1. XYZ Corporation is a manufacturer of widgets. Over the past several months, i
ID: 1176904 • Letter: 1
Question
1. XYZ Corporation is a manufacturer of widgets. Over the past several months, it has been selling its widgets for $100 each and unit sales have averaged 5,000 units per month. This month its competitor, ABC, Inc. raised the price of its widgets from $100 to $110. XYZ noted that its unit sales increased by 200 units. Please answer part B
a. What is the cross price elasticity of demand between XYZ%u2019s and AB C%u2019s widgets?
We know this is .4
b. If XYZ knows that the price elasticity of demand for its widgets is -2.0, what price would XYZ be able to charge and still sell 5,000 widgets, assuming ABC keeps its price at $110?
Explanation / Answer
a) dP = 10
dQ = 200
(P1 + P2)/2 = (100+110)/2 = $105 ;
(Q1+Q2)/2 = (5000+5200)/2 = 5100 ;
Elasticity = (dQ/dP)*(P/Q) = 0.4111;
b) (dQ/dP)*(P/Q) = - 2 ;
P /dP = -2*Q/dQ ;
Q = 5100 ;
dQ = 200 ;
P/dP = -51
(P1+P2)/2 = -51*(P2-100)
100 + P2 = -102*P2 + 10200
103*P2 = 10100
P2 = $98.058
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