Final answer:
The total revenue function for a company selling Blu-ray players at $98 each is TR = $98 × Q. Fixed costs are $262,500, and variable cost per unit is $23. To evaluate profitability, total costs are computed by combining fixed costs with the total variable costs from the produced units.
Step-by-step explanation:
Understanding the Total Revenue Function of a Company
The total revenue (TR) function of a company represents the total money received from the sale of products at a given price. In the case of the Blu-ray player manufacturer mentioned, to find the TR, we multiply the quantity of units sold (Q) by the selling price per unit (P). Therefore, the total revenue function is TR = P × Q. Given the selling price is $98 per Blu-ray player, the TR function becomes TR = $98 × Q. This function will give us the company's total revenue at different levels of output.
Total costs (TC) and profit can also be calculated; however, these are not directly part of the total revenue function. The TC includes both variable and fixed costs and is important when examining profitability. Fixed costs remain constant regardless of the number of units produced, while variable costs increase with more production.
For example, if 5 units are produced, and sold, the total revenue at this level of output would be TR = 5 × $98 = $490. However, if we factor in the total costs, profit can be calculated as Profit = TR - TC. The TC for producing 5 units would include the fixed costs plus 5 times the variable cost per unit, which is $262,500 + (5 × $23) = $262,615. So, at this level, the firm would be experiencing a loss of $262,615 - $490 = $262,125. The student's goal is to understand how changes in the quantity sold affect total revenue and identify the point at which the company makes a profit.