Final answer:
To find the optimal output, you need to differentiate the profit function with respect to quantity and set it equal to zero. By taking the derivative of the total cost function, setting the marginal cost equal to the price, you can find the optimal output quantity.
Step-by-step explanation:
Based on the total revenue and total cost curves, a firm can calculate the quantity of output that will provide the highest level of profit. One way to determine the most profitable quantity is to see at what quantity total revenue exceeds total cost by the largest amount.
In this case, the firm's total cost function is given by TC=50+3Q+2Q², and the price of the product is $31. To find the optimal output, we need to find the quantity that maximizes profit by subtracting the total cost from the total revenue.
To find the optimal output, we need to find the quantity that maximizes profit by subtracting the total cost from the total revenue. The formula for profit is given by Profit = TR - TC. We can find the optimal output by finding the quantity at which profit is maximized.
To find the optimal output, we need to differentiate the profit function with respect to quantity and set it equal to zero. By taking the derivative of the total cost function, we can find the marginal cost function, which represents the change in total cost as output changes. Setting the marginal cost equal to the price, we can solve for the optimal output quantity. In this case, the optimal quantity is the output level at which the marginal cost equals the price.