Question

1. Profit maximization Suppose Hannah 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 Hannah in giving haircuts is her time. As she gives more haircuts, Hannah 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. Hannah's clients are a varied group willing to pay between $18.00 and $30.00 for a haircut. Assume that Hannah cannot charge her varied clients different prices. If Hannah charges $30.00 per haircut, she can have one client per week; if she charges $27.00, she can have two; if she charges $24.00, three, and so forth. The following table contains data for the revenues and costs of Hannah's haircut business as a function of her price-quantity choice. (The costs are based on the value of Hannah's alternative activities, in dollar terms. For example, the total cost of the first haircut is $4.00—the value to Hannah of being able to read the paper after breakfast.) Also, marginal profit is the additional profit Hannah 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 production causes total profit to fall. Fill in the missing cells of the table and then use them to answer the questions that follow.

Answer 1

(1) When Quantity (Q) = 4,

(a) Total revenue (TR) = Price x Q = 21 x 4 = 84

(b) Marginal revenue (MR) = change in TR / change in Q = (84 - 72) / (4 - 3) = 12/1 = 12

(c) Marginal cost (MC) = change in TC / change in Q = (35 - 18) / (4 - 3) = 17/1 = 17

(d) Profit = TR - TC = 84 - 35 = 49

(e) Marginal profit = change in profit / change in Q = (49 - 54) / (4 - 3) = - 5/1 = - 5

(2)

COST, REVENUE, AND PROFIT (Dollars per week) 100 Total Revenue Total Cost Profit 2 3 4 5 OUTPUT (Haircuts per weekl Help Clear All

(3)

MC AND MR (Dollars per week) Marginal Revenue O Marginal Cost 1 2 3 4 5 OUTPUT (Haircuts per week) Help Clear All

(4) Hanna maximizes profit by serving 3 haircuts (when MR > MC) by charging $24.

(5) If she gives more haircuts (Q > 3), following is true:

- Marginal profit is negative

- Marginal revenue is less than marginal cost

- Total profit will decline from optimal