(Screening Problem) A monopolist decides both the price p and the quality q of the producthe sells. Each buyer buys exactly one unit, but buyers vary in terms of their preferences forquality. There are two types of buyers: high-type with utility functions UH (q, t) = 2/q-pand low-type with utility function U (q, t) = vq – p. Let the probability of drawing ahigh-type buyer is 0.2. The cost of production for quality level q is just q (i.e., c(q) =q). The monopolist attempts to maximize his revenue by offering a menu of contracts{(qL, PL), (qH, PH)}. Find the optimal screening contract for the monopolist.%3D

Screening is a method by means of which a single entity acquires and examines details in an attempt…

(Screening Problem) A monopolist decides both the price p and the quality q of the product he sells. Each buyer buys exactly one unit, but buyers vary in terms of their preferences for quality. There are two types of buyers: high-type with utility functions UH (q, t) = 2√q-p and low-type with utility function UL (q,t) = √9 - p. Let the probability of drawing a high-type buyer is 0.2. The cost of production for quality level q is just q (i.e., c(q) = q). The monopolist attempts to maximize his revenue by offering a menu of contracts {(9L.PL), (9H,PH)}. Find the optimal screening contract for the monopolist.

(Screening Problem) A monopolist decides both the price p and the quality q of the product he sells. Each buyer buys exactly one unit, but buyers vary in terms of their preferences for quality. There are two types of buyers: high-type with utility functions UH (q, t) = 2√q-p and low-type with utility function UL (q,t) = √9 - p. Let the probability of drawing a high-type buyer is 0.2. The cost of production for quality level q is just q (i.e., c(q) = q). The monopolist attempts to maximize his revenue by offering a menu of contracts {(9L.PL), (9H,PH)}. Find the optimal screening contract for the monopolist.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter16: Bargaining

Section: Chapter Questions

Problem 16.1IP

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Suppose that Pokhara manages to hire an even better (and still costless) market research team, allowing Pokhara to acquire even finer information about consumers' valuations. It can now tell whether a consumer's valu- ation v belongs to either of Groups 1, 2 or 3 with valuations within the intervals [0,1/3], (1/3,2/3], or (2/3, 1] respectively. As such, Pokhara can respectively charge p₁, p2 and p3 separately to these three groups of con- sumers. h. i. Write down Pokhara's profit maximization problem for each group of consumers. Derive the optimal prices for each group pi", p2" and p**. (Hint: note that for each group, the firm can at most has a demand of 1/3.) Following [h], write down Pokhara's profit ***, consumer surplus CS*** and total surplus W*** when it can set group-based prices to three groups. 2 j. Compare your results in [c], [f] and [i] and explain the im- pact of Pokhara having more precise consumer information on prof- its, consumer surplus and total welfare. (i.e., does…
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Question about HOTELLING MODEL Two burrito shops at either end of a one-mile road. The road has a uniform distribution of customers along it. People's reservation price for burrito is $10.00, The disutility that people get from walking is $5.00 per mile. If the vendors charge $8.00 for a burrito, what proportion of people on the road will buy a burrito (answer should be number between 0 and 1)? Could you also provide formulas that you used? Answer:
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