Question

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 number 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). 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. Calculate the total profit earned by the park. (Copy the values from the spreadsheet in part a). c. Now suppose the manager uses two-part pricing with a per-ride price equal to marginal cost and a profit-maximizing entry fee. Determine the price per ride, the number of rides, and the total profit (including profit from ticket sales and the entry fee) in this case.

Answer 1

(a) p=25-Q/2

TR= p*Q= 25Q-Q^2/2, hence MR= 25- Q

TC= 20+5Q, MC=5, hence at MR=MC, Q=20, P=15, MR=5, TR= 300 and CS= 150, profit= 300-120=180

(b) Price per ride= 15, and let entry fee be E,

Now, we will have E+ 15= 25-Q/2 (The total price is 15+Entry fee), hence the new equation is 10-Q/2

Upon maximising TR, we get Q=5, E=7.5 and Total Profit = 22.5*5- 45= 67.5

(c) Use the same approach, MC=5 be the price per ride, hence E+5= 25-Q/2, which gives E=20-Q/2

Maximise TR to get final answer. MR= 20-Q, Q=15 and E= 12.5, TR= (12.5+ 5)*15= 262.5 and TC= 20+ 5(15)= 95, Profit= 167.5

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