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- \\ 4 Suppose you estimate the demand equation (It = 050 + 011% + U45 (1) using OLS by running qi on pi. Note however, that the observed prices and quantities are simultaneously determined from the system of equations (1H2), where (2) is the supply equation: pi = 50 + 131% + 'Ui- (2) (a) Solve for the equilibrium price as the fimction of the demand and supply shocks, u;- and U5. (b) Let am, = comma-mi), 03 = Var(m) and 03 = Va'r(v,-). Derive the formula for the asymptotic bias in 31,0143 in terms of a, 6, 0.1 ((2) Do you expect 31,0113 to at least capture the correct sign? That is, would the estimated demand curve be downward sloping? If this is not true in general, would this be true if the demand and supply shocks are positively correlated (am, > 0)