4. Marginal analysis and profit maximization Suppose Kate gives haircuts on Saturdays to make extra money. She is the only person in town cutting hair on Saturdays, so she has some market power. Assume that she does not incur fixed costs and that the only signicant variable cost to Kate in giving haircuts is her time. As she gives more haircuts, Kate must increasingly forgo other valuable Saturday activities. For example, if she gives one haircut, she forgoes reading the paper after breakfast. If she gives two haircuts, she gives up reading the paper, sleeping an extra halfhour, and so on. Kate's clients are a varied group willing to pay between $16.00 and $28.00 for a haircut. Assume that Kate cannot price discriminatethat is, charge different clients different prices. If Kate charges $28.00 per haircut, she will have one client per week; if she charges $24.00, she will have two; if she charges $20.00, three, and so forth. The following table contains data on the revenues and costs of Kate's haircut business as a function of her price quantity choice. (The costs are based on the value of Kate's alternative activities, in dollar terms. For example, the total cost of the first haircut is $4 the value Kate places on reading the newspaper after breakfast.) Also, marginal profit is the additional profit Kate earns from producing one more unit of output. Marginal profit is positive when a rise in output increases total profit and negative when a rise in output causes total profit to fall. Fill in the missing cells of the table and then use them to answer the questions that follow. Total Marginal Output Price Revenue Revenue Total Cost Marginal Cost Profit Marginal Profit (Dollars (Haircuts per (Dollars per (Dollars per (Dollars (Dollars per (Dollars per (Dollars per per week) haircut) week) haircut) per week) haircut) week) haircut) 0 0 0 O 28.00 4.00 24.00 1 28.00 28.00 4.00 24.00 20.00 8.00 12.00 2 24.00 48.00 12.00 36.00 12.00 8.00 4.00 12.00 5 8.00 20.00 16.00 80.00 56.00 24.00 On the following graph, use the blue points (circle symbol) to plot Kate's total revenue curve, use the orange points (square symbol) to plot her total cost curve, and use the purple points (diamond symbol) to plot her total prot curve. Note: Be sure to graph from left to right, starting with zero haircuts and ending with five. Line segments will automatically connect the points. 50 O 64 Total Revenue El 48 Total Cost + 32 Prot 16 o TOTAL REVENUE, TOTAL COST, AND PROFIT (Dollars per week) QUANTITY OF OUTPUT (Haircuts per week) On the following graph, use the blue points (circle symbol) to plot Kate's marginal revenue (MR) curve, and then use the orange points (square symbol) to plot her marginal cost (MC) curve for the first five haircuts. Note: Marginal values are sometimes plotted between integers (to indicate that they represent changes incurred in moving from one integer to the next), and sometimes they are plotted directly on the integers with which they are associated. On the following graph, be sure to plot marginal values directly on the integers with which they are associated. For example, if Kate's marginal cost of increasing her production from one haircut to two haircuts is x, then you would plot a point at (2, x). Line segments will automatically connect the points. 30 O :3 25 Marginal Revenue .2 E a El a 20 U) E Marginal Cost 0 El 15 . (I) O o o z 10 at M Q n: o. 5 ' 0 I u 1 2 3 4 5 6 QUANTITY OF OUTPUT (Haircuts per week) Kate maximizes her prot by serving 7 per week and charging Y per haircut. If Kate gave more haircuts than her optimal quantity of haircuts, which of the following statements would be true? Check all that apply. C] Kate's marginal profit would be negative. B Kate's total profit (total revenue minus total cost) would decline. C] Kate's marginal revenue would be less than her marginal cost