Final answer:
To calculate the new level of sales on a soy farm when profits decrease given the degree of operating leverage, determine the percentage change in profits and apply it using the provided DOL. For the student's farm, a decrease in profits from $2.4 million to $2.1 million with a DOL of 2.8 leads to new sales of approximately $4.68 million.
Step-by-step explanation:
The question involves a scenario where a student has a soy farm with expected profits and sales under normal economic conditions and wishes to find out what the sales would be if the profits were different, given the degree of operating leverage. To solve this, we need to understand the degree of operating leverage (DOL), which indicates the percentage change in operating income relative to a percentage change in sales. It can be calculated using the formula: DOL = Percentage Change in EBIT (Earnings Before Interest and Taxes) / Percentage Change in Sales. Since the student has provided the DOL, we can rearrange the formula to solve for the new level of sales. This question also encompasses the understanding of economic principles such as revenue, costs and profit maximization in a perfectly competitive firm. The objective is to identify the quantity at which the profit maximization occurs, which is when the marginal cost equals the marginal revenue.
If the student's soy farm has a degree of operating leverage of 2.8 and the profits decrease from $2.4 million to $2.1 million, we first determine the percentage change in profits, which is (2.1 - 2.4) / 2.4 = -12.5%. Given the DOL of 2.8, the percentage decrease in sales is -12.5% / 2.8 = -4.46%. If the original sales were $4.9 million, then a decrease of 4.46% implies the new sales figure would be 95.54% of $4.9 million, which is approximately $4.68 million.