Homework 7: Price Discrimination

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Homework 7: Price Discrimination (to be handed in on Tuesday 6th April)

  1. Suppose a firm can perfectly price discriminate. What is the lowest price it will charge, and what will its total output be? (1 point)

When a firm can perfectly price discriminate, it will sell each unit at each consumer’s reservation price. Thus, marginal revenue is simply the price of the last unit sold. Firms maximize profits my setting MR=MC, so the monopolist will produce up to where its MC crosses the demand curve. Thus, the lowest price is where P = MC, and the firm will produce the competitive level of output.

  1. When pricing automobiles, American car companies typically charge a much higher percentage mark-up over cost for “luxury operation” items such as leather trim, etc., than for the car itself or for more “basic” options such as power steering and automatic transmission. Explain why. (1 point)

This is an example of third degree price discrimination, where we assume that the cost of production car options is a function of the total number of options produced and the production of each type of options affects costs in the same way. The higher price is charged for the package with the lower elasticity of demand. Thus, this pricing can be explained if the “luxury” options are purchased by consumers with low elasticities of demand relative to consumers of more “basic” packages.

  1. Price discrimination requires the ability to sort customers and the ability to prevent arbitrage. Explain how the following can function as price discrimination and discuss both “sorting” and “arbitrage” in your answer. (3 points)

  1. Requiring airlines travelers to spend at least one Saturday night away from home to qualify for a low fare: this separates business travelers from vacation travelers. Arbitrage is not possible when the ticket specifies the traveler’s name.

  1. Insisting on delivering cement to buyers and basing prices on buyers’ locations: by pricing on location, customers are sorted by their geography. Prices may then include transportation charges which could be significant given the bulkiness of cement (so will not arbitrage). Plants used “based-point-price” systems where all firms use the same base point and calculate transportation charges from this base point. Individual consumers are then charged the same price.

  1. Charging high-income patients more than low-income patients for plastic surgery: one strategy to separate high income from low income is to charge a high price initially, and then negotiate. Many insurance policies do not cover elective surgery. Note since plastic surgery cannot be transferred, arbitrage is not a problem!

  1. A monopolist is deciding how to allocate output between two markets. The two markets are separated geographically (East Coast and Midwest). The monopolist’s total cost is TC = 5 + 3(Qa + Qb), and thus, MC = 3. The monopolist’s demand and marginal revenue for the two markets are as follows below. Calculate the monopolist’s price, output, profit and the deadweight loss to society if s/he can price discriminate. (2 points)

Pa = 15 – Qa; MRa = 15-2Qa

Pb = 25 – 2Qb; MRb = 25 – 4Qb
15 – 2Qa = 3, Qa = 6, Pa = $9

25 – 4Qb = 3, Qb = 5.5, Pb = $14

Profit = TR – TC = (9*6) + (14*5.5) – [5 + 3(6+5.5)] = 131 – 39.5 = $91.50
In perfect competition, the firm would price at marginal cost. In market a, Pa = 3, Qa = 12. In market b, Qb = 11. DWL = 0.5*(Qc – Qm)(Pm – Pc).
In market a, DWLa = 0.5*(12 – 6)(9 – 3) = $18. In market b, DWLb = 0.5*(11 - 5.5)(14 – 3) = $30.25. Total DWL = $48.25

  1. Many retail video stores offer two alternative plans for renting films:

  • Two-Part Tariff: pay an annual membership fee (e.g. $40) and then pay a small fee per film rented (e.g. $2 per film per day)

  • Straight rental fee: pay no membership fee but pay a higher daily rental fee (e.g. $4 per film).

Why do you think the store might offer the two-part tariff? Why offer customers a choice rather than merely offering the two-part tariff? (1.5 points)
By using this strategy, the firm allows customers to sort themselves into two groups: high-volume who rent many films per year and low-volume who rent only a few films per year (less than 20). If only the two-part tariff is used, the firm has the problem of determining the profit-maximizing entry and rental fees with many different consumers. I.e. a high entry fee discourages low-volume consumers; a low entry fee with a high rental fee encourages membership but discourages high-volume consumers from joining. Instead of forcing customers to pay both an entry and rental fee, the firm effectively charges two different prices to two different types of consumers.

  1. Sal’s satellite company broadcasts TV to subscribers in Los Angeles and New York. The demand and marginal revenue are below. The TC of providing Q units of service is given by TC = 1000 + 30Q, and MC = 30. What are the profit maximizing prices and quantities for the New York and Los Angeles markets? What would happen if people in LA were able to receive Sal’s NY broadcasts and vice versa due to a new improved satellite? (1.5 points)

Pny = 150 - 3Qny MRny = 150-6Qny

Pla = 120 – 3/2Qla MRla = 120 – 3Qla
New York: 150 – 6Qny =-30; Qny= 20, Pny = $90

Los Angeles: 120 – 3Qla = 30; Qla = 30, Pla = $75

If people in LA could receive the broadcasts, and vice versa, then there would be no basis for price discrimination as the two markets could no longer be separated.

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