Chapter 8.3, Problem 23P

To determine

(a)

The sign of the derivatives $\frac{\partial q_1}{\partial x}\text{ and }\frac{\partial q_2}{\partial y}$ if x is the price of one brand of gasoline and the surrogate of this brand is sold for y price. Then, the quantity of the first brand that is sold in a fixed time period is $q_1$ and it is dependent to both the prices x and y as $q_1=f\left(x,y\right)$ similarly the quantity of the second brand is given by $q_2=g\left(x,y\right)$.

To determine

(b)

The sign of the derivatives $\frac{\partial q_1}{\partial y}\text{ and }\frac{\partial q_2}{\partial x}$ if x is the price of one brand of gasoline and the surrogate of this brand is sold for y price. Then, the quantity of the first brand that is sold in a fixed time period is $q_1$ and it is dependent to both the prices x and y as $q_1=f\left(x,y\right)$ similarly the quantity of the second brand is given by $q_2=g\left(x,y\right)$.