Question

Please show formulas

Anil is planning a birthday party at an amusement park for his young daughter and her friends. The manager of the park is considering whether to use uniform pricing or two-part-pricing. Anil's willingness to pay for rides for the party is p 25-0.5Q where p is the ticket price per ride and Q is the num ber of rides. The amusement park has a marginal cost of $5. its fixed cost for handling the party is $20. MR-25-Q: CS-0.5"(25-p)"Q a. Fill in the spreadsheet's cells for p, CS, R, MR, C, MC and profit. If the manager uses uniform pricing, what is the profit- maximizing ticket price per ride, the number of rides, and the profit earned by the park? (Indicate this by highlighting the row) MR CS MC profit 10 15 20 25 30 35 40 45 50 b. Suppose that the manager uses two-part pricing: an entry fee for the entire party and a price per ride. Calculate the profit- maximizing entry fee if the price per ride is the same as the monopoly price that you determined in part a. Review slide 22 in Chapter 10 on the Powerpoint I provided to determine how to find the entry fee. Calculate the total profit earned by the park. (Copy the values from the spreadsheet in part a) Profit-maximizing entry fee Total profit earned by the park:

Answer 1

Suppose a person A plans a birthday party at an amusement park. The manager decides between charging uniform pricing or two-part pricing. The willingness to pay of person A for rides is, p 25-0.5Q The marginal cost (MC) is $5 and fixed cost is $20. The MR and CS functions are given as follows MR 25-Q CS 0.5 (25-p)*Q a. The spreadsheet cells are filled as follows: B E A C D G H MC Profit -D2-F2 D3-F3 -D4 - F4 -D5 -F5 -D6 - F6 -D7 - F - D8 - F8 - D9 - F9 D10-F10 |-D11-F11 MR -25-A2| - 20+5*(A2) 5 - 25-A3 | - 20+5*(A3) 5 - 25-A4| - 20+5*(A4) 5 - 25-A5 - 20+5*(A5) 5 - 25- A6 - 20+5*(A6) 5 =25-A7- 20+5*(A7) 5 - 25- A8 - 20+5*(A8) 5 - 25-A9 - 20+5*(A9) 5 1 Q 2 525-0.5*(A2)0.5*(25-B2) A2 3 10-25-0.5*(A3)0.5*(25-B3)*A3 4 15 25-0.5*(A4)0.5*(25-B4) A4 5 20-25-0.5*(A5)0.5*(25-B5)*A5 6 25 25-0.5*(A6) 0.5*(25-B6)*A6 7 30-25-0.5*(A7) 0.5*(25-B7)*A7 8 35 25-0.5 (A8) 0.5*(25-B8)*A8 9 4025-0.5*(A9) 0.5*(25-B9)*A9 P CS C - A2*B2 =A3*B3 -A4 *B4 -A5 *B5 -A6 *B6 A7 -A8 *B8 -A9* B9 10 4525-0.5*(A10)-0.5*(25-B10)*A10A10*B10-25-A10 - 20+5*(A10) 5 11 50-25-0.5*(A11)0.5*(25-B11) Al-Al1*B11-25-A11- 20+5*(A11)5 The filled spreadsheet is shown below A B C G H P CS R MR C MC Profit 1 22.5 6.25 5 112.5 20 45 5 67.5 2 200 10 20 25 15 70 5 130 3 56.25 262.5 15 17.5 10 95 5 167.5 4 100 20 300 5 120 5 180 5 15 156.25 312.5 12.5 145 167.5 25 6 300 170 30 10 225 -5 5 130 7 306.25 262.5 195 67.5 35 7.5 -10 5 8 200 -15 5 400 220 5 -20 40 506.25 112.5 45 2.5 -20 245 5 -132.5 10 0 625 50 0 -25 270 5 -270 11

Suppose the manager use uniform pricing. The manager decides number of rides where MR is equal to MC. The values can be seen in the above table and can be computed as follows MR MC 25 Q 5 Q= 20 The profit-maximizing ticket price per ride is, p 25-0.5(20) -25-10 =15 The profit of the park is Profit TR TC (15 x20)-(20+5x 20) = 300-120 -180 Hence, the profit-maximizing ticket price per ride is S15|, the number of rides is 20. and the profit earned is S1S0 (b) In optimal two-part pricing strategy, usage fee is equal to the marginal cost at the output level supplied and entry fee is equal to the consumer surplus monopoly price, that is, $15. Compute the entry It is given that the price-per ride is same as fee as follows 1 x20x(25-15) 2 entry fee = =x20 x10 2 - 100 Hence, the entry fee is 100

The profit will be, Profit $100+(15 x 20) - (5 x 20) 100+300-100 300 Hence, the profit is $300