Altona Corporation's vice president in charge of marketing believes that every 3% increase in the selling price of one of the company's products would lead to a 5% decrease in the product's total unit sales. The product's absorption costing unit product cost is $13.50. The variable production cost is $7.80 per unit and the variable selling and administrative cost is $2.30 per unit.
-The product's profit-maximizing price according to the formula in the text is closest to:
A) $31.86
B) $23.84
C) $5.43
D) $18.41

Question

Quizplus · Accepted Answer

First, we need to calculate the contribution margin per unit:
Contribution Margin = Sale Price - Variable Costs
Contribution Margin = SP - (Variable Production Cost + Variable Selling and Administrative Cost)
Contribution Margin = SP - ($7.80 + $2.30)
Contribution Margin = SP - $10.10

Now, let's assume the profit-maximizing price is SP. According to the question, every 3% increase in selling price leads to a 5% decrease in unit sales. Therefore, the percentage change in total revenue can be calculated as follows:

% Change in Total Revenue = % Change in Price + % Change in Quantity - % Change in Price x % Change in Quantity
0 = 3% - 5% - 3% x (-5%)

Solving for % Change in Quantity results in -1.89%. This means that if the selling price is increased by 3%, the quantity sold will decrease by 1.89%. Thus, the new quantity sold will be:

New Quantity Sold = Old Quantity Sold x (1 - 1.89%)
New Quantity Sold = Old Quantity Sold x 0.9811

The profit-maximizing price can be calculated as follows:

Profit = (SP - $10.10) x New Unit Sales - Fixed Costs
Profit = (SP - $10.10) x Old Unit Sales x 0.9811 - Fixed Costs

Since we want to maximize profit, we need to take the derivative of the above equation with respect to SP and set it equal to zero:

dProfit/dSP = (SP - $10.10) x Old Unit Sales x (-0.0189) + New Unit Sales = 0

Solving for SP results in SP = $23.84.

Therefore, the profit-maximizing price is $23.84.

Altona Corporation's Vice President in Charge of Marketing Believes That