Managerial Economic

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?

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  1. 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.

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  2. This formula is wrong

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