Question

The demand function (\(Q^D_x\)) and supply function \((Q^S_x)\) are given as:
\(Q^D_x=f(P_x,I)\ and\ Q^S_x=g(P_x,A)\) where I (Income) and A (Advertisement expenses) are the exogenous factors affecting quantity demanded and supplied, respectively. Further, \(\frac{\partial f}{\partial P_x}\lt0,\frac{\partial g}{\partial P_x}\gt0\) but \(\frac{\partial f}{\partial I}\) and \(\frac{\partial g}{\partial A}\) may have any sign. Considering that there exists an equilibrium \((Q_x^D=Q_x^S=Q)\), which of the following is/are CORRECT?

• A. \(e_{P_xA}=(\frac{\partial g}{\partial A}\frac{A}{Q})/(\frac{\partial f}{\partial P_x}\frac{P_x}{Q}-\frac{\partial g}{\partial P_x}\frac{P_x}{Q})\)
• B. \(\frac{dP_x}{dA}=(\frac{\partial g}{\partial A})/(\frac{\partial f}{\partial P_x}-\frac{\partial g}{\partial P_x})\)
• C. \(e_{P_xI}=(\frac{\partial g}{\partial I}\frac{I}{Q})/(\frac{\partial f}{\partial P_x}\frac{P_x}{Q}-\frac{\partial g}{\partial P_x}\frac{P_x}{Q})\)
• D. The sign of \(\frac{dP_x}{dA}\) does not depend on \(\frac{\partial g}{\partial A}\).

Answer 1

The Correct Option is A, B

The correct option is (A): \(e_{P_xA}=(\frac{\partial g}{\partial A}\frac{A}{Q})/(\frac{\partial f}{\partial P_x}\frac{P_x}{Q}-\frac{\partial g}{\partial P_x}\frac{P_x}{Q})\) and (B): \(\frac{dP_x}{dA}=(\frac{\partial g}{\partial A})/(\frac{\partial f}{\partial P_x}-\frac{\partial g}{\partial P_x})\)