Final answer:
In a perfectly competitive market, firms maximize profit by producing at the quantity where price equals marginal cost. Profit maximization occurs where the gap between total revenue and total cost is the widest. Madison's pop-up shop should follow the rule of producing where P=MC for maximum profitability.
Step-by-step explanation:
In a perfectly competitive market structure, firms maximize profits by producing at the quantity where price (P) equals marginal cost (MC). Profit is calculated as the difference between total revenue (TR) and total cost (TC). Total revenue is found by multiplying the price per unit by the quantity sold, and the profit-maximizing quantity is where this revenue is largest after covering total costs. The firm will continue to produce as long as price covers average variable costs even if it is making a loss because shutting down would mean a loss equal to total fixed costs.
For Madison's handicraft pop-up shop, the total revenue curve would be a straight line starting from the origin with a slope equal to the price, as the price is constant in a perfectly competitive market. The total cost curve is likely to have a curvature due to diminishing marginal returns at higher levels of output. The maximum profit Madison can achieve is at the output level where the gap between the total revenue and total cost is the widest.
The rule for profit maximization in perfectly competitive markets where firms are price takers is to produce at the quantity where P=MC, since the marginal revenue is equal to the price.