The Economics of Price Discrimination - Assignment Example

PRICES AND PROFITS By (Name) Course Professor’s Name University Name City, State Date of Submission Question 1 a The table below shows the monthly demand for movies for three individuals: Kat, Peeta and Primrose. Kat MB ($/unit) Sales (units/ yr) 10.00 1 8.00 2 6.00 3 2.00 4 Peeta MB ($/unit) Sales (units/ yr) 9.00 1 4.00 2 1.00 3 0.00 4 Primrose MB ($/unit) Sales (units/ yr) 7.00 1 3.00 2 0.00 3 0.00 4 Suppose the cinema has marginal cost $3. i Suppose that last month the cinema only had 2 customers: Kat and Peeta. What would have been the cinema’s profit maximizing linear price? For MR, consider the following: KAT PEETA Primrose TR MR MB ($/unit) Sales (Unit/month) TR MR MB ($/unit) Sales (Unit/month) TR MR MB ($/unit) Sales (Unit/month) 10 1 10 10 9 1 9 9 7 1 7 7 8 2 16 6 4 2 8 -1 3 2 6 -1 6 3 18 2 1 3 3 -5 0 3 0 -6 2 4 8 -10 0 4 0 -3 0 4 0 0 MR=δTR/δQ Total sales=8units Thus MR=72q/8 =9q Profit is maximized when MC=MR MC=$3 3=9q The maximizing quantity is 3 units, making the maximizing price become $3.5 ii Suppose that this month the cinema obtained an additional customer: Primrose. (Thus, this month the cinemas has 3 customers.) What would be the cinema’s new profit maximizing linear price? For additional customer, Primrose, the total revenue becomes $85 with the total units sold being 12 as shown in the table above. Thus MR=85q/12 =7.08q Profit is maximized when MC=MR MC=$3 3=7.08q The maximizing quantity is 2.36 units, making the maximizing price become $3.5 that becomes $5 from the table. iii Provide intuition for the difference in your results in parts a and b. There is a tendency of the price increment when the number of customers increase, i.e. price increasing with demand. Thus, in a, the profit maximizing price is low due to two customers compared to the b, where there are three customers. iv In the above example, does the cinema’s profit increase or decrease when Primrose joins the market? Since the marginal revenue is more than the marginal cost, but at the introduction of the third customer, Primrose, the total revenue increases, but the marginal revenue remains constant, thus the profit is increased when Primrose joins the market. v Would the addition of extra customers ever cause the firm’s profit to fall? Provide a succinct explanation. Economically, increase in customers into the market is optimally good for profit realization in the market. Basing arguments from the above analysis, the marginal revenue seems considering the consumption of the last customer. However, the total revenue, that majorly determines the profit realized in the market have an increasing attribute. Therefore, it is logical to argue that the addition of the extra customers would make the profit to increase if the total cost remains constant. b Consider the following data for three consumers. Tyrion MB ($ per unit) Sales (units a month) 24.00 1 18.00 2 12.00 3 6.00 4 0 5 Jamie MB ($ per unit) Sales (units a month) 20.00 1 14.00 2 8.00 3 2.00 4 0 5 Cersei MB ($/movie) Sales (movies/ month) 16.00 1 7.00 2 5.00 3 0.00 4 0 5 Suppose a firm sells to these two customers, and has a fixed cost of $0 and marginal cost of $4, so that total cost is TC = 4Q, where Q represents output. i Find the profit maximizing two part tariffs if the firm can conduct direct price discrimination, i.e. can identify Tyrion and Jamie and Cersei. Tyrion, TR=120 Jamie, TR=72 Cercei, TR=45 Combined=237 Making the demand equation be, 237p=q, since the fixed cost is zero According to the tables above, the price charged per unit decreases with increase in the quantities sold for each customer. The purpose of a two-part tariff is to extract more if the consumer surplus, by using a pricing scheme made of two parts: a fixed one-time fee charged to each customer and price on each unit purchased. Fixed cost= $0 MC=4 But MC=MR at profit maximization Q=15 units Then, 237p=q, P=237/15 =$15.8 ii. Suppose it is possible for the firm to restrict access to those who pay an access fee. What is the profit maximizing two part tariff if the firm must conduct indirect price discrimination (i.e. cannot identify Tyrion and Jamie and Cersei), but can tell whether they have paid the access fee? (In this case the firm can only distinguish between those who have a have not paid an access fee.) MC=4 The Marginal benefit for Tyrion and Jamie and Cersei are 60, 44, and 28 respectively. The inverse demand function for each becomes, P=60-6Q and P=44-6Q, and P=28-6P respectively. To maximize profit, the MC=MR in a two part tariff. Therefore, we first need to solve for the marginal revenue curves for each type. Since the linear inverse demand equation are shown above, the MR curves will have the same vertical intercept but twice slope. Therefore, For Tyrion, MR=60-6Q while for Jamie, MR=44-6Q, and Cersie, MR=28-6Q Since MR=MC, then 2= 60-6q, 2=44-6Q, and 2=28-6Q, leading to 9.667,7 and 4.33. For the optimal quantities above, p=60-3Q, p=44-3Q, and p=28-3Q, making the price be, 31, 23, and 15 iii. The essence of price discrimination is for the benefit of the producer in maximizing the consumer surplus in different markets. The prices are charged differently in different markets using different strategies. In some cases, like the above, firms charge each consumer’s reservation price (their maximum willingness to pay) for their product. The producer controls the access with individual consumers having similar demand curves, to a level where the marginal cost equals the price. Question 2 a Suppose a coffee shop sells coffee, cake and muffins. Further assume the firm has three customers. Customers will purchase at maximum one cup of coffee and one serve of either cake or muffin (i.e. customers may have a cake or a muffin, but not both). Each customer’s reservation price for the product given in the following table: Product Coffee Cake Muffin Customer 1 5 5 3 Customer 2 8 1 1 Customer 3 6 3 4 Customer 4 1 2 8 The firm has zero production costs. i Find the firm profit maximizing linear prices for coffee, cake and muffin. Customers are constrained to consuming 1 cup of coffee 1 serve of either cake or muffin Consider the table below: Product valuations Coffee Cake Muffin Coffee+ Cake Coffee+ Muffin Customer 1 5 5 3 10 8 Customer 2 8 1 1 9 9 Customer 3 6 3 4 9 10 Customer 4 1 2 8 3 9 This is a case where the two goods (cake and muffin) are sold differently but each is combined with coffee (no tying). For customers, 1, 2, 3, and 4, P (coffee +Cake) =10, 9, 9, 3 And P (coffee + Muffin)=8,9,10,9 clearly, the preferable price is $9 for the 2nd and the 4th customers. Thus, at zero cost of production, the firm profit maximizing linear prices for coffee, cake, and muffin are $8, $1, $1 for coffee, Cake, and Muffin respectively. ii Find the profit maximizing price when the firm enacts pure tying. In pure tying, only the two goods are sold together. There are three alternatives in this case to maximize profit; Setting the profit the firm profit maximizing linear prices for coffee, cake and muffin at i. P(coffee and either cake or muffin)=$8 Suggesting that all the consumers will buy The profit becomes 8*4=$32 ii. P(coffee and either cake or muffin)=9 In this case, only customers 2, 3, and 4 will buy while customer 1 does not buy. Profit becomes 3*9=$36 iii. P(coffee and either cake or muffin)=10 No customers will buy except customer 3. In this case, the profit becomes $10. Thus, the profit maximizing prices when the firm enacts pure tying becomes $8, $1, $1 for coffee, cakes, and muffin respectively with the profit becoming $36. iii Find the profit maximizing prices under mixed tying In mixed strategy, the products are sold two together in package as well as separately. Setting P (coffee and either cake or muffin) =$10 keeps customer 3 P (coffee and either cake or muffin) =8 extracts the maximum from customer 1, while P (coffee and either cake or muffin) =9 extracts the maximum from customers 2 and 4. Therefore, customer 1 buys coffee and cake Customer2 and 4 can buy the package of all the goods Customer 3 buys coffee and muffin iv Provide intuition for the relative profitability of the three pricing strategies. The intuition is that customers 2 and 4 have low valuation of each of the products but have higher valuation for the package while customer 1 and 3 give no extra valuation for the package and each has a high valuation for one of the products. By using mixed tying the monopolist can extract maximum surplus from consumer 2 and 4 by selling them their desired package and extract the entire surplus from consumers 1 and 3 by selling them their desired product. b. Suppose a firm has a fixed cost of $0 and marginal cost of $2, so that total cost, TC, is given by TC = 2Q, where Q represents output. Suppose it is possible to ‘bundle’ output. Further suppose a firm sells to two customers, whose marginal benefit is given in the following tables: Robert Quantity ($ per unit) MB ($ per unit) 1 13 2 9 3 6 4 1 5 0 6 0 Ned Quantity ($ per unit) MB ($ per unit) 1 7 2 4 3 3 4 2.5 5 0.5 6 0 i Find the profit maximizing bundles and their prices if the firm can identify which customer is Robert and which is Ned? If the firm can identify which customer is Ned and Robert, then it is a case of 1st degree price discrimination. If the firm can charge each person his maximum willingness to pay, then MR = price as found on the demand curve. So it would be willing to sell its products up to the point where the MC curve crosses the demand curve, i.e. where MC = price = MR. Marginal benefit is equivalent to the marginal revenue. Thus, for Robert, the MB=15, the MC=2 P(q)-Q-1(p) is the inverse function of demand. At the maximum profit, MC=MR, hence MR=2=price P (Robert) =15-6 (2) =$3 3=q-6(2) q=12-3=9units The bundle for Robert= (3, 9) For Ned, P (Ned) =6 (2)-6.5=$5.5 5.5=q-6(2) q=6.5units (5.5, 6.5) ii Find the profit maximizing bundles and prices if the firm cannot identify which customer is Robert and which is Ned? In the case where the firm cannot identify which customer is Robert and which is Ned, it is a case of second-degree price discrimination. Producer surplus= (price-MC) q MC=2 The Marginal benefit for Robert and Ned are 29 and 17 respectively. The inverse demand function for each becomes, P=29-6Q and P=17-6Q respectively. To maximize profit, the MC=MR. Therefore, we first need to solve for the marginal revenue curves for each type. Since the linear inverse demand equation are shown above, the MR curves will have the same vertical intercept but twice slope. Therefore, For Robert, MR=29-6Q while for Ned, MR=17-6Q Since MR=MC, then 2=29-6q Q=4.5units For Ned, 2=17-6q Q=2.5units For the optimal quantities above, For Robert, p=29-3Q P=29- 3(4.5) =15.5 For Ned, P=17-3(2.5) =9.5 Question 3 Suppose consumers are willing to purchase one unit of a good. However, each customer is one of two types: type H and type L. Customers types differ in their marginal benefit from quality. The marginal benefit of quality of each member of a given type is given in the following tables. A type H customer Quantity (Production costs per unit) MB ($) 1 10 2 8 3 6 4 4 5 2 6 0 A type L customer Quantity (Production costs per unit) MB ($) 1 9 2 7 3 5 4 3 5 1 6 0 One firm supplies output to all customers. a Suppose there are 100 type H customers and 15 type L customers i Find the profit maximizing varieties and their prices if the firm can identify which group a particular customer belongs to? Demand for type H customer, P=a+bq From the above table, q=6units and MB=30 and the MC=6 MC=MR at profit maximizing points. Thus, MR=MC=P=6 30=6 (q) Q=5units For 100 type H customers, then q=500 units and for 15 type L customers, q=75units P=6 ii Find the profit maximizing varieties and prices if the firm cannot identify whether a particular customer belongs to group H or group L? For type H, MR=30-6Q while for Ned, MR=25-6Q Since MR=MC, then 6=30-6q Q=4units For 100 customers, this would be 100 units For type L, 6=25-6q Q=3.167units For 15 customers, this would be 47.505 units For the optimal quantities above, For type H, p=30-3Q P=30- 3(4) =$18 For type L, P=25-3(3.167) =15.499 The price-discriminating monopolist earns more producer surplus than the single-price monopolist does. This makes intuitive sense, because a firm that segments the market can charge higher prices to more price inelastic customers and capture more of their consumer surplus. References Carroll, D and Coates, D. (2009). Teaching price discrimination: Some clarification, Southern Economic Journal,66(2), 466-480. Phlips, L. (1999). The economics of price discrimination. Cambridge [u.a.], Cambridge Univ. Press. Read More