problem 1: Your firm sells a perfume. The everyday 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 as well constant at $2.
a) prepare down the expression for the Marginal Revenue.
b) Select the quantity and the price of a bottle of perfume to maximize your profit, supposing that you can only charge one price.
c) find out the profit from part (b).
d) Find out the profit you could earn if you were capable 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 describe briefly.
problem 2: Your firm sells a perfume for women. You suppose you can get more profit by capturing more consumer excess 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:
P = 30 – 5Q
a) Implement a 2-part pricing scheme for your perfume.
b) Describe briefly why total profit (profit from whole sales) is still likely to be lower with this pricing scheme than with perfect price discrimination, in spite of charging a fixed fee equivalent to the whole Consumer Surplus of a typical consumer?
problem 3: You and the other firm are the only producers of plastic bags. You are firm 1 and the other firm is firm 2. You are thinking regarding what price to charge next period and have the given information.
a) You have 2 choices - charge a high or a low price. So does firm 2.
b) If you both charge a high price, you divide the market and each earns a profit of $10 next period.
c) If both charge a low price, you divide the market again; however profit to each is $4.
d) 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 since the high priced firm will lose most of the market.
Use the above information to answer the given problems.
i) Draw the payoff matrix representing this one-time strategic interaction.
ii) Does your firm have a dominant strategy? Does firm 2? If so, point out what this strategy is for each.
iii) Given (b), find out the Nash Equilibrium outcome (actions, payoffs) for the one-time interaction.
iv) Is Nash Equilibrium the best outcome for both, that is, there an incentive for both firms to cooperate rather? Show this incentive (profit difference).
v) What might prevent this cooperative outcome?
vi) If these firms were to merge, what would be the likely outcome? Describe briefly.