Question

Janet has a $350 monthly hair budget, which she spends on haircuts (H) and hair product (P). The price of hair products is $10 per bottle, and the price of haircuts is $50 per cut. Use a separate graph for each part below and plot haircuts on the horizontal axis and hair product on the vertical axis. Label all axes, intercepts and possible kink points, and treat each case separately. a. Draw Janet's budget constraint for haircuts and hair product. (5 points) b. Draw Janet's budget constraint if now after every 3 haircuts she buys, she gets the next 1. haircut for half price. (10 points) Draw Janet's budget constraint if now after she purchases 4 haircuts, she can (and does) join a hair club. Membership in the club costs $50, but once you're a member each haircut only costs $10. (10 points) c.

Answer 1

"M = 350, P_H = 50, P_P = 10, a) B. C M = H P_H + P . P_P 350 = 50 H + 10P H rightarrow on Horizontal axis P rightarrow on vertical b) Now H > 3, for H = 4, P'_H = 25 after H = 3, M' = 350 - 50 times 3 = 200 for H = 5, 6, 7, P_H = 50. After H = 4, M' = 200 - 25 = 175 so after H = 7 M"" = 175 - 3 times 50 = 25 so buy H = 8 at P = 25 thus buy Max H = 8 or Max P = 350/10 = 35 c) H > 4, then M' = 350 - 50 times 4 = 350 - 200 = 150 after paying for club fees = 50 M"" = 100, then P'_H = 10, so max, H = 10, "