Consider the supply and demand model below:

a. Find the reduced-form equations for \(p\) and \(q\) as a function of the exogenous variable \(x\).

b. Now suppose that the demand equation is \(q=-5 p+11+8 x+e_{1}^{*}\). Find the reduced-form equations for \(p\) and \(q\) using this demand equation and the original supply equation.

c. Show that the new demand equation is a mixture of the original supply and demand equations. Specifically, it is three times the original demand equation plus two times the supply equation. 

d. If we have \(N\) observations on \(p, q\), and \(x\), can we consistently estimate the demand equation by OLS? Why?

e. If we have \(N\) observations on \(p, q\), and \(x\), can we consistently estimate the reduced-form equations by OLS? Why?

f. Given the true reduced-form equations, can we deduce whether \(q=-p+3+2 x+e_{1}\) or \(q=-5 p+11+8 x+e_{1}^{*}\) is the true demand equation?

g. Is the demand equation "identified" using the necessary condition?

Transcribed Image Text:

Demand: q=p+3+2x+e Supply: pq+1+x+ e