A brief introduction to economics Part III Tyler Moore Computer - - PDF document

A brief introduction to economics

Part III Tyler Moore

Computer Science & Engineering Department, SMU, Dallas, TX

September 11, 2012

Markets Exercises

Outline

1

Markets From individual to aggregate Equilibrium Efficiency

2

Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

2 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

Making an optimal choice under budget constraint

Budget constraint: o1 ∗ p1 + o2 ∗ p2 ≤ m

• 1
• 2

Indifference curves

b u d g e t l i n e

m p1 m p2

p2∗ p1∗

Diagrams adapted from Varian’s Intermediate Microeconomics 4 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

Making an optimal choice under budget constraint

We just saw one example of an optimal choice for prices p1 and p2 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 o1 and o2 and budget m returns the optimal choice of outcomes demanded do1(p1, p2, m) for given prices and budget.

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Notes Notes Notes Notes

Markets Exercises From individual to aggregate Equilibrium Efficiency

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

• 1 for n agents is given by

Do1(p1, p2, m1, m2, . . . , mn) =

n

• i=1

do1(p1, p2, mi) (1)

6 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

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(p1) similar to the market demand function D(p1)

7 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

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 Markets Exercises From individual to aggregate Equilibrium Efficiency

Market equilibrium

quantity price

demand curve constant supply

p∗ q∗

Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26

Notes Notes Notes Notes

Markets Exercises From individual to aggregate Equilibrium Efficiency

Market equilibrium

quantity price

demand curve constant price

p∗ q∗

Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

Market equilibrium

quantity price

demand curve supply curve

pd = ps q∗

Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

Market equilibrium

quantity price

demand curve supply curve

pd = ps q∗ pd Willing to buy ps Willing to sell

Diagrams adapted from Varian’s Intermediate Microeconomics 9 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

Equilibrium in the stock market

quantity price

shares issued

Stock-market pricing

demand curve

p∗ q∗ 20 21 19

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Notes Notes Notes Notes

Markets Exercises From individual to aggregate Equilibrium Efficiency

Equilibrium in the stock market

quantity price

shares issued

20 21 19

Stock-market pricing: increase

new demand curve

• ld demand curve

ask=bid: $21

p′∗ p∗ q∗

10 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

Equilibrium in the stock market

quantity price

shares issued

20 21 19

Stock-market pricing: decrease

new demand curve

• ld demand curve

ask=bid: $19

p′∗ p∗ q∗

10 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

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 Markets Exercises From individual to aggregate Equilibrium Efficiency

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

• 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 ≻ oi such that o′ j ∼ oj

for j = 1..n, j = i.

12 / 26

Notes Notes Notes Notes

Markets Exercises From individual to aggregate Equilibrium Efficiency

Is market equilibrium Pareto efficient? Yes!

quantity price

demand curve supply curve

pd = ps q∗ pd Willing to buy ps Willing to sell

Diagrams adapted from Varian’s Intermediate Microeconomics 13 / 26 Markets Exercises From individual to aggregate Equilibrium Efficiency

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 Markets Exercises From individual to aggregate Equilibrium Efficiency

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 Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

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?

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Notes Notes Notes Notes

Markets Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

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 Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

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 Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

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 Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

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

Notes Notes Notes Notes

Markets Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

Exercise 2: let’s model a security investment decision

Suppose GoDaddy is approached by a security firm XYZSec

• ffering a “DDoS protection” product

XYZSec claims to be able to eradicate DDoS threats using a shared-bandwidth pool, will sell for $100,000. Your task: model GoDaddy’s security investment choice using rational choice theory

1

What are the outcomes?

2

What are the actions?

22 / 26 Markets Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

Exercise 2: Actions-outcomes table

1 Fill in the following table 2 Note which items are missing from the description and can’t

be filled in

• utcome o1
• utcome o2

Action U(o1) P(o1|action) U(o2) P(o2|action) E[U(action)] action a1 ? ? ? ? ? action a2 ? ? ? ? ?

23 / 26 Markets Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

Exercise 2: Actions-outcomes table

• utcome o1
• utcome o2

Action U(o1) P(o1|action) U(o2) P(o2|action) E[U(action)] a1 a2

24 / 26 Markets Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

Exercise 2: Calculate the effectiveness of DDoS prevention

Suppose that GoDaddy expects an outage would cost them $10 million to deal with. How well must XYZSecurity’s DDoS prevention system work in order to be worth the cost? (Hint: use the action-outcome table from the last slide) State the assumptions that you must make for the model to work, and qualitatively assess whether or not they are reasonable

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Notes Notes Notes Notes

Markets Exercises Exercise 1: antivirus software Exercise 2: DDoS protection

Exercise 2: Calculate the effectiveness of DDoS prevention

My answer: P(DDoS) ≥ .001 Solution details: see whiteboard My assumptions

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