Answer to Question #268345 in Microeconomics for Chilu

Question

Kanoso is the sole owner of a nail salon. Her costs for a manicure are given byTC = 10 + Q2 Where TC is the Total Cost and Q is the number of manicures.The nail salon is open only 2 days a week – Tuesday and Thursday. On both days Kanoso acts as a price taker, but price is much higher on Tuesday. Specifically, P = K10 on Tuesday and P = K20 on Thursday.Calculate how many manicures Kanoso will perform on each day.Calculate Kanoso profits on each day.The National Association of Nail Salons has proposed a uniform pricing for all its members. They must always charge P=K15 to avoid the claim that consumers are being ripped off on Thursday. Should Kanoso join the association and adhere to pricing regulations? (Quantitatively justify your answer)

Answer 1

It is given that Abby is the price taker. In this situation the equilibrium is achieved at the point where the price (P) is equal to the Marginal Cost (MC)

Part a) Wednesday when price is 10

P = MC

10 = 2q

Equilibrium number of manicures by Abby on Wednesday is 5

Saturday when price is 20

P = MC

20 = 2q

Equilibrium number of manicures by Abby on Saturday is 10

Part b) Profit = Total Revenue (TR) × Total Cost (TC)

For Wednesday

TR = Price × Quantity = 10 × 5 = 50

TC = 10 + q² = 10 + (5)² = 10 + 25 = 35

Wednesday Profit = 50 – 35

Wednesday Profit = 15

For Saturday

TR = Price × Quantity = 20 × 10 = 200

TC = 10 + q² = 10 + (10)² = 10 + 100 = 110

Saturday Profit = 200 – 110

Saturday Profit = 90

Total Profit = 15 + 90 = 105

Part c) It is given that National Association of Nail Salons have fixed the price at 15

P = MC

15 = 2q

Equilibrium number of manicures by Abby is 7.5

TR = Price × Quantity = 15 × 7.5 = 112.5

TC = 10 + q² = 10 + (7.5)² = 10 + 56.25 = 66.25

Profit = 112.5 – 66.25

Profit = 46.25

Since, the total profit has declined from 105 to 46.25 so Abby should not join the Association and follow its pricing rules