John Smith, C.E.O. of A.B.Co. is attempting to estimate the quantity of his prod

Question

John Smith, C.E.O. of A.B.Co. is attempting to estimate the quantity of his product that will be demanded during April. At the current price of $2.00, A.B. Co. is selling 100,000 units per month. Mr. Smith has been informed that on April 1st, Delta Co., a producer of a substitute good, will be decreasing the price of its product by 10%. Given a cross elasticity of 2, answer the following questions. **Please show ALL work.... A) How many units can Smith expect to sell during April? B) If Mr. Smith wants to maintain his current sales of 100,000 units, to what level should he change his price? (Assume Ep = -4) **

Explanation / Answer

A : Given that cross elasticity is 2, cross elasticity of demand: Change in Quantity demanded A ( A.B. Co.)/ Change in price of product B ( Competitor) 2 = [( 100,000 - x) / 100,000 ] / [ 2 -1.8] / 2 2 = [( 100,000 -x) / 100,000 ] / 0.1 0.2 = [( 100,000 -x ) / 100,000 ] 20,000 = 100,000 - x x = 80,000 , hence quantity demanded in April will be 80,000 units if he wants to keep the same price. B: Price elasticity of demand is = -4 Price elasticity of demand is: Change in quantity demanded / change in price - 4 : [( 80,000 - 100,000 ) / 100,000 ] / [ x - 2] / 2 - 4 : 2 / ( x - 2) (x - 2) : 2 / -4 x - 2: -0.5 x: 1.5 , hence price is 1.5 . Few things, change in quantity demanded is nil due to the fact that Mr Smith wants to keep the same current sales, so it only needs to alter his price.

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