(Continue problem 9.1.) Given the demand function is expressed as an equation p
ID: 2911980 • Letter: #
Question
(Continue problem 9.1.) Given the demand function is expressed as an equation p +0.005x = 30. 9.2 (1) Express the revenue as a function of price p. (2) Calculate the elasticity function E(p). (3) Assume the current price is $ 10. Calculate the elasticity at this price. Is the demand (4) Based on the answer in part (3), if the price is increased by 5%, what is the approximate (5) Based on the answer in part (3), to increase the revenue, should the price increase or (6) Assume the current price is $ 22. Calculate the elasticity at this price. Is the demand (7) Based on the answer in part (6), if the price is decreased by 5%, what is the approxi- (8) Based on the answer in part (6), to increase the revenue, should the price increase or elastic or inelastic at this price? percentage change in demand? decrease'? elastic or inelastic at this price? mate percentage change in demand? decrease?Explanation / Answer
given demand p+0.005x =30
=>0.005x=30-p
=>x=(30-p)/0.005
=>x=200(30-p)
=>x=6000-200p
(1)
revenue R=px
=>R=p(6000-200p)
=>R=6000p-200p2
(b)
x=6000-200p
=>dx/dp=-200
elasticity,E(p) = (dx/dp)*(p/x)
elasticity,E(p) = (-200)*(p/(6000-200p))
elasticity,E(p) = p/(p-30)
(3)
p=10
elasticity,E(10) = 10/(10-30)
elasticity,E(10) = -1/2
|E(10)| = 1/2
|E(10)|<1
the demand is inelastic at this price
(4)
approximate change in demand = -(1/2)*(5/100)
approximate change in demand = -0.025
demand decreases by 2.5 %
(5)
to increase the revenue price should be increased
(6)
p=22
elasticity,E(22) = 22/(22-30)
elasticity,E(22) = -11/4
|E(22)| = 11/4
|E(22)|>1
the demand is elastic at this price
(4)
approximate change in demand = -(11/4)*(-5/100)
approximate change in demand = -0.1375
demand increases by 13.75 %
(5)
to increase the revenue price should be decreased
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