Quiz 4 Ec21 S2016 Solutions.pdf

Quiz 4 Ec21 S2016 Solutions.pdf - Economics 21 Spring 2016...

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Page 1 of 6 Economics 21, Spring 2016 Prof. Luttmer Solutions to Quiz 4 1. Short Answer Questions (17 points) a. [3 points] Define “Nash equilibrium.” A Nash equilibrium is a set of actions such that, taking the actions of others as given, no player has an incentive deviate (change his/her action). Note: You need to be clear that the actions of others are taken as given, or equivalently, that it is a unilateral deviation for which there is no incentive. Some of you gave the definition of a Cournot Equilibrium. A Cournot equilibrium is a specific kind of Nash equilibrium, namely one that involves firms choosing their quantity, but I asked for the general definition of a Nash equilibrium. A Nash equilibrium also exists for games (situations) where players are not firms (e.g., they could be people, robots, or aliens) and where actions are something other than choosing quantity (e.g. choosing quantity, which move to make in checkers, whether to invade planet earth). b. [3 points] Define “Minimum Efficient Scale.” The lowest quantity at which the average total cost reaches its minimum value. c. [3 points] List the conditions that need to hold for price discrimination to be possible. 1. The firm must have some market power 2. Resell of the product must be impossible or very difficult 3. The firm must be able to identify groups of consumers with different demand functions (or distributions of willingness to pay). d. [4 points] Suppose a monopolist is the only seller of a Giffen good. (Reminder: A Giffen good has an upward- sloping demand curve). The profit-maximizing quantity of the Giffen good sold is 100 units and the resulting price is $8/unit. Is the marginal revenue of the last unit sold less than, equal to, or greater than $8? Carefully explain your answer. If the monopolist sells one more unit, it receives a revenue of P=8 from that unit. In addition, because price goes up with quantity sold in the case of a Giffen good, it receives a higher price on all existing sales, which brings in additional revenue. Hence, the marginal revenue is 8 plus the additional revenue of the higher prices received on the existing sales. This means that marginal revenue is greater than $8. Note: the questions asked you to explain your answer. Stating that MR lies above demand is merely another way of saying that MR is greater than price, and thus does not explain why this is the case. Stating that MR is twice as steep as the demand curve is not true in general (only true for linear demand functions) and also does not explain why that is the case. Calculating that MR is greater than 8 for an example you make up of an upward-sloping demand curve does not explain why this is true in other cases with upward-sloping demand functions.
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Page 2 of 6 e. [4 points] The graph above shows a monopolist’s total revenue, total cost, and variable cost as a function of quantity. What is the monopolist’s profit-maximizing quantity of output? Explain in one or two sentences how you arrived at your answer.
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