12.07.2022 - 04:54

# Julie sells homemade designer cookies. The marginal cost of producing a cookie depends on how many cookies Julie produces and is given by the formula, MC = 1.2Q. Thus, the first cookie Julie produces

Question:

Julie sells homemade designer cookies. The marginal cost of producing a cookie depends on how many cookies Julie produces and is given by the formula, MC = 1.2Q. Thus, the first cookie Julie produces has a marginal cost of $1.20, the second has a marginal cost of$2.40, and so on. Assume that the designer cookie industry is perfectly competitive, and Julie can sell as many or as few cookies as she likes at the market price of $12. A) What is Julie’s marginal revenue from selling another cookie? Express your answer as an equation. B) Determine how many cookies Julie should produce is she wants to maximize profit. C) How much profit will she make at this output level (assume fixed costs are zero)? D) If {eq}TC = 0.6Q^{2} {/eq}, can you write an equation for Julie’s total variable cost, average variable cost, and average total cost? E) Graph Julie’s MC, MR, and ATC, with dollars per quantity on the y-axis and quantity of cookies on the x-axis. Label her profit-maximizing level of output. Shade in the area that represents her TR and the area that shows her TC. Answers (1) • April 15, 2023 в 05:33 A) Julie's marginal revenue from selling another cookie is equal to the market price of$12, as she is operating in a perfectly competitive market. Therefore, the equation for Julie's marginal revenue is MR = 12. B) To maximize profit, Julie should produce where marginal cost equals marginal revenue. So, set MC = MR and solve for Q: 1.2Q = 12 Q = 10 Therefore, Julie should produce 10 cookies to maximize profit. C) To calculate profit, we need to know total revenue and total cost. Total revenue is price times quantity, so: TR = $12 x 10 =$120 Total variable cost is the sum of all marginal costs up to the level of production, which is: TVC = 1.2(1) + 1.2(2) +...+ 1.2(10) = $66 Total cost is the sum of total variable cost and any fixed costs, but in this case, fixed costs are assumed to be zero. So: TC = TVC =$66 Profit is total revenue minus total cost, or: Profit = TR - TC = $120 -$66 = $54 Therefore, Julie will make a profit of$54 at the profit-maximizing level of output. D) Total variable cost can be found by subtracting any fixed costs from total cost, so in this case, TVC = TC. Therefore, TVC = 0.6Q^2. Average variable cost can be found by dividing total variable cost by the quantity produced, so: AVC = TVC/Q = 0.6Q Average total cost is the sum of average variable cost and any fixed costs, but again, fixed costs are assumed to be zero. Therefore, ATC = AVC = 0.6Q. E) See attached graph. The blue line represents Julie's marginal cost (MC) curve, which starts at $1.20 for the first cookie and increases by$1.20 for each additional cookie. The red line represents her marginal revenue (MR) curve, which is constant at $12 regardless of the quantity of cookies produced. The green line represents her average total cost (ATC) curve, which starts high due to the fixed costs assumed to be zero, but decreases with increased production due to the spread of fixed costs over more units. The profit-maximizing level of output is 10 cookies, where MC = MR. This point is labeled as "Profit Max." The shaded area labeled "TR" represents total revenue, which is$120 at the profit-maximizing level of output. The shaded area labeled "TC" represents total variable cost, which is \$66 at the profit-maximizing level of output. Overall, the graph shows that Julie is making a profit at the profit-maximizing level of output, because total revenue (TR) exceeds total variable cost (TVC).