1 / 27

Profit Maximization

Profit Maximization. What is the goal of the firm? Expand, expand, expand: Amazon. Earnings growth: GE. Produce the highest possible quality: this class. Many other goals: happy customers, happy workers, good reputation, etc.

bhibbler
Download Presentation

Profit Maximization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Profit Maximization • What is the goal of the firm? • Expand, expand, expand: Amazon. • Earnings growth: GE. • Produce the highest possible quality: this class. • Many other goals: happy customers, happy workers, good reputation, etc. • It is to maximize profits: that is, present value of all current and future profits (also known as net present value NPV).

  2. Firm Behavior under Profit Maximization • Monopoly • Oligopoly • Price Competition • Quantity Competition • Simultaneous • Sequential

  3. Monopoly • Standard Profit Maximization is max r(y)-c(y). • With Monopoly this is Max p(y)y-c(y) (the difference to competition is price now depends upon output). • FOC yields p(y)+p’(y)y=c’(y). This is also Marginal Revenue=Marginal Cost.

  4. Example (from Experiment) • We had quantity Q=15-p. While we were choosing prices. This is equivalent (in the monopoly case) to choosing quantity. • r(y)= y*p(y) where p(y)=15-y. Marginal revenue was 15-2y. • We had constant marginal cost of 3. Thus, c(y)=3*y. • Profit=y*(15-y)-3*y • What is the choice of y? What does this imply about p?

  5. Rule of thumb prices • Many shops use a rule of thumb to determine prices. • Clothing stores may set price double their costs. • Restaurants set menu prices roughly 4 times costs. • Can this ever be optimal? • q=Apє (p=(1/A) 1/єq1/є) • Notice in this case that p(y)+p’(y)y=(1/ є)p(y). • If marginal cost is constant, then p(y)= є·mc for any price. • There is a constant mark-up percentage! • Notice that (dq/q)/(dp/p)= є. What does є represent?

  6. Bertrand (1883) price competition. • Both firms choose prices simultaneously and have constant marginal cost c. • Firm one chooses p1. Firm two chooses p2. • Consumers buy from the lowest price firm. (If p1=p2, each firm gets half the consumers.) • An equilibrium is a choice of prices p1 and p2 such that • firm 1 wouldn’t want to change his price given p2. • firm 2 wouldn’t want to change her price given p1.

  7. Bertrand Equilibrium • Take firm 1’s decision if p2 is strictly bigger than c: • If he sets p1>p2, then he earns 0. • If he sets p1=p2, then he earns 1/2*D(p2)*(p2-c). • If he sets p1 such that c<p1<p2 he earns D(p1)*(p1-c). • For a large enough p1 that is still less than p2, we have: • D(p1)*(p1-c)>1/2*D(p2)*(p2-c). • Each has incentive to slightly undercut the other. • Equilibrium is that both firms charge p1=p2=c. • Not so famous Kaplan & Wettstein (2000) paper shows that there may be other equilibria with positive profits if there aren’t restrictions on D(p).

  8. Bertrand Game Marginal cost= £3, Demand is 15-p. The Bertrand competition can be written as a game. Firm B £9 £8.50 35.75 18 £9 18 0 Firm A 17.88 0 £8.50 17.88 35.75 For any price> £3, there is this incentive to undercut. Similar to the prisoners’ dilemma.

  9. Cooperation in Bertrand Comp. • A Case: The New York Post v. the New York Daily News • January 1994 40¢ 40¢ • February 1994 50¢ 40¢ • March 1994 25¢ (in Staten Island) 40¢ • July 1994 50¢ 50¢

  10. What happened? • Until Feb 1994 both papers were sold at 40¢. • Then the Post raised its price to 50¢ but the News held to 40¢ (since it was used to being the first mover). • So in March the Post dropped its Staten Island price to 25¢ but kept its price elsewhere at 50¢, • until News raised its price to 50¢ in July, having lost market share in Staten Island to the Post. No longer leader. • So both were now priced at 50¢ everywhere in NYC.

  11. Collusion • If firms get together to set prices or limit quantities what would they choose. As in your experiment. • D(p)=15-p and c(q)=3q. • Price Maxp (p-3)*(15-p) • What is the choice of p. • This is the monopoly price and quantity! • Maxq1,q2 (15-q1-q2)*(q1+q2)-3(q1+q2).

  12. Anti-competitive practices. • In the 80’s, Crazy Eddie said that he will beat any price since he is insane. • Today, many companies have price-beating and price-matching policies. • A price-matching policy (just saw it in an ad for Nationwide) is simply if you (a customer) can find a price lower than ours, we will match it. A price beating policy is that we will beat any price that you can find. (It is NOT explicitly setting a price lower or equal to your competitors.) • They seem very much in favor of competition: consumers are able to get the lower price. • In fact, they are not. By having such a policy a stores avoid loosing customers and thus are able to charge a high initial price(yet another paper by this Kaplan guy).

  13. Price-matching • Marginal cost is 3 and demand is 15-p. • There are two firms A and B. Customers buy from the lowest price firm. Assume if both firms charge the same price customers go to the closest firm. • What are profits if both charge 9? • Without price matching policies, what happens if firm A charges a price of 8? • Now if B has a price matching policy, then what will B’s net price be to customers? • B has a price-matching policy. If B charges a price of 9, what is firm A’s best choice of a price. • If both firms have price-matching policies and price of 9, does either have an incentive to undercut the other?

  14. Price-Matching Policy Game Marginal cost= £3, Demand is 15-p. If both firms have price-matching policies, they split the demand at the lower price. Firm B £9 £8.50 17.88 18 £9 18 17.88 Firm A 17.88 17.88 £8.50 17.88 17.88 The monopoly price is now an equilibrium!

  15. Quantity competition (Cournot 1838) • Л1=p(q1+q2)q1-c(q1) • Л2= p(q1+q2)q2-c(q2) • Firm 1 chooses quantity q1 while firm 2 chooses quantity q2. • Say these are chosen simultaneously. An equilibrium is where • Firm 1’s choice of q1 is optimal given q2. • Firm 2’s choice of q2 is optimal given q1. • If D(p)=13-p and c(q)=q, what the equilibrium quantities and prices. • Take FOCs and solve simultaneous equations. • Can also use intersection of reaction curves.

  16. FOCs of Cournot • Л1=(15-(q1+q2))q1-3q1=(12-(q1+q2))q1 • Take derivative w/ respect to q1. • Show that you get q1=6-q2/2. • This is also called a reaction curve (q1’s reaction to q2). • Л2= (15-(q1+q2))q2-3q2= (12-(q1+q2))q2 • Take derivative w/ respect to q2. • Symmetry should help you guess the other equation. • Solution is where these two reaction curves intersect. It is also the soln to the two equations. • Plugging the first equation into the second, yields an equation w/ just q2.

  17. Cournot Simplified • We can write the Cournot Duopoly in terms of our Normal Form game (boxes). • Take D(p)=4-p and c(q)=q. • Price is then p=4-q1-q2. • The quantity chosen are either S=3/4, M=1, L=3/2. • The payoff to player 1 is (3-q1-q2)q1 • The payoff to player 2 is (3-q1-q2)q2

  18. Cournot Duopoly: Normal Form Game Profit1=(3-q1-q2)q1 and Profit 2=(3-q1-q2)q2 S=3/4 M=1 L=3/2 9/8 9/8 5/4 S=3/4 9/8 15/16 9/16 15/16 1 3/4 M=1 5/4 1 1/2 1/2 9/16 0 L=3/2 9/8 3/4 0

  19. Cournot • What is the Nash equilibrium of the game? • What is the highest joint payoffs? This is the collusive outcome. • Notice that a monopolist would set mr=4-2q equal to mc=1. • What is the Bertrand equilibrium (p=mc)?

  20. Quantity competition (Stackelberg 1934) • Л1=p(q1+q2)q1-c(q1) • Л2= p(q1+q2)q2-c(q2) • Firm 1 chooses quantity q1. AFTERWARDS, firm 2 chooses quantity q2. • An equilibrium now is where • Firm 2’s choice of q2 is optimal given q1. • Firm 1’s choice of q1 is optimal given q2(q1). • That is, firm 1 takes into account the reaction of firm 2 to his decision.

  21. Stackelberg solution • If D(p)=15-p and c(q)=3q, what the equilibrium quantities and prices. • Must first solve for firm 2’s decision given q1. • Maxq2 [(15-q1-q2)-3]q2 • Must then use this solution to solve for firm 1’s decision given q2(q1) (this is a function!) • Maxq1 [15-q1-q2(q1)-3]q1 • This is the same as subgame perfection. • We can now write the game in a tree form.

  22. Stackelberg Game. (0,0) L M (.75,.5) B S L (1.13,.56) (.5,.75) L M A M A B B (1,1) S (1.25,.94) L (.56,1.13) S M B B (.94,1.25) (1.13,1.13) S

  23. Stackelberg game • How would you solve for the subgame-perfect equilibrium? • As before, start at the last nodes and see what the follower firm B is doing.

  24. Stackelberg Game. (0,0) L M (.75,.5) B S L (1.13,.56) (.5,.75) L M A M A B B (1,1) S (1.25,.94) L (.56,1.13) S M B B (.94,1.25) (1.13,1.13) S

  25. Stackelberg Game • Now see which of these branches have the highest payoff for the leader firm (A). • The branches that lead to this is the equilibrium.

  26. Stackelberg Game. (0,0) L M (.75,.5) B S L (1.13,.56) (.5,.75) L M A M A B B (1,1) S (1.25,.94) L (.56,1.13) S M B B (.94,1.25) (1.13,1.13) S

  27. Stackelberg Game Results • We find that the leader chooses a large quantity which crowds out the follower. • Collusion would have them both choosing a small output. • Perhaps, leader would like to demonstrate collusion but can’t trust the follower. • Firms want to be the market leader since there is an advantage. • One way could be to commit to strategy ahead of time. • An example of this is strategic delegation. • Choose a lunatic CEO that just wants to expand the business.

More Related