The ABC Company manufactures AM/FM clock radios and sells on average 3,000 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 ABC's product as coefficient of-3, how many will be sell per month if the price is lowered to 22$?
b. The competitor decrease its price to 24$. If the cross-elasticity between the two radio os 0.3, what will ABC's monthly sales be?

3 answers

a) Ed = (% Change in Quantity Demanded)/(% Change in Price)
-3 = (Q2 - 3000)/(22 - 25)*(22 + 25)/(Q2 + 3000)
(Q2 - 3000)/3*47/(Q2 + 3000) = 3
(Q2 - 3000)/(Q2 + 3000) = 9/47
Q2 - 3000 = 9/47*Q2 + 27000/47
38/47Q2 = 168000/47
38Q2 = 168000
Q2 = 4421 units
b) Cross-price elasticity equals:
0.3 = (28 + 24)/(3000 + Q2)*(Q2 - 3000)/(24 - 28)
52/(3000 + Q2)*(Q2 - 3000)/(-4) = 0.3
(Q2 - 3000)/(Q2 + 3000) = -0.3/13
Q2 - 3000 = -3/130Q2 - 900/13
133/130Q2 = 381000/130
133Q2 = 381000
Q2 = 2865 units.
This formula is wrong
According to a study, the price elasticity of shoes in the United States is 0.7, and the income elasticity is 0.9.
a. Would you suggest that the Brown Shoe Company cut its prices to increase its revenue?
b. What would be expected to happen to the total quantity of shoes sold in the country if incomes rise by 10 percent?