Final answer:
The optimal advertising-to-sales ratio for the firm is 0.08 or 8%, and the profit-maximizing level of advertising is $2,400 based on the given elasticities and revenue.
Step-by-step explanation:
To determine the optimal advertising-to-sales ratio, one would typically use the Dorfman-Steiner theorem, which states that the optimal advertising-to-sales ratio is equal to the advertising elasticity of demand divided by the absolute value of the price elasticity of demand. In this case, the formula would be:
Optimal Advertising-to-Sales Ratio = Advertising Elasticity of Demand / |Price Elasticity of Demand|
Given that the advertising elasticity of demand is 0.32 and the price elasticity of demand is -4, the calculation is as follows:
Optimal Advertising-to-Sales Ratio = 0.32 / |-4| = 0.32 / 4 = 0.08
The optimal advertising-to-sales ratio for the firm's product is therefore 0.08, or 8%.
To find the profit-maximizing level of advertising expense, we multiply the optimal advertising-to-sales ratio by the firm's revenues:
Profit-Maximizing Advertising = Optimal Advertising-to-Sales Ratio x Firm's Revenues
Profit-Maximizing Advertising = 0.08 x $30,000 = $2,400
The firm's profit-maximizing level of advertising is $2,400.