11. Profit maximization using total cost and total revenue curves

Suppose Rian operates a handicraft pop-up retail shop that sells cardigans. Assume a perfectly competitive market structure for cardigans with a market price equal to $20 per cardigan.

The following graph shows Rian's total cost curve.

Use the blue points (circle symbol) to plot total revenue and the green points (triangle symbol) to plot profit for cardigans for quantities zero through seven (including zero and seven) that Rian produces.

Total RevenueProfit0123456782001751501251007550250-25TOTAL COST AND REVENUE (Dollars)QUANTITY (Cardigans)Total Cost

Calculate Rian's marginal revenue and marginal cost for the first seven cardigans they produce, and plot them on the following graph. Use the blue points (circle symbol) to plot marginal revenue and the orange points (square symbol) to plot marginal cost at each quantity.

Marginal RevenueMarginal Cost0123456784035302520151050COSTS AND REVENUE (Dollars per cardigan)QUANTITY (Cardigans)

Rian's profit is maximized when they produce a total of

cardigans. At this quantity, the marginal cost of the final cardigan they produce is

, an amount less than the price received for each cardigan they sell. At this point, the marginal cost of producing one more cardigan (the first cardigan beyond the profit maximizing quantity) is

, an amount greater than the price received for each cardigan they sell. Therefore, Rian's profit-maximizing quantity occurs at the point of intersection between themarginal cost and marginal revenue curves. Because Rian is a price taker, the previous condition is equivalent to P=MC

.

Calculate Rian's marginal revenue and marginal cost for the first seven cardigans they produce, and plot them on the following graph. Use the blue points (circle symbol) to plot marginal revenue and the orange points (square symbol) to plot marginal cost at each quantity. 40 O 35 Marginal Revenue 30 25 Marginal Cost COSTS AND REVENUE (Dollars per cardigan) 20 15 10 5 0 0 1 2 3 4 5 6 7 8U 9 Lu 20 3 2 Lu 5 15 D! D z