Question

The demand equation is estimated to be 50 – 3P + 2Po , where Po is the price of some other good. Assune the average value of P is $ 3 and the average value of Po is $ 6.

a. what is the price elasticity at the average values of P and Po? how should the price of the good be changed to increase total revenues ?
b. what is the cross elasticity at the average values of P and Po? what is the relationship between the two goods?
c. if the equation is correctly estimated, is the good inferiod, a necessity, or a luxury? Explain

Answer 1

Answer on Question #73568 -Economics - Microeconomics

The demand equation is estimated to be $50 - 3P + 2Po$, where Po is the price of some other good. Assume the average value of P is $3 and the average value of Po is $6.

a. what is the price elasticity at the average values of P and Po? how should the price of the good be changed to increase total revenues?

b. what is the cross elasticity at the average values of P and Po? what is the relationship between the two goods?

c. if the equation is correctly estimated, is the good inferior, a necessity, or a luxury? Explain

Answer.

a) Find the first derivative of the demand function with respect to P and PO

$$Q'(P) = -3$$ $$Q'(PO) = 2$$

Then

$$K_{d(P)} = -3 \times \frac{3}{50 - 9 + 12} = -0.17$$ $$K_{d(PO)} = 2 \times \frac{6}{50 - 9 + 12} = 0.23$$

b)

$$K_{d(x,y)} = \frac{dQx}{dPy} \div \frac{Qx}{Py}$$ $$K_{d(x,y)} = 2 \div \frac{50 - 9 + 12}{6} = 0.23$$

The goods are substitutes $(K>0)$

c) The coefficient near P is negative, so demand increases when price decreases, so the good is normal. As Kd<1, it is necessity good

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