Question

1. Profit maximization

Suppose Frances gives haircuts on Saturdays to make extra money. She is the only person in town cutting hair on Saturdays. and therefore has some market power. Assume that she does not incur fixed costs, and the only significant variable cost to Frances in giving haircuts is her time. As she gives more haircuts, Frances 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 half-hour, and so on.

Frances's clients are a varied group willing to pay between $16.00 and $28.00 for a haircut. Assume that Frances cannot charge her varied clients different prices. If Frances charges $28.00 per haircut, she can have one client per week; if she charges $25.00, she can have two; if she charges $22.00, three, and so forth. The following table contains data for the revenues and costs of Frances's haircut business as a function of her price-quantity choice. (The costs are based on the value of Frances's alternative activities, in dollar terms. For example, the total cost of the first haircut is $4.00-the value to Frances of being able to read the paper after breakfast.) Also, marginal profit is the additional profit Frances eams 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 production causes total profit to fall.

Fill in the missing cells of the table and then use them to answer the questions that follow.

On the following graph, use the blue points (circle symbols) to plot Frances's total revenue curve, use the orange points (square symbols) to piot her total cost curve, and use the purple points (diamond symbols) to plot her total profit curve. Be sure to graph from left to right, starting with zero haircuts and ending with five. Line segments will automatically connect the points.

Frances maximizes her profit by serving _______  per week and charging _______  per haircut.

If Frances gave more haircuts than her optimal quantity of haircuts, which of the following statements would be true? Check all that apply.

• Frances's marginal profit (marginal revenue minus marginal cost) from giving another haircut would be negative.

• Frances's total profit from giving haircuts (total revenue minus total cost) would decline from the amount at the optimal quantity.

• Frances's marginal revenue would be less than her marginal cost of giving a haircut.

Answer 1

Refer the attached picture below

24 QP TR MR TC MC Profit Marginal Profit To - -|- 0 -| - 1 28 28 28 4 4 | 24 2 25 50 22 8 4 42 18 3 22 66 16 13 5 4 19 76 10 18 5 5 16 80 4 25 7 55 53 58

Refer the attached picture

0 1 5 2 — 3 — 4 Profit G TR TC Profit

Frances maximizes her profit by serving 4 customers per week and charging $ 19 per haircut.

When she gives more haircut than the optimal then the total profit declines and the marginal profit becomes negative that is the marginal cost increases. Her marginal revenue is $4 and MC is $7 thus mr is less than MC.

All are correct. Refer the table for clarification.

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