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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.

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Jarrod Robel
Jarrod RobelLv2
17 Dec 2019
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Related questions

Suppose you are the proprietor of the only bar in Dallas. Since you are the only place in town for people to get drinks you exercise some market power and face a downward sloping demand curve for drinks given by P = 10 - (3/2)Q for each individual. Your total costs are given by TC = Q. There are 100 individuals with identical demand.

  1. Assuming that you must follow a uniform pricing strategy, what is the profit maximizing price and quantity and the associated profit? What is consumer surplus? Is the market efficient?
  2. If each person is charged their reservation price, what type of price discrimination is this? Assuming you can engage in this pricing scheme, what is your profit maximizing price and quantity and the associated profit? What is consumer surplus? Is the market efficient?
  3. Now assume that you decide to try a two-part tariff scheme instead, charging a price per drink and a cover charge at the door. What is the optimal two-part tariff charged to each person? How many drinks will be sold to each person? What is your total profit associated with this scheme? What is the total consumer surplus? Is the market efficient?
  4. Assume that your clientele is composed of two types: 50 customers are heavy drinkers with individual demand described by P_H = 15 - Q_H and 50 customers are light drinkers with individual demand described by P_L = 10 -3Q_L. Which group would you rather charge a higher price? Why?
  5. Assume that the market is split as described before. There is no constraint on the number of drinks you can sell. You can charge a different price to each group. What is the optimal price and corresponding quantity for each segment of the market? What is your total profit under this scheme? What type of price discrimination is this?
  6. Assume that the market is split as described before. The city of Dallas tells you that can only sell 325 drinks in total. You can charge a different price to each group. What is the optimal price and corresponding quantity for each segment of the market? What is your total profit under this scheme?

EZ Sharp Industries, Inc., manufactures the Kleen Edge(TM) line of diamond-abrasive cutlery sharpeners for home use. EZ Sharp holds a patent on its unique design and can earn substantial economic profit if it prices its Kleen Edge(TM) products wisely. EZ Sharp sells two models of its Kleen Edge(TM) sharpeners: The Classic, which is the entry-level model, and the Professional, which has a sonic sensor that controls the speed of the sharpening wheels.

Short run production of sharpeners is subject to constant costs: AVC = SMC for both models. The constant costs of production at EZ Sharp Industries are estimated to be:

$20.00 = AVCc = SMCc

$30.00 = AVCp = SMCp

Where

AVCc and SMCc are constant cost for the classic model and

AVCp and SMCp are constant costs for the professional model

Total fixed costs each month are $10,000. The sole owner of EZ Sharp also manages the firm and makes all pricing decisions. The owner-manager believes in assuring himself a 200% profit margin by using the cost-plus pricing methodology to set prices for his two product lines. At these prices, EZ Sharp is selling 3,750 units of Classic model per month and 2,000 units of the Professional model per month.

a. Using the cost-plus technique, compute the prices the owner-manager charges for the Classic and the Professional models, based on his required 200% profit margin.

b. How much profit is EZ Sharp earning each month using the cost-plus prices in part a? The owner-manager is ready to sell the firm, but he knows the value of the firm will increase if he can increase the monthly profit somehow. He decides to hire Andrews Consulting to recommend ways for EZ Sharp to increase its profits. Andrew reports that production is efficient, but pricing can be improved. Andrews argues a new pricing plan based on optimal pricing techniques (i.e., the MR = MC rule).

To implement the MR = MC methodology, Andrews undertakes a statistical study to estimate the demands for two Kleen Edge (TM) products. The estimated demands are:

Qc = 6,000 – 75Pc + 25 Pp

Qp = 5,000 – 50Pp + 25Pc

Where QC and QP are the monthly quantities demanded of Classic and Professional models, respectively, and PC and PP are prices of Classic and Professional models, respectively. Andrews Consulting solved the demand equations simultaneously to get the following inverse demand functions, which is why Anderson gets paid the “big bucks”:

Pc = 136-0.016Qc -0.008Qp

Ps = 168 -0.008Qc -0.024Qp

c. Find the two marginal revenue functions for the Classic and Professional model sharpeners.

d. Set each marginal revenue function in part c equal to the appropriate cost and solve for the profit-maximizing quantities.

e. Using the results from part d, what prices will Andrews Consulting recommend for each model?

f. When the owner-manager sees the prices recommended by Andrews Consulting, he brags about how close his simple cost-plus pricing method had come to their suggested prices. Compute the profit EZ Sharp can earn using the consultants’ prices in part d. Is there any reason for the owner-manager to brag about his cost-plus pricing skills?

Assume that KPM's demand function for coffee is: Q = 1 - p, where p is the price of a cup of espresso.

a) Assume that the marginal cost of a cup of coffee is 10 cents. Assume that the seller can use a two-part tariff coffee purchasing plan (where the plan has a price per cup and an entry fee). Concretely, the amount of money that consumer spends on X cups of the espresso is given by T = F + p*X, where F is the entry fee in dollars. Under that plan, what is the profit-maximizing price of a cup of coffee? How many cups will KPM drink? What is the maximum entry fee that the seller can charge KPM to participate in the plan? [Hint: Use the fact that entry fee should extract consumer's surplus, when possible. Consumer surplus is the area of the triangle above the equilibrium price and the price at which demand equals zero. Given the demand function, that price is equal to p^=1.]

b) Assume that CAD's demand for coffee is given by Z = 0.5 - p.
What is the profit-maximizing plan (price plus entry fee) that the seller can charge CAD? How many cups of coffee will CAD drink under the plan designed for them?

c) Assume that the seller cannot differentiate between CAD and KPM. In such a situation, would you expect that KPM will purchase under the plan designed for them? (as in point (a), above) or under the plan designed for CAD (as in point (b), above).

d) What can the seller do to make CAD's plan unattractive to KPM? In answering this question discuss the following ideas: (i)participation constraint; (ii) self-selection or individual rationality constraint; (iii) informational rent.

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