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monopoly help, Microeconomics

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Monopoly and Oligopoly help?!?
1. Your firm sells a perfume. The daily demand for your perfume estimated by your economists is
given by
P=150-5Q
Your marginal cost is constant at $2 per bottle, fixed cost is 0, and ATC is also constant at $2.
(a) Write down the expression for Marginal Revenue.
(b) Choose the quantity and the price of a bottle of perfume to maximize your profit, assuming
that you can only charge one price.
(c) Compute the profit from part (b)
(d) Find the profit you could earn if you were able to perfectly price discriminate.
(e) An experienced salesman offers his service (help you perfectly price discriminate) for $800.
Based on c) and d), do you accept the salesman’s offer? Show work, and explain briefly.
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3. Your firm sells a perfume for women. You believe you can get more profit by capturing more
consumer surplus from each customer by implementing 2-part pricing at your store. Your
marginal cost is $2 per bottle of perfume. The demand of a representative customer for your
perfume is given by
P = 30 – 5Q
(a) Implement a 2-part pricing scheme for your perfume.
(b) Explain briefly why TOTAL profit (profit from entire sales) is still likely to be lower with this
pricing scheme than with perfect price discrimination, despite charging a fixed fee equal to the
entire Consumer Surplus of a typical consumer?
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4. You and another firm are the only producers of plastic bags. You are firm 1 and the other firm is
firm 2. You are thinking about what price to charge next period, and have the following
information.
i. You have 2 choices—charge a high or a low price. So does firm 2.
ii. If you both charge a high price, you split the market and each earns a profit of $10
next period.
iii. If both charge a low price, you split the market again, but profit to each is $4.
iv. If one firm charges a high price while the other charges a low price, the high price
firm earns $-1 while the low priced firm earns $25. This is because the high priced
firm will lose most of the market.
Use the above information to answer the following questions.
(a) Draw the payoff matrix representing this one-time strategic interaction.
(b) Does your firm have a dominant strategy? Does firm 2? If so, indicate what this
strategy is for each.
(c) Given b., find the Nash Equilibrium outcome (actions, payoffs) for the one-time
interaction.
(d) Is the Nash Equilibrium the best outcome for both, i.e. is there an incentive for both
firms to cooperate instead? Show me this incentive (profit difference).
(e) What might prevent this cooperative outcome? Hint: think about conditions that
support cooperation.
(f) Bonus 1 point: (Thinking outside the box, not covered in class!) If these firms were
to merge, what would be the likely outcome? Explain briefly.

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