Final answer:
The profit-maximizing quantity for a monopolist is determined by finding where marginal revenue (MR) equals marginal cost (MC). Total revenue is maximized at the level of output where marginal revenue is zero. Calculation of profits involves deducting total costs from total revenue at the profit-maximizing output.
Step-by-step explanation:
The question pertains to the determination of elasticity (e) and the quantity (q) at which total revenue is maximized for a demand function in the context of a monopolist's decision-making process. According to the provided information, a monopolist undergoes a three-step process to choose the profit-maximizing output level, set prices, and determine total revenue, total cost, and profit.
This involves calculating total revenue using the demand curve, then determining the marginal revenue (MR) curve, and finding the point where MR equals marginal cost (MC) to maximize profits.
Without specific data on actual demand and cost functions, a generic approach to determine the profit-maximizing quantity is to identify the level of output where MR=MC. For total revenue to be maximized, one needs to find the highest point on the total revenue curve or when marginal revenue is zero, indicating that further increases in output would not increase total revenue.
In the context of the problem for Andrea's Day Spa, one would calculate total revenue by multiplying the price with the quantity sold for each output level. Marginal revenue is the change in total revenue from selling an additional unit, while marginal cost is the change in total costs from producing an additional unit.
Average cost is the total cost divided by the quantity produced. The profit-maximizing output is where marginal revenue is equal to marginal cost. Profits are then determined by subtracting total costs from total revenue at this output level.