Final answer:
A monopolist's profits can be derived by subtracting total cost from total revenue, and the profit-maximizing level of output can be found by equating marginal revenue to marginal cost. The profits at the profit-maximizing level can be calculated using the derived formula.
Step-by-step explanation:
A. To derive a general formula for the firm's profits, we need to subtract the total cost (TC) from the total revenue (TR). The general formula for profits (π) can be expressed as:
π = TR - TC
To arrive at this answer, we subtracted the quadratic equations representing total cost and total revenue. The resulting formula represents the profit as a function of quantity.
B. To find the profit-maximizing level of output, we need to equate the marginal revenue (MR) to the marginal cost (MC) and solve for the quantity. To do this, we first need to find the derivatives of the total revenue and total cost equations. At the maximum point, the derivative of total revenue will equal the derivative of the total cost.
C. Once we have determined the profit-maximizing level of output in part B, we can substitute that quantity into the profit formula derived in part A to calculate the profits at the profit-maximizing level.