Homework 5
1. Suppose that the popcorn market is currently a monopoly. In this market, the monopolist's marginal cost curve is given by the equation MC=2Q+8. The monopolist's demand curve is given by the equation P=56-3Q.
a) If this monopolist acted as if it were a perfectly competitive firm in a perfectly competitive industry, what would the market price and quantity equal? What would the value of consumer surplus equal if this firm acted as if this was a perfectly competitive industry? What would the value of producer surplus equal if this firm acted as if this was a perfectly competitive industry? [Hint: the numbers for this problem are a bit challenging...you may want to pull out your calculator for this one!]
b) Suppose this monopolist acts as a monopolist. What is the monopolistic price and quantity in the popcorn market? Calculate the value of consumer surplus, producer surplus and dead weight loss for this monopoly.
c) Suppose this monopolist knows what the maximum price each consumer of popcorn is willing to pay for popcorn and is therefore able to practice first degree price discrimination. What is the monopolist's profit equal to when it practices first degree price discrimination.
2. Suppose a market has a single producer and that this producer is able to distinguish two types of customers, Group A and Group B (such as men and women, or young and adult). Group A's demand curve is P = 16 - 3Q, and Group B's demand curve is P = 10 - Q. In both markets, MC=ATC=4.
a) If the monopolist is required to charge the same price to the two groups of people, what is the best output level and price? What is the profit for this single price monopolist? [Hint: to find these answers you will need to find the market demand curve: this will entail the horizontal summation of the demand curves for the two groups.]
b) Suppose the monopolist is able to practice third degree price discrimination. What price will the monopolist charge Group A and what price will the monopolist charge Group B? What quantity will be sold to Group A and what quantity will be sold to Group B?
c) Derive the total profit for this monopolist who practices third degree price discrimination.
3. This problem considers the possibility that increasing the payoff to a player can sometimes result in the player being made worse off. Suppose there are two players: Player 1 and Player 2. Player 1 has two possible strategies: "up" or "down"; Player 2 has two possible strategies: "left" or "right". The payoff matrix is given in the table below where the first cell entry refers to Player 1's payoff while the second cell entry refers to Player 2's payoff (Player 2's payoff are underlined).
| Player 2 |
|
Player 1
|
|
Left
|
Right
|
|
Up
|
8, 8
|
1, 7
|
|
Down
|
3, 0
|
2, -1
|
a) What is Player 2's dominant strategy? Explain your answer.
b) What is the equilibrium you expect given this payoff matrix? What is the payoff to Player 2 in your equilibrium?
Suppose the payoffs to Player 2 increase if Player 2 pursues the "right" strategy. The table below provides the new payoffs.
Player 2
|
|
Player 1
|
|
Left
|
Right
|
|
Up
|
8, 8
|
1, 9
|
|
Down
|
3, 0
|
2, 1
|
c) What is Player 2's dominant strategy now? Explain your answer.
d) What is the new equilibrium? What is the payoff to Player 2 in the new equilibrium?
e) Compare the payoffs to Player 2 in parts (b) and (d)? Explain intuitively why this example illustrates "The greater the payoff the worse off I am" or "The less the payoff the better off I am". [Hint: you can use a story to illustrate how this result could occur.]
4. Suppose there are only two firms in the market for shoes and that these two firms, Company A and Company B, compete with each other. Company A has a marginal cost of $10. Company B has a marginal cost of $8. Neither company has any fixed costs. Further, suppose that you told that in this market if there was only a single producer of shoes that the monopoly price in this market would be equal to $12.
a) What is the equilibrium price?
b) Explain why $12 is not the equilibrium price.
5. There are only two companies, A and B, in the spring water market. The market demand function for spring water in this market is P=20-2Q, so the MR is MR=20-4Q (why?). The MC is constant and equal for both firms and can be expressed as MC=ATC = 4. (For this question assume that firms only play this game once.)
a) The two companies decide to try and cooperate in this market so that the price they charge for the product and the amount of the product they jointly produce is equal to the price and quantity that would prevail if the market were served by a monopoly. After they set this profit maximizing price and quantity the two firms plan to share the resultant profit fifty-fifty. What is the market price, total quantity produced, and the profit for each company if they both successfully adhere to this plan?
b) Suppose that Company A decides to deviate from this coordination with Company B. Company A decides to set its price equal to $10. What is the profit for Company A when it sets price equal to $10? What is the profit for Company B given Company A's actions? [Hint: No one wants to buy higher price goods.]
c) Suppose Company B decides to match Company A's price of $10. Furthermore, assume that each company ends up serving half of the total market when Company B lowers its price to $10 to match Company A's price. Calculate the value of profits for each company with this pricing decision?
d) Now, let's create a payoff matrix for Company A and Company B that illustrate these two choices that each firm faces. Both companies can charge either $12 or $10 for the good. Create a payoff matrix illustrating the profits that the companies will receive given these two possible strategies. What is the dominate strategy for this game? What is the outcome of this game?
e) Explain the intuition for your answer in part (d).