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

Answer: (A), (B)

$e_{P_xA}=(\frac{\partial g}{\partial A}\frac{A}{Q})/(\frac{\partial f}{\partial P_x}\frac{P_x}{Q}-\frac{\partial g}{\partial P_x}\frac{P_x}{Q})$

Answer 2

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): $\frac{dP_x}{dA}=(\frac{\partial g}{\partial A})/(\frac{\partial f}{\partial P_x}-\frac{\partial g}{\partial P_x})$