lai_146_sp13_ps5key - ECO 146 Applied Microeconomics Spring...

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ECO 146 Ernest Lai Applied Microeconomics Problem Set 5 Solution Spring 2013 Remark: This solution is meant to be a learning tool for you. It may be more comprehensive than what you need in order to get full credit. 1. A monopolist sells music CDs. It has a constant marginal and average cost of $20. It faces two groups of potential customers: honest and dishonest customers. The hon- est customers’ demand function for music CDs is Q h = 120 - p h , and the dishonest customers’ demand function is Q d = 120 - p d . (a) Given that the marginal cost is constant and equal to the average cost, does the monopolist incur any fixed cost? Explain. (b) Suppose it is not possible for the dishonest customers to steal the music so that both groups of customers are willing to buy the CDs from the monopolist. i. What will be the monopolist’s profit-maximizing output and price? ii. What are the consumer surplus, producer surplus (profit of the monopolist) and total surplus? (c) Suppose now the dishonest customers can pirate the music, and thus they are no longer willing to buy the CDs from the monopolist. i. What will be the monopolist’s profit-maximizing output and price? ii. Suppose the dishonest customers, who are now burning the music onto CD-Rs, have to pay $20 for a CD-R. How many pirated copies of the music CD they will have? iii. How will the consumer surplus (of both groups of consumers), producer surplus (profit of the monopolist) and total surplus change when piracy occurs? (a) Given that the marginal cost is constant at 20, the total variable cost of producing q unit is 20 q . Thus, the total cost is 20 q + F , where F is the fixed cost. This also implies that the average cost is 20+ F 20 . But given that the average cost is constant at 20, 20 + F 20 = 20 implies that F = 0. So, there is no fixed cost. Alternatively, we can argue that when the marginal cost is constant it is also the same as the average variable cost; given that average cost = average variable cost + average fixed cost and the marginal cost here is the same as the average cost, the average fixed cost, and thus the fixed cost, must be zero. [0.2] (b) i. If the monopolist is selling to both groups of customers, it will face a market demand which is the horizontal sum of the demands from the two groups: Q = (120 - p ) + (120 - p ) = 240 - 2 p . The inverse demand is p = 120 - Q 2 , and 1 https://www.coursehero.com/file/11504266/lai146sp13ps5key/ This study resource was shared via CourseHero.com
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the monopolist’s revenue is R ( Q ) = (120 - Q 2 ) Q . Taking the derivative, we find that its marginal revenue is MR ( Q ) = 120 - Q . Equating the marginal revenue with marginal cost, which is 20, we have 120 - Q = 20 Q * = 100. With profit- maximizing output at 100, the monopolist will charge p * = 120 - 100 2 = 70.
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