Question

Allen Corporation's vice president in charge of marketing believes that every 7% increase in the selling price of one of the company's products would lead to a 11% decrease in the product's total unit sales. The product's absorption costing unit product cost is $13.00. The variable production cost is $4.00 per unit and the variable selling and administrative cost is $6.90 per unit.

The product's profit-maximizing price according to the formula in the text is closest to: (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

$49.08

$19.09

$6.93

$25.99

Answer 1

Elasticity of demand = Natural log(1+ percentage change in quantity sold)/Natural log(1+percentage change in price)

% change in quantity sold = - 11%

% change in price = 7%

Elasticity of demand = Natural log(1 + (-0.11))/Natural log(1 + 0.07) = Natural log(0.89)/Natural log (1.07)

= -0.1165/0.0677 = -1.72

Profit maximizing mark up on variable cost = -1/(1+ Elasticity of demand) = -1/(1+ (-1.72)) = -1/-0.72 = 1.39

Profit maximizing price = Profit maximizing mark up on variable cost * Variable Cost

= 1.39*10.90 = 26.04

= approximately 25.99

The answer is (d)