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Consider $p=g(p,y)$. Rewrite this equation as $p-g(p,y)=F(p,y)=F(P(y),y)=0$, where $P(y)$ is the implicit function of $p$. By the implicit function theorem, we obtain $\partial P(y)/\partial y=-F_y/F_p$.

In this case, $F_y=-\partial g/\partial y$. This interpretation is straightforward. On the other hand, $F_p=1-\partial g/\partial p$. How should I interpret this denominator?

Since $p=g(p,y)$ is a recurrent equation of $p$, the direct effect of $y$ on $p$ (the numerator) should be discounted by the denominator. This makes sense.

What I am confused is that, depending on the sign of the denominator $1−∂𝑔/∂𝑝$, the effect of the numerator is overturned.

What is the meaning or the intuition of the denominator? What does $1−∂𝑔/∂𝑝>0$ or $1−∂𝑔/∂𝑝<0$ exactly mean??

For example, $1−∂𝑔/∂𝑝<0$ means that a marginal increase in $p$ increases $p$ itself more than 1, and thus it overturns the direct effect of the numerator???

I greatly appreciate your help!

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