The price of a product has signficant impact on the total sales. Hence modeling sales would give the incentive to include price as a regressor (amongst other variables). Suppose we would estimate this using OLS, this gives something like
$sales_t=\alpha_0+\beta_1\times price_t+...+\epsilon_t\;\;\;\;\;\;\;\;\;(1)$.
In addition, we know that
$price=\frac{sales}{volume} \iff sales=price\times volume \;\;\;\;\;\;\;(2) $.
Estimating (1) results in a large Variance Inflation Factor (VIF) for price, which is comes from the relation (2).
It seems that one can never include price in a sales model, simply because of relation (2). Equation (1) shows a linear relationship, and under ceteris paribus, whenever price increase by one unit, sales should increase with $\beta_1$. But whenever price increases, the sales increases as well because of (2). And price and volume have a non-linear relationship: a price increase of \$0.05 would have a different impact on volume than an increase of \$50000.-
Hence simultaneity occurs and the OLS estimator $\beta_1$ seems to be invalid.
One could reason to use an instrument, but equation (2) implies than any instrument correlated to price is automatically correlated to sales which suggests that there exists no valid instrument.
What is your opinion about modeling sales including the price as a regressor? Am I making a mistake in reasoning here?