Consider the supply and demand model below, where \(x\) and \(w\) are exogenous.

a. Find the reduced-form equations for \(p\) and \(q, q=\pi_{11} x+\pi_{21} w+v_{1}\) and \(p=\pi_{12} x+\pi_{22} w+v_{2}\), expressing the reduced-form parameters in terms of \(\alpha\) 's and \(\beta\) 's.

b. Suppose \(\pi_{11}=1 / 5, \pi_{21}=1 / 5, \pi_{12}=2 / 5\), and \(\pi_{22}=2 / 5\). Solve for as many of the \(\alpha\) 's and \(\beta\) 's as you can.

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= Demand: qap+x+w+e Supply: p Bg + e =