moves down and to the right. This means that as B decreases in the pool, the price of B/A increases.

Conversely, as the point moves up and to the left on the curve, the slope of the curve increases. This means that as A decreases, the price of A/B increases.

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Graphical market making

Going back to the beginning of this article, the mistake of the little bee.

When users participate in market making. Both A and B in the pool are increasing, so the point is moving up and to the right. Moreover, market making cannot change the ratio of A and B.

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The meaning of swap

What is the meaning of swap? Is it just one more trading place? Is it just a place to issue and list coins with a low threshold? Not only that.

We know that in fact the transaction of the two coins should be in line with the demand curve. But in CEX, that is, traditional exchanges, there will be price fluctuations. So its curve is wavy.

And we know that the slope can reflect the transaction price. Then, when there is a price difference between CEX and SWAP exchanges, some users will move bricks. Buy coins from SWAP and recharge to sell in CEX, or buy and recharge from CEX to SWAP exchange to sell. Eventually, it will lead to the convergence of the currency prices in the SWAP exchange and CEX.

It should be noted that the so-called X*Y=m, m is a constant, but not a constant quantity. When more funds are added to market making, m will increase; when funds are withdrawn from market making, m will decrease.

In fact, in the swap exchange, all currency transactions use the same model. The specific value of m in this model and the specific size of this fund pool depend on the markets of these two currencies.

AMM is an artificially defined model, but it is closer to economic laws. The SWAP exchange is actually an invisible hand in the currency trading market.

While CEX seems to be free, it is full of room for human manipulation. It is possible that there is a visible hand hidden in CEX.

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The meaning of market making

If the scale of the swap exchange is very small, it is not enough to affect CEX. On the contrary, the swap exchange will become a follower of cex.

As for market making, we see that the AMM model curve will move to the upper right, and its scale will be closer to CEX. Just imagine, if a certain trading pair has a large trading capital pool, then price manipulation will be greatly controlled.

write at the end

write at the end

Little Bee doesn't know whether liquidity mining is a flash in the pan. But the swap exchange and the AMM model are remarkable existences in the currency market.

The larger the pool of a certain group of currency transactions, the greater the impact on CEX, and the healthier this group of trading pairs will be. Liquidity mining can push the AMM model curve to the upper right in a period of time, which is of positive significance to the development of swap exchanges and even the health of the currency market.

Even if this positive meaning is temporary, it is necessary.

This article is supported by the Roast Boy Creators Affiliate Program.