Question

When the price of good X falls from the demand for good Y
increase from 20 Kg. to 25 Kg.
a) What is the cross elasticity of demand of good Y for good X?
b) Are goods X and Y compliments or substitutes?
06
Given the production function:
Q = 100 + P – 0.01P2 + 2N – 0.03N2
Determine the marginal rate of technical substitution

Answer 1

A) $E_{xy} = \frac{\Delta Q_y}{\Delta P_x} = \frac{25 - 20}{-P} = \frac{-5}{p}$

B) goods X and Y are compliments because cross elasticity has negative sigh "-"

C) $MRTS = \frac{-x_1}{x_2} = \frac{MP_2}{MP_1}$

$$M P (p) = 1 - 0,02 P$$ $$M P (N) = 2 - 0,06 N$$ $$M R T S = \frac {2 - 0 , 0 6 N}{1 - 0 , 0 2 P}$$