## Managerial Economics (MGT 203) – Global Homework Experts

University of California, Riverside Graduate School of Management Managerial Economics (MGT 203) Winter 2017 Professor Roberto Pedace Problem Set #5 1. Grinch is the sole owner of a mineral water spring that burbles forth as much mineral water as Grinch cares to bottle. It costs $2 per gallon (constant marginal cost) to bottle this water. The demand curve for mineral water is = 100 ? 5. (a) Find the profit-??maximizing price and quantity for Grinch. (b) Suppose now, that Grinch’s neighbor, Finch finds a mineral spring that produces mineral water that is just as good as Grinch’s water, but it costs Finch $4 per gallon to get his water out of the ground and bottle it. Assume that they simultaneously choose their profit-??maximizing output. Find their profit-??maximizing quantities and their profits (assuming they have no fixed costs). )

2. The market demand for a pair of duopolists (Firms A and B) is given by = 12 ? , *

where = , + . . Suppose Firm A faces a constant marginal cost of $6 (, = 6) and Firm B’s marginal cost is given by . = 4. . Neither firm has any fixed costs, so their cost functions are , = 6, and . = 2.* . (a) Assume Firm A is a price leader and Firm B is a price follower. Find the profit-??

maximizing output for each firm. (b) How much profit does each firm make? 3. Two firms (A and B) are considering bringing out competing brands of a healthy cigarette. Payoffs to the companies (in millions of dollars) are given in the matrix below Firm B Produce Don’t Produce Firm A Produce (3,3) (5,4) Don’t Produce (4,5) (2,2) (a) What is the Nash equilibrium (or equilibria)? (b) Is the Nash equilibrium (or equilibria) Pareto efficient? 1 (c) Does this game present any first-??mover advantages for either Firm A or Firm B? Construct the decision trees and explain your answer. 4. Consider the following game in an industry dominated by two firms. The firms must decide on the level or amount of advertising (low or high) given the following payoff matrix. Firm B Low High Firm A Low (2,4) (4,3) High (3,3) (5,2) (a) What is the Nash equilibrium (or equilibria)? (b) Is the Nash equilibrium (or equilibria) Pareto efficient? (c) Does Firm A have a dominant strategy? Does Firm B have a dominant strategy? Is the Nash equilibrium a dominant strategy equilibrium?

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