Innes Company recently changed the selling price of one of its products.Data concerning sales for comparable periods before and after the price change are presented below. The product's variable cost is $23.20 per unit. According to the formula in the text,the product's profit-maximizing price is closest to:
A)$44.10
B)$25.23
C)$40.95
D)$44.71

Question

Innes Company recently changed the selling price of one of its products.Data concerning sales for comparable periods before and after the price change are presented below.  The product's variable cost is $23.20 per unit. According to the formula in the text,the product's profit-maximizing price is closest to:
A)$44.10 
B)$25.23 
C)$40.95 
D)$44.71

Quizplus · Accepted Answer

Percent change in price = ($76.00 - $78.00) F1F1F1S1F1F1F10 $78.00 = -2.5641%
Percent change in total unit sales = (3,610 - 3,400) F1F1F1S1F1F1F10 3,400 = 6.1765%
Price elasticity of demand
= ln(1 + % change in quantity sold) F1F1F1S1F1F1F10 ln(1 + % change in price)
= ln(1 + 6.1765%) F1F1F1S1F1F1F10 ln(1 + -2.5641%) = -2.3074
Profit maximizing markup on variable cost
= -1 F1F1F1S1F1F1F10 (1 + ed) = -1 F1F1F1S1F1F1F10 (1 + -2.3074) = 0.7649
Profit-maximizing price = (1 + Profit-maximizing markup on variable cost) F1F1F1S1F1F1F10 Variable cost per unit = (1 + 0.7649) F1F1F1S1F1F1F10 $23.20 = 1.7649 F1F1F1S1F1F1F10 $23.20 = $40.95

Innes Company Recently Changed the Selling Price of One of Its