Consider a product market with a supply function (Q_{i}^{s}=beta_{0}+beta_{1} P_{i}+u_{i}^{s}), a demand function (Q_{i}^{d}=gamma_{0}+u_{i}^{d}), and a market

Question:

Consider a product market with a supply function $Q_{i}^{s}=\beta_{0}+\beta_{1} P_{i}+u_{i}^{s}$, a demand function $Q_{i}^{d}=\gamma_{0}+u_{i}^{d}$, and a market equilibrium condition $Q_{i}^{S}=Q_{i}^{d}$, where $u_{i}^{s}$ and $u_{i}^{s}$ are mutually independent i.i.d. random variables, both with a mean of 0.

a. Show that $P_{i}$ and $u_{i}^{s}$ are correlated.

b. Show that the OLS estimator of $\beta_{1}$ is inconsistent.

c. How would you estimate $\beta_{0}, \beta_{1}$, and $\gamma_{0}$ ?

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