SeaSide Industries currently spends 5 percent of its sales on advertising.Suppose that the elasticity of advertising for Seaside is 0.2.Determine the optimal profit margin over price (P − MC)/P.

Question

Quizplus · Accepted Answer

The optimal profit margin over price (P − MC)/P can be calculated as follows:

% Change in Quantity Demanded = Elasticity of Advertising x % Change in Advertising
% Change in Advertising = (New Advertising - Old Advertising)/Old Advertising = (x - 5)/5

As we want to maximize profits, we need to find the advertising spend that maximizes the profit margin. This is achieved when (P - MC)/P is maximized.

Using the formula for price elasticity of demand, we get:

% Change in Quantity Demanded = Elasticity of Advertising x % Change in Advertising
% Change in Quantity Demanded = 0.2 x (x - 5)/5
% Change in Quantity Demanded = (x - 5)/25

Profit margin = (P - MC)/P
Profit margin = (P - (1-0.05)P)/P
Profit margin = 0.05

Therefore, we need to choose the value of x that maximizes the expression (P - MC)/P, which is equal to 0.05.

To maximize profit margin, we want to find the value of x that makes the % change in quantity demanded equal to 0. This is achieved when:

(x - 5)/25 = 0
x - 5 = 0
x = 5

Therefore, Seaside should spend 5% of its sales on advertising to maximize its profit margin.

The optimal profit margin over price is:
(P - MC)/P = 0.05
(1 - MC/P) = 0.05
MC/P = 0.95
(P - MC)/P = (P - 0.95P)/P = 0.05 = 5%

Hence, the correct choice is C.

SeaSide Industries Currently Spends 5 Percent of Its Sales on Advertising.Suppose