Regression, Extension, and Convergence: The Formation Process of the $F_{damage}$ Theory

1. Regression: How Much Did House Prices Actually Fall?

Do you remember that I initially started discussing and estimating the decline of the Chinese housing market with the AI assistant? Actually, we were not planning to discuss exchange rates at the beginning.

However, looking back at the chat history with my AI assistant just now, its initial understanding was somewhat off. The actual logic is:

$\text{应然价格倍数} = \frac{1}{1 - F_{damage}}$

When $F_{damage} = 0.33$, the should-be price multiple is $\approx 1.49$. That is to say, if the domestic price is depressed by 33%, then its "should-be price" should be 1.49 times the actual price.

Another point occurred to me later: since price can be "damaged," it can also be "benefited." This is obvious. In the new formula, when $W \gg L$ (individual retention far exceeds the survival redline), the denominator can become negative, making $F_{damage} < 0$. This is the "benefit"—for example, in Nordic welfare states, wages are artificially inflated, not because they are more efficient, but because they "can choose not to work."

Of course, in the new formula, the positive range of $F_{damage}$ is no longer "1 to negative infinity", but can tend toward positive infinity—when $W \to L$ and the system fragility coefficient $\beta \to 1$, the denominator approaches zero, and $F_{damage}$ goes off the charts. This is not a mathematical bug, but an ontological fact of the non-existence of the market: no matter how much money is offered, they won't work, because the biological organism has entered energy-saving mode.

So as we were discussing back then, I said, "Then let's bring in the price being damaged by 1/3 as a parameter." Thus, the exchange rate calculated by the AI assistant was 6.27. As for the decline in real estate, we estimated it to be $7.95 \times 1.5 \approx 12\%$. However, this decline was still not what I considered the real decline. Therefore, I later adjusted $F_{damage}$ to 50%, which brought the real estate decline to about 16%. This is more in line with reality. Under this $F_{damage}$, the should-be exchange rate becomes 8.4, which also matches people's perception of the economic capacity reflected by current GDP, so our current exchange rate is already overvalued.

2. Shift: Price Damage and Benefit Is the Price Formation and Fluctuation Mechanism Itself

We have all studied Marxist Political Economy. No matter what views we hold on Marxist Economics, it got one observation right: "prices fluctuate." As for Western Economics, it also recognizes that prices fluctuate. Although their explanations for the sources of price fluctuations differ somewhat.

Thus, our $F_{damage}$, the price damage/benefit factor, as a theory to explain the source of price fluctuations, is not a passing whim.

Actually, in the beginning, I didn't expect that my "price damage/benefit factor" theory could develop this way. Initially, I asked the AI assistant to find the connection between $F_{damage}$ and Fisher's interest theory, to see if we could construct a beautiful formula using Fisher's interest theory to write a paper in memory of Fisher—my most respected economic elder of all, without exception.

I remember being unable to sleep in the early morning of December 20, so I asked the AI if we could combine $F_{damage}$ with Fisher's concept of "impatience." The result was that the AI wrote a bunch of flattery, introducing messy new parameters like the "three-channel deflation model" and $\Delta Y_{Shock}$, and even claimed that my model achieved a "soul-bone-flesh" trinity. I felt that letting it run wild like this wouldn't work—the reason I introduced $F_{damage}$ in the first place was that I didn't want so many messy parameters and models that couldn't provide a unified explanation.

However, there was one term in the AI's reply that I found quite good: "forced patience." Against the backdrop of falling house prices and shrinking assets, households are forced to divert all current income from consumption to debt repayment to avoid defaulting. This is not the voluntary "deferred consumption" Fisher spoke of, but a structural coercive behavior. This "forced patience" is precisely the manifestation of $F_{damage}$ at the individual level.

But Fisher's framework ultimately operates under the assumption of "equilibrium." China's reality is non-equilibrium—there are price distortions caused by low human rights factors, administrative monopolies, and credit misallocation. Using Fisher's "friction" to deal with this kind of pathology always feels like scratching an itch through the boot. So I thought, why not elevate $F_{damage}$ from a supplement to the interest theory to an independent explanatory framework that encompasses interest theory?

Later I asked it again: if house prices fall by -30%, what would Fisher's theory say? It brought up Fisher's 1933 paper The Debt-Deflation Theory of Great Depressions—debt liquidation leading to monetary contraction, falling prices, business bankruptcies, loss of confidence, and ultimately "great social unrest." But this is still a post-hoc description rather than an ex-ante explanation. I don't want to be an annotator of "balance sheet recession"; I want to be an explainer of price formation itself.

Therefore, I completely abandoned the attempt to squeeze $F_{damage}$ into Fisher's framework.

After much discussion, I finally clarified the positioning of this theory.

$F_{damage}$ is not a supplement or a patch to existing economic theories, but a reconstruction of price formation itself. It studies not "efficiency," but "fairness"—or rather, the degree to which price deviates from equivalent exchange.

In any transaction, both buyers and sellers have a psychological anchor for the "acceptable exchange ratio." In reality, however, neither party can escape a synthetic, irresistible composite influence—stemming from the positioning of the individual by the intraspecific structure and the rewriting of the survival mode by the level of tools. The price ultimately agreed upon is not the equilibrium result of free negotiation, but the "damaged price" under the influence of $F_{damage}$.

So I elevated $F_{damage}$ from a supplement to Fisher's interest theory to an independent explanatory framework that encompasses interest theory.

The core formula of this framework is:

$$F_{damage} = \frac{S_s \cdot T^{\alpha}}{1 - \beta \cdot e^{-\gamma(L - W)}}$$

The numerator $S_s \cdot T^{\alpha}$ is the coupling tension between structure and tools; the denominator $1 - \beta \cdot e^{-\gamma(L - W)}$ is the biological behavioral feedback damping. When the individual retention $W$ approaches the survival redline $L$, the denominator approaches zero, and $F_{damage}$ tends toward infinity—this is the singularity state, where price signals break down, and no amount of money will make them work. When $W \gg L$, the denominator can become negative, making $F_{damage} \lt 0$, entering the compensatory state (such as Nordic welfare states).

The relationship between the natural price and the actual price is:

$$P_{natural} = \frac{P_{actual}}{1 - F_{damage}}$$

$T$ (tool level) is neutral. In a rigid structure, the improvement of $T$ only amplifies $F_{damage}$ ($\alpha > 1$), where total factor productivity increases but well-being does not—the increment is intercepted by the structure, which is the "total factor productivity illusion." Only in a flexible structure can the improvement of $T$ possibly reduce $F_{damage}$.

See Chapter 6 for complete variable definitions and formula derivations. Let us first establish the core intuition here.

Economy studies efficiency, while $F_{damage}$ studies fairness.

3. Evolutionary Patterns Across Species: From Natural Selection to Intraspecific Instrumentalization

This kind of damage and benefit is not just an economic phenomenon; it is a universal law of biological evolution.

• Low $T$ Stage (Natural Selection): Tools are rudimentary, $T^{\alpha}$ is extremely small, and $F_{damage}$ is mainly determined by $S_s$. The damage or benefit at this stage is manifested as the most primitive natural selection—the slower gazelle is eaten by the lion. This is the direct screening of individuals by the external environment. Nature also has social organisms, such as bees and ants. Worker ants and worker bees are born with no rights but only duties; their $F_{damage}$ is $S_s$ itself—because $T$ is too low, the denominator barely functions.
• High $T$ Stage (Intraspecific Instrumentalization): When a species acquires advanced tools, $T^{\alpha}$ increases rapidly. To govern these tools, the intraspecific structure ($S_s$) must be upgraded simultaneously. If the optimization rate of $S_s$ cannot keep up with the translation rate of $T$ (i.e., $\alpha > 1$), $F_{damage}$ will explode in a power-law fashion. Members of the same species are no longer merely companions, but are defined as "tool components" to achieve purposes. This instrumentalization of intraspecific relationships shifts the competition from "human versus nature" to a brutal "human versus human." Individuals must face not only the entropy increase of nature but also high-intensity squeeze from the intraspecific structure. This is an evolutionary strategy that sacrifices the quality of life of some individuals for the overall efficiency of the population.

4. Unification and Upgrade of the Theory: A Reconstruction of Classical Economics

$F_{damage}$ is not about patching existing theories, but about reducing their dimensionality and integrating them into a biological framework. On the basis of respecting "value," it uses the "price damage/benefit factor" to explain the formation of the final "price."

In the next chapter, we will explain $F_{damage}$ and price formation from different intraspecific levels.