Answer to Question #272969 in Math for Thelma 22

Question

a) Given the demand function for computers to be P = 2400 – 0.4Q

i. Determine the coefficient of point elasticity of demand when P = 1800, P = 1200,

and P = 600 and give an interpretation of each result. [7]

ii. If the price of computers increases by 12%, calculate the percentage change in

quantity demanded at P = 1800, P = 1200, and P = 600. [12]

Answer 1

i.

$$P=2400 – 0.4Q$$

$$1=-0.4\dfrac{dQ}{dP}$$

$$\dfrac{dQ}{dP}=-2.5$$

$$\eta=\dfrac{dQ}{dP}\times\dfrac{P}{Q}$$

$$\eta=-2.5\times\dfrac{P}{Q}$$

$P=1800, 1800=2400 – 0.4Q=>Q=1500$

$$\eta=-2.5\times\dfrac{1800}{1500}=-3$$

Therefore, at this point on the demand curve, a 1 percent change in price causes a 3 percent change in quantity demanded in the opposite direction (because of the negative sign).

$P=1200, 1200=2400 – 0.4Q=>Q=3000$

$$\eta=-2.5\times\dfrac{1200}{3000}=-1$$

Therefore, at this point on the demand curve, a 1 percent change in price causes a 1 percent change in quantity demanded in the opposite direction (because of the negative sign).

$P=600, 600=2400 – 0.4Q=>Q=4500$

$$\eta=-2.5\times\dfrac{600}{4500}=-1/3$$

Therefore, at this point on the demand curve, a 1 percent change in price causes a 1/3 percent change in quantity demanded in the opposite direction (because of the negative sign).

ii.

$P=1800, 12\times(-3)=-36$

If the price of computers increases by 12%, the percentage change in quantity demanded decreases by 36%.

$P=1200, 12\times(-1)=-12$

If the price of computers increases by 12%, the percentage change in quantity demanded decreases by 12%.

$P=600, 12\times(-1/3)=-4$

If the price of computers increases by 12%, the percentage change in quantity demanded decreases by 4%.