Gordy Corporation's management has found that every 3% increase in the selling price of one of the company's products leads to a 6% decrease in the product's total unit sales. The product's absorption costing unit product cost is $22.00. The variable production cost of the product is $6.80 per unit and the variable selling and administrative cost is $2.40 per unit. According to the formula in the text, the product's profit-maximizing price is closest to:
A)$17.77
B)$31.39
C)$17.61
D)$42.12

Question

Quizplus · Accepted Answer

To find the profit-maximizing price, we need to use the formula:

P = (V + F) / (1 - m)

where:

P = price
V = variable cost per unit
F = fixed cost per unit
m = markup percentage

We can calculate V and F as follows:

V = variable production cost + variable selling and administrative cost
V = $6.80 + $2.40
V = $9.20

F = fixed manufacturing overhead / number of units produced
F = ($22.00 - $6.80 - $2.40) / 1.5
F = $12.80 / 1.5
F = $8.53

Next, we need to find the value of m. We are given that a 3% increase in price leads to a 6% decrease in unit sales. This means that the price elasticity of demand is -2. To find m, we can use the formula:

m = 1 / (1 + price elasticity of demand)

m = 1 / (1 - (-2))
m = 1 / 3
m = 0.333

Finally, we can plug in the values for V, F, and m into the profit-maximizing price formula:

P = (V + F) / (1 - m)
P = ($9.20 + $8.53) / (1 - 0.333)
P = $17.73 / 0.667
P = $26.59

Therefore, the product's profit-maximizing price is closest to $17.61 (Choice C).

Gordy Corporation's Management Has Found That Every 3% Increase in the Selling