Notes A brief introduction to economics Part III Tyler Moore Computer Science & Engineering Department, SMU, Dallas, TX September 11, 2012 Markets Exercises Notes Outline Markets 1 From individual to aggregate Equilibrium Efficiency Exercises 2 Exercise 1: antivirus software Exercise 2: DDoS protection 2 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Making an optimal choice under budget constraint Budget constraint: o 1 ∗ p 1 + o 2 ∗ p 2 ≤ m o 2 m p 2 b u d g e t l i n e p 2 ∗ Indifference curves p 1 ∗ o 1 m p 1 Diagrams adapted from Varian’s Intermediate Microeconomics 4 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Making an optimal choice under budget constraint We just saw one example of an optimal choice for prices p 1 and p 2 given a budget m What happens when prices change? The optimal choice does too We can systematically vary prices and obtain the optimal demand Definition (Demand function) A demand function for outcomes o 1 and o 2 and budget m returns the optimal choice of outcomes demanded d o 1 ( p 1 , p 2 , m ) for given prices and budget. 5 / 26
From individual to aggregate Markets Equilibrium Exercises Efficiency Notes What about other agents? We can measure overall market demand by adding up all individual market demand functions Definition (Market demand function) A market demand function for outcome o 1 for n agents is given by n � D o 1 ( p 1 , p 2 , m 1 , m 2 , . . . , m n ) = d o 1 ( p 1 , p 2 , m i ) (1) i =1 6 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes What about supply? Thus far we have focused on consumer preferences But production also matters (the supply side) Suppliers of goods are individually willing to produce goods at different prices We can construct a market supply function S ( p 1 ) similar to the market demand function D ( p 1 ) 7 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Market equilibrium Definition (Market equilibrium) Market equilibrium is achieved at the price p ∗ where D ( p ∗ ) = S ( p ∗ ). The market price is in equilibrium because agents are individually optimizing their demand functions d based on the prices they observe 8 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Market equilibrium price constant supply p ∗ demand curve q ∗ quantity Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26
From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Market equilibrium price constant price p ∗ demand curve q ∗ quantity Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Market equilibrium price supply curve p d = p s demand curve q ∗ quantity Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Market equilibrium price supply curve p d Willing to buy p d = p s p s Willing to sell demand curve q ∗ quantity Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Equilibrium in the stock market Stock-market pricing price shares issued 21 p ∗ 20 19 demand curve q ∗ quantity 10 / 26
From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Equilibrium in the stock market Stock-market pricing: increase price shares issued p ′∗ 21 ask=bid: $21 p ∗ 20 19 old demand curve new demand curve q ∗ quantity 10 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Equilibrium in the stock market Stock-market pricing: decrease price shares issued 21 p ∗ 20 p ′∗ 19 ask=bid: $19 new demand curve old demand curve q ∗ quantity 10 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Properties of the stock market Stock market value = p ∗ q Stock market value: present value of expected future profits While the expected future profits can be highly uncertain, the stock price is very certain Stockholders want firms to adopt strategies that maximize future profits Firms can adopt strategies that maximize stock market value, and by doing so act in the best interest of stockholders 11 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Pareto efficiency Informally: a situation is Pareto efficient if no agent can be made better off without making another agent worse off. Definition (Pareto efficiency) Suppose n agents have selected outcomes o i ∈ O for all i = 1 .. n . A system is Pareto efficient if there is no feasible outcome o ′ i for an agent i where o ′ i ≻ o i such that o ′ j ∼ o j for j = 1 .. n , j � = i . 12 / 26
From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Is market equilibrium Pareto efficient? Yes! price supply curve p d Willing to buy p d = p s p s Willing to sell demand curve q ∗ quantity Diagrams adapted from Varian’s Intermediate Microeconomics 13 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes Pareto efficient or not? Pareto efficiency makes no judgment about what constitutes a ‘fair’ distribution of outcomes Can totalitarian dictatorship be Pareto efficient? Can complete socialism be Pareto efficient? What about waiting in line to buy tickets? 14 / 26 From individual to aggregate Markets Equilibrium Exercises Efficiency Notes First Fundamental Theorem of Welfare Economics Definition (First Fundamental Theorem of Welfare Economics) Any competitive equilibrium leads to a Pareto efficient allocation of resources. This definition begs the question: under what circumstances do we get competitive equilibrium? Assume complete markets (perfect information, no transaction costs) Assume price-taking behavior (infinite buyers and sellers, no barriers to entry) Next time we will discuss market failures , and explain why information security suffers from many of them 15 / 26 Markets Exercise 1: antivirus software Exercises Exercise 2: DDoS protection Notes Risk attitude example (take 2): antivirus software Suppose you have $10,000 in wealth. You have the option to buy antivirus software for $x. Outcomes available: O = { hacked (decreases wealth by $2,000) , not hacked (no change in wealth) } Without AV software, probability of being hacked is 0.1 ( P ( hacked | no antivirus ) = 0 . 1) With AV software, probability of being hacked is 0 ( P ( hacked | antivirus ) = 0) Exercise 1: How much would you pay for antivirus software if you were risk-neutral and the probability of getting hacked is 0.1 if you don’t have AV installed? 17 / 26
Markets Exercise 1: antivirus software Exercises Exercise 2: DDoS protection Notes Risk attitude example (take 2): antivirus software First question: what is the constraint that makes buying AV affordable? Recommended approach: draw out the table of outcomes and actions, along with probabilities Solve for x 18 / 26 Markets Exercise 1: antivirus software Exercises Exercise 2: DDoS protection Notes Another example Modeling real-world situations using rational choice theory is a fundamental skill There usually is no single “correct” model; instead you must justify your choices for approximating reality This includes a statement of the limitations of the model, so that we are clear on its shortcomings Let’s practice together on a newsworthy topic 19 / 26 Markets Exercise 1: antivirus software Exercises Exercise 2: DDoS protection Notes GoDaddy, world’s largest web hosting provider, hacked? Source: http://www.zdnet.com/anonymous-hacker-claims-godaddy-attack-outage-hits-millions-7000003925/ 20 / 26 Markets Exercise 1: antivirus software Exercises Exercise 2: DDoS protection Notes Turns out GoDaddy experienced a non-malicious outage Source: http://www.cnn.com/2012/09/11/tech/mobile/godaddy-response-outage/index.html 21 / 26
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