Equilibrium Price - OLS Regression I have asked another question related to price elasticity, which pretty much left me with this problem:

I want to analyze the factors influencing the price of a product. The underlying assumption is that of a classic market equilibrium situation where the price equals the point of demand=supply. Now - how do I model such equilibrium prices and estimate the estimators correctly? How do I treat the problem of simultanious equations in this specific case? And can I simply use OLS regression in the case of price-unelastic demand since price is only included in the supply function? 

I already tried reading the relevant chapters in some of the most common pieces of literature (Wooldridge etc.), but I just do not fully understand how to effectively solve the issue. 

The goal is to construct a simple linear regression formula that looks like this:

$P_{t}=\beta _{0}+\beta _{1}X_{t}+\varepsilon _{t}$ 

where P = Price is the dependent variable. 

I am sorry for bothering but I am trying to understand this topic for weeks now and I just need some basic explanation on how to solve this issue. I am really thankful for any comment/answer that sheds some light on this. The more I think about it, the more confused I get.
The same factor affect how a product is supplied and demanded in different ways. If you want to model what the effect of change in a given independent variable has on equilibrium as a whole you need convert both your equations to a single reduced form equation.

If you have two equations a supply and demand equation both of the forms:
$$P_s=\alpha_0+\alpha_1X_i+\mu_i$$
$$P_d=\beta_0+\beta_1X_i+\epsilon_i$$

for estimating how $X_i$ affects equilibrium price set $P_s=P_d$

$$\alpha_0+\alpha_1X_i+\mu_i=\beta_0+\beta_1X_i+\epsilon_i$$

$$X_i(\alpha_1-\beta_1)=(\beta_0-\alpha_0)+(\epsilon_i-\mu_i)$$

letting the terms $(\alpha_1-\beta_1)$,$(\beta_0-\alpha_0)$ and $(\epsilon_i-\mu_i)$ be equal to $\gamma_1$,$\gamma_0$ and $z$ respectively we solve and find that the effect of $X_i$ on equilibrium price is:

$$\gamma_1=\frac{\gamma_0+z}{X_i}$$
based on this formula we see that the 
coefficents value actually changes based on the the amount of $X_i $ provided.  Using this method you can get an accurate estimate of your factor's influence on equilibrium price and see how it changes.