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

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

b. Suppose \(\pi_{11}=1 / 5, \pi_{21}=3 / 5, \pi_{12}=2 / 5\), and \(\pi_{22}=6 / 5\). Solve for as many of the \(\alpha\) 's and \(\beta\) 's as you can.

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= Demand: qap + + 3 x +e Supply: p 19 + B + e =