Is price in this situation exogenous or endogenous?

My supply function is $Q = a + bP + u$. My demand function is $Q = c + u$. The error terms $u$ in both equations are mutually i.i.d random variables with a mean of zero and a constant variance. My question is: since the demand curve is a constant, is price an endogenous or exogenous variable?

• What are you trying to estimate? Both a and b, just b or a,b,c? – BB King Mar 28 '17 at 13:10
• The question is if we can estimate the supply, equation – user12655 Mar 28 '17 at 17:42

$$P = \alpha + \beta Q + \epsilon$$ $$Q = c \quad \quad \ + \mu$$
This is a simultaneous equation system, where both $Q$ and $P$ are endogenous. Here you can see more clearly that a demand shock $\mu$ affects prices via $\beta$ (if $\beta=0$, the two equations are independent).
This means that the OLS estimation of $b$ is inconsistent. A consistent estimation can be obtained with 2SLS, using a proper instrument.