Final answer:
The profit-maximizing output level for Kayla in a competitive market at a price of $45 is found by determining the output level at which the difference between total revenue and total cost is highest.
Step-by-step explanation:
For a profit-maximizing producer like Kayla in a competitive market, the goal is to determine the optimal level of output to maximize profits. Let's say that if the price (P) is $45, we need to find the quantity that maximizes profit. You can find the profit-maximizing output level by calculating the level of output where total revenue (price times quantity) minus total cost is at its highest. This value represents the profit gained at that output level.
Calculating the Profit at Each Output Level
For instance, at an output quantity of 5, when the total revenue exceeds the total cost by the largest amount, the profit is $40. This represents the profit-maximizing level for Kayla. When we relate this to the theoretical context of a perfectly competitive firm, like a raspberry farm example, we look for the output level where the vertical gap (representing profit) between the total revenue and total cost curves is the greatest.
In the provided scenario, maximum profits are made at an output between 70 and 80, with a profit of $90, recognizing this as the most profitable quantity. Thus, this process helps us understand how firms in competitive markets decide on their output levels to maximize profits.