Final answer:
The optimal advertising-to-sales ratio for the firm is 0.20 or 20%. If the firm's revenues are $60,000, its profit-maximizing level of advertising would be $12,000.
Step-by-step explanation:
The elasticity of demand for a firm’s product is −1.5 and its advertising elasticity of demand is 0.3. To determine the firm’s optimal advertising-to-sales ratio, we divide the absolute value of advertising elasticity of demand by the absolute value of elasticity of demand for the firm's product. This gives us the optimal advertising-to-sales ratio as:
Advertising-to-Sales Ratio = Advertising Elasticity of Demand / |Elasticity of Demand|
Advertising-to-Sales Ratio = 0.3 / 1.5
Advertising-to-Sales Ratio = 0.20
Therefore, the optimal advertising-to-sales ratio is 0.20 or 20% when rounded to two decimal places.
For part b, if the firm’s revenues are $60,000, we multiply this revenue by the optimal advertising-to-sales ratio to find the profit-maximizing level of advertising.
Profit-Maximizing Advertising = Revenue × Advertising-to-Sales Ratio
Profit-Maximizing Advertising = $60,000 × 0.20
Profit-Maximizing Advertising = $12,000
The profit-maximizing level of advertising is $12,000.