# Next Tuesday: Amit Gandhi guest lecture on empirical work on auctions Next Wednesday: first problem set due

Save this PDF as:

Size: px
Start display at page:

Download "Next Tuesday: Amit Gandhi guest lecture on empirical work on auctions Next Wednesday: first problem set due"

## Transcription

1 Econ 805 Advanced Micro Theory I Dan Quint Fall 2007 Lecture 6 Sept Next Tuesday: Amit Gandhi guest lecture on empirical work on auctions Next Wednesday: first problem set due Today: the price-discriminating monopolist problem and marginal revenue Bulow and Roberts, The Simple Economics of Optimal Auctions ) the value of an optimal auction versus the value of an additional bidder Bulow and Klemperer, Auctions Versus Negotiations ) auctions with reserve prices The Price-Discriminating Monopolist Today, we consider the problem of a monopolist who can sell in multiple markets and charge different prices in each; and we show that the problem has a very similar structure to the optimal-auctions problem. We then use this to answer the question of which is more valuable to the seller, running the optimal auction with N bidders or a simple ascending auction with N + 1 bidders. First, consider the following problem, from Bulow and Roberts, The Simple Economics of Optimal Auctions. A monopolist has Q units of a divisible good, which he can sell in N different markets of equal size, which we normalize to be 1. For i {1, 2,..., N}, customers in market i have valuations for the good on the interval [, ], distributed according to the probability distribution function F i. Bulow and Roberts complicate things by assuming the monopolist s supply varies stochastically, but this doesn t end up changing things.) Instead of thinking of the monopolist as setting a price, or a quantity, in each market, Bulow and Roberts think of the monopolist choosing a set of functions p i : [, ] [0, 1] representing the probability that a buyer in market i with value will choose to buy the product. Of course, given a price of P in a given market, this is just 1 when > P and 0 when < P.) The monopolist s capacity constraint then becomes p i v)f i v)dv Q 1

2 Note that if a buyer in market i values the good at v, his surplus is v p i x)dx because p i will generally be either 0 or 1, so this will integrate to v v, where v is the type who is indifferent about buying the good given its price, and therefore values it at exactly the price it is offered at. Given this, we can write the seller s revenue as the total value of all goods sold minus total consumer surplus, which is vp i v)f i v)dv v f i v) p i x)dxdv Changing the order of integration in the second integral, and then evaluating the inner integral, gives = so we can rewrite revenue as v f i v) p i x)dxdv = 1 F i x))p i x)dx = p i v) v 1 F ) iv) f i v)dv f i v) x f i v)p i x)dvdx 1 F i x) p i x)f i x)dx f i x) so this is what the monopolist will maximize, subject to the feasibility of {p i }. Now let s interpret the term in parentheses. Demand in market i is Q i = 1 F i P i ), or P i = Fi 1 1 Q i ), so revenue is Q i Fi 1 1 Q i ). Differentiating with respect to Q i, marginal revenue is Qi Fi 1 1 Q i ) ) = F 1 1 i 1 Q i ) Q i Q i f i 1 Q i ) = P i 1 F ip i ) f i P i ) so going back to our expression for the monopolist s revenue, the term in parentheses is simply marginal revenue in market i at price P i = v, or the marginal revenue of selling to customer n market i. We can rewrite expected revenue as MR i v)p i v)f i v)dv The monopolist s problem, then, becomes very straightforward to solve: sell to every customer with positive marginal revenue if the capacity constraint does not bind, or to the customers in all markets) with the highest marginal revenues if the capacity constraint binds. 2

3 Of course, there is one problem. If F i is regular, then within each market, marginal revenue is increasing in type; so the seller can sell only to the high-marginal-revenue customers simply by setting the correct price, knowing that the high-marginal-revenue types have valuations above this threshold. If F i is not regular, MR i v) is not monotonic in v, in which case it is not possible to cherry-pick only the customers with the highest marginal revenues, since once you announce a price, everyone in that market with values at least that high will want to buy. This is the same as saying that if F i is regular, the constraint that p i be increasing in v does not bind. Like in Myerson, then, some smoothing is required for the irregular case.) Back to Auctions, and Bulow and Klemperer, Auctions Versus Negotiations Like the monopolist s problem, recall from Myerson that we can rewrite the IPV auctioneer s expected revenue as { t 0 + E t p i t) t i 1 F ) } it i ) t 0 U i p, x, a i ) f i t i ) i N i N Consider mechanisms where U i p, x, a i ) = 0. Expected revenue can be rewritten as ) } t 0 E t { i N p i t)mr i t) + 1 i N p i t) So if we think of the seller as being another possible buyer, with marginal revenue of t 0, then the expected revenue is simply the expected value of the marginal revenue of the winner. Jump back to the symmetric case, so F i = F. Continue to assume regularity. In an ordinary second-price or ascending auction, with no reserve price, the object sells to the bidder with the highest type, which is also the bidder with the highest marginal revenue; so the expected revenue in this type of auction what Bulow and Klemperer call an absolute English auction ) is Expected Revenue = E t max{mrt 1 ), MRt 2 ),..., MRt N )} This is Bulow and Klemperer Lemma 1.) The fact that expected revenue = expected marginal revenue of winner also makes it clear why the optimal reserve price is MR 1 t 0 ) this replaces bidders with marginal revenue less than t 0 with t 0. So counting the seller s value from keeping the unsold object) an English auction with an optimal reserve price has expected revenue Expected Revenue = E t max{mrt 1 ), MRt 2 ),..., MRt N ), t 0 } So here s the gist of Bulow and Klemperer, Auctions Versus Negotiations. They compare the simple ascending auction with N + 1 bidders, to the optimal auction with N 3

4 bidders. We discovered last week that with symmetric independent private values, the optimal auction is an ascending auction with a reserve price of MR 1 t 0 ).) The gist of Bulow and Klemperer is that the former is higher, that is, that E max{mrt 1 ), MRt 2 ),..., MRt N ), MRt N+1 )} E max{mrt 1 ), MRt 2 ),..., MRt N ), t 0 } so the seller gains more by attracting one more bidder than by holding the perfect auction. They normalize t 0 to 0, but this doesn t change anything.) Bulow and Klemperer do require both independence and symmetry for the result as I ve stated it, although they relax private values. They allow each bidder s value to depend in pretty much any symmetric way on his own and his opponents signals, provided the game stays symmetric and the signals stay independent. In that case, the optimal auction is not an ascending auction with reserve price, but an ascending auction followed by a take-it-orleave-it offer to the last man standing after everyone else has dropped out. They show that once again, with independent signals and risk-neutral bidders, adding one more bidder and running a straight ascending auction is better in expectation than the optimal mechanism. Last week, we did the example with correlated types where the optimal auction extracted all bidder surplus, and you can t outperform that by finding one more bidder and going back to an ascending auction; but they cite another result that when types are affiliated a particular type of positive correlation that we ll cover in a couple of weeks), the ascendingplus-offer auction is optimal among all mechanisms where losers don t pay anything, the winner when someone wins) has the highest type, and his payment is weakly increasing in his own type; so in this setting affiliated types), adding one more bidder is still better than running the best among all standard-looking mechanisms. So the results of Bulow and Klemperer are basically: Assume symmetry, risk-neutrality, and serious bidders, that is, v t 0. If either i) bidders have private values, or ii) bidders signals are independent or affiliated, expected revenue is higher in an absolute N + 1-bidder English auction than an N-bidder English auction followed by a take-it-or-leave-it offer With independent signals, the latter auction is optimal, so adding an extra bidder and running a simple ascending auction outperforms any feasible sales mechanism With affiliated signals, the latter auction is not optimal, and the optimal auction outperforms the former; but the latter is optimal among auctions where losers don t pay, the winner has the highest signal, and his payment is weakly increasing in his own signal for any realization of his opponents signals; so adding a bidder outperforms any sales mechanism that meets these criteria We ll do the proof in the special case of independent private values. Without private values, the proof is similar, you just have to condition everything on the other bidders 4

5 signals, which get revealed as they drop out in an ascending auction. We ll cover affiliated signals in a few weeks, so we ll ignore that part for now.) The proof is surprisingly simple. All we need to do is to show that E max{mrt 1 ), MRt 2 ),..., MRt N ), MRt N+1 )} E max{mrt 1 ), MRt 2 ),..., MRt N ), t 0 } since the left-hand side is the expected revenue in an ascending auction with N + 1 bidders and no reserve price, and the right-hand side is the expected revenue in the optimal auction with N bidders. First of all, note that E{MRt N+1 )} 0. This is because the revenue from selling to nobody is 0, the revenue from selling to everybody is v 0, and the difference between these is the integral of marginal revenue, integrated over all types, so the expected marginal revenue is v. This is where their serious bidder assumption is crucial. The fact that t 0 = 0 is just a normalization; but the requirement that v t 0 is a real assumption, and their result breaks down without it.) If x is a constant, then the function gy) = max{x, y} is a convex function of y draw it), so by Jensen s inequality, E y max{x, y} max{x, Ey)} If we take an expectation over x, this gives us E x {E y max{x, y}} E x max{x, Ey)} or E max{x, y} E max{x, Ey)} Now let x = max{mrt 1 ), MRt 2 ),..., MRt N )} and y = MRt N+1 ); E max{mrt 1 ), MRt 2 ),..., MRt N ), MRt N+1 )} E max{mrt 1 ), MRt 2 ),..., MRt N ), EMRt N+1 ))} E max{mrt 1 ), MRt 2 ),..., MRt N ), t 0 } Finally and leading to the title of the paper), Bulow and Klemperer point out that negotiations really, any process for allocating the object and determining the price cannot outperform the optimal mechanism, and therefore leads to lower expected revenue than a simple ascending auction with one more bidder. They therefore argue that a seller should never agree to an early take-it-or-leave-it offer from one buyer when the alternative is an ascending auction with at least one more buyer, etc. 5

6 Reserve Prices We haven t really done much with reserve prices yet. In our symmetric IPV world, we ve shown that the optimal reserve price in a second-price auction is MR 1 t 0 ), which does not depend on the number of bidders. A couple of points worth making. In a second-price auction with a reserve price r, bidders with values t > r still have a dominant strategy of bidding their type. Bidders below r won t submit serious bids. Exactly what they do is undetermined, but doesn t affect the outcome.) In a first-price auction with a reserve price r, bidders with values t < r won t submit serious bids. It s also clear that V r) = 0, that is, a bidder with value t equal to the reserve price has expected payoff 0. Expected payoffs, and therefore equilibrium bids, can be calculated for types above r using the envelope theorem, since the equilibrium will be symmetric and bids strictly increasing in types above r: V t) = V r) + t r F N 1 s)ds = t r F N 1 s)ds = F N 1 t) t bt)) By the usual envelope-theorem logic, first- and second-price auctions with the same reserve price will be revenue-equivalent The proofs are all basically identical to the proofs without reserve prices.) By revenue-equivalence, calculating the optimal reserve price in the first-price auction is the same as in the second-price auction. In the second-price auction, the seller s revenue is 0 if v 1 < r revenue = r if v 2 < r < v 1 v 2 if v 2 > r so if we let F 1) and F 2) be the distributions of v 1 and v 2, ERr) = Differentiating with respect to r gives ) ER r) = F 2) r) F 1) r) + ) F 2) r) F 1) r) r v 0 ) + = v r v v 0 )df 2) v) ) f 2) r) f 1) r) r v 0 ) r v 0 )f 2) r) ) F 2) r) F 1) r) f 1) r)r v 0 ) With IPV, and F 1) r) = F N r) F 2) r) = NF N 1 r)1 F r)) + F N r) 6

7 and, differentiating F 1), f 1) r) = NF N 1 r)fr) Plugging these in, ER r) = NF N 1 r)1 F r)) NF N 1 r)fr)r v 0 ) The NF N 1 r) terms drop out, so r does not depend on N; setting this equal to 0 and rearranging gives r 1 F r) fr) = v 0 that is, the optimal reserve price is found by setting marginal revenue equal to v 0, marginal cost OK, we already knew this.) With correlated values, the gain from setting a reserve price is lower: since v 1 and v 2 are more likely to be close together, the events where the reserve price makes you money you gain r v 2 when v 2 < r < v 1 ) are both fewer and, on average, less valuable This is one of my working papers...) 7

8 Finally, if there s time... Last week, we did a bit on second-order stochastic dominance, and mentioned the result that for two random variables X and Y with the same mean, these three conditions are equivalent: E{uX)} E{uY )} for every increasing, concave u SOSD) Y = D X + Z, where EZ X) = 0 for every X x F s)ds x Gs)ds for every x, where F and G are the distributions of X and Y, respectively That answered the question, when does every risk-averse utility maximizer prefer one distribution of outcomes to another? Another question is, when does every utility maximizer risk-averse, risk-neutral, or risk-loving) prefer one distribution of outcomes to another? Now we no longer consider only distributions with the same mean. The following two are equivalent: E{uX)} E{uY )} for every increasing function u FOSD) F s) Gs) for every s Like before, we can express u as a positive sum of basis functions, and use this to show the equivalence between the two conditions. differentiable. Then which we can rewrite as or θ ux) = a + u θ)dθ ux) = a + u θ)1 θ<x dθ ux) = a + u θ)1 x>θ dθ We ll do the special case where u is Since u is increasing, u θ) 0, and so we ve expressed u as a positive sum of basis functions h θ x) = 1 x>θ, that is, the jump functions. By the same logic as before, then, EuX) EuY ) if and only if Eh θ x) Eh θ y) for every θ. If this holds for every θ, we can multiply the inequality by u θ), integrate over θ, and we re done; if it fails for some θ, that s a valid increasing function which doesn t prefer X to Y.) But E {h θ x)} = 1 x>θ df x) = θ df x) = F ) F θ) = 1 F θ) and similarly, E {h θ y)} = 1 Gθ), so X first-order stochastically dominates Y if and only if F θ) Gθ) for every θ. 8

### Optimal Auctions Continued

Lecture 6 Optimal Auctions Continued 1 Recap Last week, we... Set up the Myerson auction environment: n risk-neutral bidders independent types t i F i with support [, b i ] residual valuation of t 0 for

### ECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015

ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1

### Hybrid Auctions Revisited

Hybrid Auctions Revisited Dan Levin and Lixin Ye, Abstract We examine hybrid auctions with affiliated private values and risk-averse bidders, and show that the optimal hybrid auction trades off the benefit

### Bayesian Nash Equilibrium

. Bayesian Nash Equilibrium . In the final two weeks: Goals Understand what a game of incomplete information (Bayesian game) is Understand how to model static Bayesian games Be able to apply Bayes Nash

### Managerial Economics

Managerial Economics Unit 8: Auctions Rudolf Winter-Ebmer Johannes Kepler University Linz Winter Term 2012 Managerial Economics: Unit 8 - Auctions 1 / 40 Objectives Explain how managers can apply game

### Chapter 11: Game Theory & Competitive Strategy

Chapter 11: Game Theory & Competitive Strategy Game theory helps to understand situations in which decision-makers strategically interact. A game in the everyday sense is: A competitive activity... according

### 1. Suppose demand for a monopolist s product is given by P = 300 6Q

Solution for June, Micro Part A Each of the following questions is worth 5 marks. 1. Suppose demand for a monopolist s product is given by P = 300 6Q while the monopolist s marginal cost is given by MC

### Universidad Carlos III de Madrid Game Theory Problem set on Repeated Games and Bayesian Games

Session 1: 1, 2, 3, 4 Session 2: 5, 6, 8, 9 Universidad Carlos III de Madrid Game Theory Problem set on Repeated Games and Bayesian Games 1. Consider the following game in the normal form: Player 1 Player

### A Theory of Auction and Competitive Bidding

A Theory of Auction and Competitive Bidding Paul Milgrom and Rober Weber Econometrica 1982 Presented by Yifang Guo Duke University November 3, 2011 Yifang Guo (Duke University) Envelope Theorems Nov. 3,

### Chapter 7. Sealed-bid Auctions

Chapter 7 Sealed-bid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)

### Games of Incomplete Information

Games of Incomplete Information Jonathan Levin February 00 Introduction We now start to explore models of incomplete information. Informally, a game of incomplete information is a game where the players

### Optimal Auctions. Jonathan Levin 1. Winter 2009. Economics 285 Market Design. 1 These slides are based on Paul Milgrom s.

Optimal Auctions Jonathan Levin 1 Economics 285 Market Design Winter 29 1 These slides are based on Paul Milgrom s. onathan Levin Optimal Auctions Winter 29 1 / 25 Optimal Auctions What auction rules lead

### ECON 600 Lecture 5: Market Structure - Monopoly. Monopoly: a firm that is the only seller of a good or service with no close substitutes.

I. The Definition of Monopoly ECON 600 Lecture 5: Market Structure - Monopoly Monopoly: a firm that is the only seller of a good or service with no close substitutes. This definition is abstract, just

### Overview: Auctions and Bidding. Examples of Auctions

Overview: Auctions and Bidding Introduction to Auctions Open-outcry: ascending, descending Sealed-bid: first-price, second-price Private Value Auctions Common Value Auctions Winner s curse Auction design

### chapter >> Consumer and Producer Surplus Section 3: Consumer Surplus, Producer Surplus, and the Gains from Trade

chapter 6 >> Consumer and Producer Surplus Section 3: Consumer Surplus, Producer Surplus, and the Gains from Trade One of the nine core principles of economics we introduced in Chapter 1 is that markets

### The Limits of Price Discrimination

The Limits of Price Discrimination Dirk Bergemann, Ben Brooks and Stephen Morris University of Zurich May 204 Introduction: A classic economic issue... a classic issue in the analysis of monpoly is the

### The Sealed Bid Auction Experiment:

The Sealed Bid Auction Experiment: This is an experiment in the economics of decision making. The instructions are simple, and if you follow them carefully and make good decisions, you may earn a considerable

### Once we allow for bidders wanting multiple auctions, things immediately get much more complicated.

Econ 805 Advanced Micro Theory I Dan Quint Fall 2009 Lecture 16 Today - a fairly brief overview of multi-unit auctions. Everything we ve done so far has assumed unit demand. In a couple of cases, we ve

### Auctioning Keywords in Online Search

Auctioning Keywords in Online Search Jianqing Chen The Uniersity of Calgary iachen@ucalgary.ca De Liu Uniersity of Kentucky de.liu@uky.edu Andrew B. Whinston Uniersity of Texas at Austin abw@uts.cc.utexas.edu

### Chapter 9. Auctions. 9.1 Types of Auctions

From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World. By David Easley and Jon Kleinberg. Cambridge University Press, 2010. Complete preprint on-line at http://www.cs.cornell.edu/home/kleinber/networks-book/

### Sealed Bid Second Price Auctions with Discrete Bidding

Sealed Bid Second Price Auctions with Discrete Bidding Timothy Mathews and Abhijit Sengupta August 16, 2006 Abstract A single item is sold to two bidders by way of a sealed bid second price auction in

### Deriving Demand Functions - Examples 1

Deriving Demand Functions - Examples 1 What follows are some examples of different preference relations and their respective demand functions. In all the following examples, assume we have two goods x

### Structural Econometric Modeling in Industrial Organization Handout 1

Structural Econometric Modeling in Industrial Organization Handout 1 Professor Matthijs Wildenbeest 16 May 2011 1 Reading Peter C. Reiss and Frank A. Wolak A. Structural Econometric Modeling: Rationales

### Bidding with Securities: Profit-Share (Equity) vs. Cash Auctions

Elmar G. Wolfstetter 1/13 Bidding with Securities: Profit-Share (Equity) vs. Cash Auctions Elmar G. Wolfstetter Elmar G. Wolfstetter 2/13 Outline 1 Introduction 2 Equilibrium 3 (Almost) full surplus extraction

### Regret Minimization for Reserve Prices in Second-Price Auctions

Regret Minimization for Reserve Prices in Second-Price Auctions Nicolò Cesa-Bianchi Università degli Studi di Milano Joint work with: Claudio Gentile (Varese) and Yishay Mansour (Tel-Aviv) N. Cesa-Bianchi

### Auctions. Economics Auction Theory. Instructor: Songzi Du. Simon Fraser University. September 15, 2016

Auctions Economics 383 - Auction Theory Instructor: Songzi Du Simon Fraser University September 15, 2016 ECON 383 (SFU) Auctions September 15, 2016 1 / 28 Auctions Mechanisms of transaction: bargaining,

### Moral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania

Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 Principal-Agent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically

### Exam #2 cheat sheet. The space provided below each question should be sufficient for your answer. If you need additional space, use additional paper.

Exam #2 cheat sheet The space provided below each question should be sufficient for your answer. If you need additional space, use additional paper. You are allowed to use a calculator, but only the basic

### Online Appendix for Anglo-Dutch Premium Auctions in Eighteenth-Century Amsterdam

Online Appendi for Anglo-Dutch Premium Auctions in Eighteenth-Century Amsterdam Christiaan van Bochove, Lars Boerner, Daniel Quint January, 06 The first part of Theorem states that for any, ρ > 0, and

### Second Degree Price Discrimination - Examples 1

Second Degree Discrimination - Examples 1 Second Degree Discrimination and Tying Tying is when firms link the sale of two individual products. One classic example of tying is printers and ink refills.

### 6.207/14.15: Networks Lectures 19-21: Incomplete Information: Bayesian Nash Equilibria, Auctions and Introduction to Social Learning

6.207/14.15: Networks Lectures 19-21: Incomplete Information: Bayesian Nash Equilibria, Auctions and Introduction to Social Learning Daron Acemoglu and Asu Ozdaglar MIT November 23, 25 and 30, 2009 1 Introduction

### Some Further Results on the Winner s Rent in the Second-Price Business Auction

Sankhyā : The Indian Journal of Statistics 28, Volume 7-A, Part 1, pp. 124-133 c 28, Indian Statistical Institute Some Further Results on the Winner s Rent in the Second-Price Business Auction Maochao

### Public Goods : (b) Efficient Provision of Public Goods. Efficiency and Private Goods

Public Goods : (b) Efficient Provision of Public Goods Efficiency and Private Goods Suppose that there are only two goods consumed in an economy, and that they are both pure private goods. Suppose as well

### A Detailed Price Discrimination Example

A Detailed Price Discrimination Example Suppose that there are two different types of customers for a monopolist s product. Customers of type 1 have demand curves as follows. These demand curves include

### Lecture 6 Part I. Markets without market power: Perfect competition

Lecture 6 Part I Markets without market power: Perfect competition Market power Market power: Ability to control, or at least affect, the terms and conditions of the exchanges in which one participates

### Chapter 22: Exchange in Capital Markets

Chapter 22: Exchange in Capital Markets 22.1: Introduction We are now in a position to examine trade in capital markets. We know that some people borrow and some people save. After a moment s reflection

### Economics 335, Spring 1999 Problem Set #7

Economics 335, Spring 1999 Problem Set #7 Name: 1. A monopolist has two sets of customers, group 1 and group 2. The inverse demand for group 1 may be described by P 1 = 200? Q 1, where P 1 is the price

### Chapter 13: Price Discrimination

Chapter 13: Price Discrimination Price (Quality) Discrimination Market Segmentation Different Demand Elasticities First-Degree Second-Degree Third-Degree Auctions Intertemporal Two-Part Tariff Bundling

### ECON 600 Lecture 3: Profit Maximization Π = TR TC

ECON 600 Lecture 3: Profit Maximization I. The Concept of Profit Maximization Profit is defined as total revenue minus total cost. Π = TR TC (We use Π to stand for profit because we use P for something

### The fundamental question in economics is 2. Consumer Preferences

A Theory of Consumer Behavior Preliminaries 1. Introduction The fundamental question in economics is 2. Consumer Preferences Given limited resources, how are goods and service allocated? 1 3. Indifference

### Linear Programming Notes VII Sensitivity Analysis

Linear Programming Notes VII Sensitivity Analysis 1 Introduction When you use a mathematical model to describe reality you must make approximations. The world is more complicated than the kinds of optimization

### Decision Making under Uncertainty

6.825 Techniques in Artificial Intelligence Decision Making under Uncertainty How to make one decision in the face of uncertainty Lecture 19 1 In the next two lectures, we ll look at the question of how

### Surplus Effects of Vertical Integration With and Without Double Marginalization - Examples 1

Surplus Effects of Vertical Integration With and Without Double Marginalization - Examples 1 What is Double Marginalization? When firms have market power, they will set price above marginal cost, which

### Intermediate Microeconomics. Chapter 13 Monopoly

Intermediate Microeconomics Chapter 13 Monopoly Non-competitive market Price maker = economic decision maker that recognizes that its quantity choice has an influence on the price at which it buys or sells

### Economics of Insurance

Economics of Insurance In this last lecture, we cover most topics of Economics of Information within a single application. Through this, you will see how the differential informational assumptions allow

### Math 018 Review Sheet v.3

Math 018 Review Sheet v.3 Tyrone Crisp Spring 007 1.1 - Slopes and Equations of Lines Slopes: Find slopes of lines using the slope formula m y y 1 x x 1. Positive slope the line slopes up to the right.

### Lecture Notes on Elasticity of Substitution

Lecture Notes on Elasticity of Substitution Ted Bergstrom, UCSB Economics 210A March 3, 2011 Today s featured guest is the elasticity of substitution. Elasticity of a function of a single variable Before

### Monopoly. E. Glen Weyl. Lecture 8 Price Theory and Market Design Fall 2013. University of Chicago

and Pricing Basics E. Glen Weyl University of Chicago Lecture 8 Price Theory and Market Design Fall 2013 Introduction and Pricing Basics Definition and sources of monopoly power Basic monopolistic incentive

### Constrained optimization.

ams/econ 11b supplementary notes ucsc Constrained optimization. c 2010, Yonatan Katznelson 1. Constraints In many of the optimization problems that arise in economics, there are restrictions on the values

### Lecture Notes on Elasticity of Substitution

Lecture Notes on Elasticity of Substitution Ted Bergstrom, UCSB Economics 20A October 26, 205 Today s featured guest is the elasticity of substitution. Elasticity of a function of a single variable Before

### An Analysis of the War of Attrition and the All-Pay Auction*

journal of economic theory 72, 343362 (1997) article no. ET962208 An Analysis of the War of Attrition and the All-Pay Auction* Vijay Krishna Department of Economics, Pennsylvania State University, University

### Profit Maximization. 2. product homogeneity

Perfectly Competitive Markets It is essentially a market in which there is enough competition that it doesn t make sense to identify your rivals. There are so many competitors that you cannot single out

### Competitive Firms and Markets

Competitive Firms and Markets Lecture 6 Reading: Perlo Chapter 8 August 2015 1 / 76 Introduction We learned last lecture what input combination a rm will use for a given level of output. But exactly how

### Economics of Uncertainty and Information

Economics of Uncertainty and Information Introduction In this lecture, we will discuss briefly some of the issues that have been at the frontiers of economics. They concern decisions when there is uncertainty

### Economics 165 Winter 2002 Problem Set #2

Economics 165 Winter 2002 Problem Set #2 Problem 1: Consider the monopolistic competition model. Say we are looking at sailboat producers. Each producer has fixed costs of 10 million and marginal costs

### Multiagent auctions for multiple items

Houssein Ben Ameur Département d Informatique Université Laval Québec, Canada benameur@ift.ulaval.ca Multiagent auctions for multiple items Brahim Chaib-draa Département d Informatique Université Laval

### C2922 Economics Utility Functions

C2922 Economics Utility Functions T.C. Johnson October 30, 2007 1 Introduction Utility refers to the perceived value of a good and utility theory spans mathematics, economics and psychology. For example,

### Marginal Decisions and Externalities - Examples 1

Marginal Decisions and Externalities - Examples 1 Externalities drive the free market away from the socially efficient equilibrium. As microeconomists, we re interested in maximizing social welfare, so

### Second-Degree Price Discrimination

Second-Degree Price Discrimination Lecture 4 Goal: Separating buyers into di erent categories by o ering suitable deals: Screening. Monopolist knows that buyers come in di erent types. Maybe some buyers

### Dynamic Auction: Mechanisms and Applications

Dynamic Auction: Mechanisms and Applications Lin Gao IERG 6280 Network Economics Spring 2011 Preliminary Benchmark Model Extensions Applications Conclusion Outline What is an Auction? An auction is a market

### governments and firms, and in particular ebay on market design; the views expressed are our own.

On the Design of Simple Multi-unit Online Auctions Thomas Kittsteiner (London School of Economics) and Axel Ockenfels (University of Cologne) 1 The increased use of online market places (like ebay) by

### UCLA. Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory

UCLA Department of Economics Ph. D. Preliminary Exam Micro-Economic Theory (SPRING 2011) Instructions: You have 4 hours for the exam Answer any 5 out of the 6 questions. All questions are weighted equally.

### Consumer and Producer Surplus. Consumer and Producer Surplus. Consumer Surplus. Consumer Surplus. Consumer Surplus Individual consumer surplus

Consumer and Consumer and February 6, 2007 Reading: Chapter 6 Introduction Consumer surplus Producer surplus Efficiency and the gains from trade s 2 Introduction Connections to: Opportunity costs to consumers

### Games of Incomplete Information

Games of Incomplete Information Yan Chen November 16, 2005 Games of Incomplete Information Auction Experiments Auction Theory Administrative stuff Games of Incomplete Information Several basic concepts:

### Maximising Consumer Surplus and Producer Surplus: How do airlines and mobile companies do it?

Maximising onsumer Surplus and Producer Surplus: How do airlines and mobile companies do it? This is a topic that has many powerful applications in understanding economic policy applications: (a) the impact

### Understanding Options: Calls and Puts

2 Understanding Options: Calls and Puts Important: in their simplest forms, options trades sound like, and are, very high risk investments. If reading about options makes you think they are too risky for

### NF5-12 Flexibility with Equivalent Fractions and Pages 110 112

NF5- Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.

### Cournot s model of oligopoly

Cournot s model of oligopoly Single good produced by n firms Cost to firm i of producing q i units: C i (q i ), where C i is nonnegative and increasing If firms total output is Q then market price is P(Q),

### Internet Advertising and the Generalized Second Price Auction:

Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords Ben Edelman, Harvard Michael Ostrovsky, Stanford GSB Michael Schwarz, Yahoo! Research A Few

### 10.1 Bipartite Graphs and Perfect Matchings

10.1 Bipartite Graphs and Perfect Matchings In bipartite graph the nodes are divided into two categories and each edge connects a node in one category to a node in the other category. For example: Administrators

### Nash Equilibrium. Ichiro Obara. January 11, 2012 UCLA. Obara (UCLA) Nash Equilibrium January 11, 2012 1 / 31

Nash Equilibrium Ichiro Obara UCLA January 11, 2012 Obara (UCLA) Nash Equilibrium January 11, 2012 1 / 31 Best Response and Nash Equilibrium In many games, there is no obvious choice (i.e. dominant action).

### Lecture Note on Auctions

Lecture Note on Auctions Takashi Kunimoto Department of Economics McGill University First Version: December 26 This Version: September 26, 28 Abstract. There has been a tremendous growth in both the number

### 2. State whether the following statements are true or false, and explain why.

1 Chapter 9 Problems 2. State whether the following statements are true or false, and explain why. a. In a perfectly competitive industry the industry demand curve is horizontal, whereas for a monopoly

### Chapter 15. Sponsored Search Markets. 15.1 Advertising Tied to Search Behavior

From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World. By David Easley and Jon Kleinberg. Cambridge University Press, 2010. Complete preprint on-line at http://www.cs.cornell.edu/home/kleinber/networks-book/

### Lecture Note 7: Revealed Preference and Consumer Welfare

Lecture Note 7: Revealed Preference and Consumer Welfare David Autor, Massachusetts Institute of Technology 14.03/14.003 Microeconomic Theory and Public Policy, Fall 2010 1 1 Revealed Preference and Consumer

### INTRODUCTORY MICROECONOMICS Instructor: Filip Vesely 12

INTRODUCTORY MICROECONOMICS Instructor: Filip Vesely 12 MIDTERM EXAM will be on March 29 Everything you earn and many things you buy are taxed. Who really pays these taxes? Tax Incidence is the division

### Chapter 6 Competitive Markets

Chapter 6 Competitive Markets After reading Chapter 6, COMPETITIVE MARKETS, you should be able to: List and explain the characteristics of Perfect Competition and Monopolistic Competition Explain why a

### Chapter 29: Natural Monopoly and Discrimination

Chapter 29: Natural Monopoly and Discrimination 29.1: Introduction This chapter discusses two things, both related to the fact that, in the presence of a monopoly, there is less surplus generated in the

### The Market-Clearing Model

Chapter 5 The Market-Clearing Model Most of the models that we use in this book build on two common assumptions. First, we assume that there exist markets for all goods present in the economy, and that

### Terminology and Scripts: what you say will make a difference in your success

Terminology and Scripts: what you say will make a difference in your success Terminology Matters! Here are just three simple terminology suggestions which can help you enhance your ability to make your

### Chapter 10. Perfect Competition

Chapter 10 Perfect Competition Chapter Outline Goal of Profit Maximization Four Conditions for Perfect Competition Short run Condition For Profit Maximization Short run Competitive Industry Supply, Competitive

### Efficiency and Fairness of Markets

1 CHAPTER CHECKLIST Efficiency and Fairness of Markets Chapter 6 1. Distinguish between value and price and define consumer surplus. 2. Distinguish between cost and price and define producer surplus. 3.

### Chapter 3 Externalities and Government Policy

Chapter 3 Externalities and Government Policy What are externalities? Externalities = Classifications 1. Negative Externalities (external costs) to third parties, other than the buyers or the sellers of

### Taylor Polynomials and Taylor Series Math 126

Taylor Polynomials and Taylor Series Math 26 In many problems in science and engineering we have a function f(x) which is too complicated to answer the questions we d like to ask. In this chapter, we will

### Optimal Bidding Strategies in Non-Sealed Bid Online Auctions of Common Products with Quantity Uncertainty

Optimal Bidding Strategies in Non-Sealed Bid Online Auctions of Common Products with Quantity Uncertainty Chonawee Supatgiat Research Group, Enron Corporation Houston, TX 77002 John R. Birge Department

### CPC/CPA Hybrid Bidding in a Second Price Auction

CPC/CPA Hybrid Bidding in a Second Price Auction Benjamin Edelman Hoan Soo Lee Working Paper 09-074 Copyright 2008 by Benjamin Edelman and Hoan Soo Lee Working papers are in draft form. This working paper

### Basic Utility Theory for Portfolio Selection

Basic Utility Theory for Portfolio Selection In economics and finance, the most popular approach to the problem of choice under uncertainty is the expected utility (EU) hypothesis. The reason for this

### How to Use the Auction Effect to Sell Your House Faster

How to Use the Auction Effect to Sell Your House Faster This approach has also been called How to Sell Your House in 24 Hours but you can take a whole weekend! Have you ever noticed that some houses seem

### I. Features of Monopolistic Competition

University of Pacific-Economics 53 Lecture Notes #15 I. Features of Monopolistic Competition Like the name suggests, a monopolistically competitive industry has features from both a monopoly market structure

### Online Supplementary Material

Online Supplementary Material The Supplementary Material includes 1. An alternative investment goal for fiscal capacity. 2. The relaxation of the monopoly assumption in favor of an oligopoly market. 3.

### I. Output Decisions by Firms

University of Pacific-Economics 53 Lecture Notes #8B I. Output Decisions by Firms Now that we have examined firm costs in great detail, we can now turn to the question of how firms decide how much output

### Price discrimination by a monopolist

Review Imperfect Competition: Monopoly Reasons for monopolies Monopolies problem: Choses quantity such that marginal costs equal to marginal revenue The social deadweight loss of a monopoly Price discrimination

### Schooling, Political Participation, and the Economy. (Online Supplementary Appendix: Not for Publication)

Schooling, Political Participation, and the Economy Online Supplementary Appendix: Not for Publication) Filipe R. Campante Davin Chor July 200 Abstract In this online appendix, we present the proofs for

economicsentrance.weebly.com Basic Exercises Micro Economics AKG 09 Table of Contents MICRO ECONOMICS Budget Constraint... 4 Practice problems... 4 Answers... 4 Supply and Demand... 7 Practice Problems...

### Adjusting Nominal Values to Real Values

OpenStax-CNX module: m48709 1 Adjusting Nominal Values to Real Values OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 By the end of this section,

### 40ǀ MARKET FOR KIDNEYS

40ǀ MARKET FOR KIDNEYS Purpose: To show the effects of government rules that govern the market for kidneys for transplant, and how a freer market might affect outcomes. Computer file: transplant.xls or

### Economics 101 Fall 2013 Answers to Homework 5 Due Tuesday, November 19, 2013

Economics 101 Fall 2013 Answers to Homework 5 Due Tuesday, November 19, 2013 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on

Two-State Options John Norstad j-norstad@northwestern.edu http://www.norstad.org January 12, 1999 Updated: November 3, 2011 Abstract How options are priced when the underlying asset has only two possible