Question #272969

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]

1
Expert's answer
2021-11-30T02:40:30-0500

i.


P=24000.4QP=2400 – 0.4Q

1=0.4dQdP1=-0.4\dfrac{dQ}{dP}

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

η=dQdP×PQ\eta=\dfrac{dQ}{dP}\times\dfrac{P}{Q}

η=2.5×PQ\eta=-2.5\times\dfrac{P}{Q}

P=1800,1800=24000.4Q=>Q=1500P=1800, 1800=2400 – 0.4Q=>Q=1500


η=2.5×18001500=3\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=24000.4Q=>Q=3000P=1200, 1200=2400 – 0.4Q=>Q=3000


η=2.5×12003000=1\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=24000.4Q=>Q=4500P=600, 600=2400 – 0.4Q=>Q=4500

η=2.5×6004500=1/3\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×(3)=36P=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×(1)=12P=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×(1/3)=4P=600, 12\times(-1/3)=-4

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



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