Answer to Question #51731 in Microeconomics for sos

Question

ABC company manufactures digital clock radios and sells on ave 3000 units monthly at $25 each to retail stores. Its closest competitor produces a similar type of radio that sells for $28.
a. If the demand for ABCs clock radio has an elasticity of -3, how many will it sell per month if the price is lowered to $22?
B. The competitor decreases its price to $24. If cross-price elasticity between the two radios is 0.3, what will abcs monthly sales be?

Answer 1

Q = 3000 units, P = $25, Pc = $28.
a. If the demand for ABCs clock radio has an elasticity of -3 and if the price is lowered to $22, it will sell:
Ed = -3 = (Q2 - 3000)/(22 - 25)*(22 + 25)/(Q2 + 3000)
(Q2 - 3000)/(Q2 + 3000) = 0.1875
Q2 - 3000 - 0.1875*Q2 - 572.5 = 0
0.8125Q2 = 3572.5
Q2 = 4384 units
B. If the competitor decreases its price to $24 and if cross-price elasticity between the two radios is 0.3, the abcs monthly sales will be:
Q3 = 3000*(28 - 24)/24/0.3 = 1667 units