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Section 11

Section 11. Intro. Microeconomics TA: Cristina Tello-Trillo. Supply/Demand: Individual demand: Consumer optimal choices: consumer maximization s.t budget constraint Individual supply: Firm profit maximization in perfect competition, monopoly and oligopoly

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Section 11

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  1. Section 11 Intro. Microeconomics TA: Cristina Tello-Trillo

  2. Supply/Demand: • Individual demand: • Consumer optimal choices: consumer maximization s.t budget constraint • Individual supply: • Firm profit maximization in perfect competition, monopoly and oligopoly • External components (outside the private market) • Taxes, subsidies • Externalities (consumption/production) • Consumer behavior • Decision making over time (smooth consumption) • Risk and uncertainty

  3. Today • Risk and Uncertainty: • Risk aversion: risk averse or risk neutral • Adverse Selection • Moral Hazard • Fair actuarial price

  4. Risk and Uncertainty • Uncertainty is a prevalent feature of the economic life. • Many events and outcomes are random: good or bad weather, shocks in pricesor incomes. Main questions: • How to describe/model uncertainty? • How the economic actors i.e. firms and individuals take the decisions under uncertainty? • What is the effect of risk?

  5. Expected Income vs Expected Utility • Two outcomes: • Expected income • Expected Utility

  6. Attitude towards risk • Risk Averse • Diminishing marginal utility of income. • Relation between the utility of expected value and expected utility: U(E[Y])>E[U(Y)]

  7. U(W) is a von Neumann-Morgenstern utility index that reflects how the individual feels about each value of Wealth. Example: U(W) Risk Aversion Utility (U) The curve is concave to reflect the assumption that marginal utility diminishes as wealth increases Wealth (W)

  8. Risk Aversion Assume that Ann is risk averse. She has Y=50$ and she has the chance to enter a lottery that has a 50-50 chance of winning or losing h$ (fair lottery). • Will Ann enter the lottery? • What are the U(E[Y]) and E[U(Y)]? • No • U(E(Y))=U(0.5(50-h)+0.5(50+h))=U(50)=U(no gamble) • E[U(Y)]=0.5U(50-h)+0.5(50+h)=U(gamble)

  9. The expected value of the gamble is U(Gamble) U(Gamble) 50* - h 50* + h Risk Aversion Utility (U) U(W) U(50) Wealth (W) 50*

  10. The expected value of gamble 1 is U(Gamble2) U(Gamble2) 50* - 0.5h 50* + 0.5h Risk Aversion Utility (U) U(W) U(50) Wealth (W) 50*

  11. Risk Aversion • Ann prefer current wealth to wealth combined with a fair gamble. • Ann might be willing to pay some amount to avoid participating in a gamble • Ann will also prefer a small gamble over a large one • This helps to explain why some individuals purchase insurance

  12. Risk Neutral • Linear marginal utility of income. • Relation between the utility of expected value and expected utility: U(E[Y])=E[U(Y)] Example: U(Y)=Y

  13. Insurance Market • Consider a person with a current wealth of $100,000 who faces a 25% chance of losing his automobile worth $20,000 • Suppose also that the person’s von Neumann-Morgenstern utility index is U(W) =

  14. The person’s expected utility will be E(U) = 0.75U(100,000) + 0.25U(80,000) E(U) = 0.75 + 0.25 E(U) =307.8 • In this situation, GEICO offers the person full insurance, for a premium of $5,000 (fair premium)

  15. The person’s expected utility with insurance will be E(Uw/insurance) = 0.75U(100,000-5000) + 0.25U(80,000-5000+20000) E(Uw/insurance) = 0.75 U(95000) + 0.25 U(95000) E(U) =308.2

  16. The individual will likely be willing to pay more than $5,000 to avoid the gamble. How much will he pay? E(U) = U(100,000 - x) = = 307.8 100,000 - x = x=5208.9 • The maximum premium is $5,209 • Where the utility with insurance is the same as the utility without insurance.

  17. Fair insurance premium • For insurance to be actuarially fair, the insurance company should have zero expected profits. Using the previous example, • Profit= 0.75(premium) + 0.25 (premium-Loss) • Profit= 0.75(premium) + 0.25 (premium-20000) • Profit = 0 • premium-0.25(20000)=0 • premium=5000$

  18. Example 1 • Suppose that there are 100 people in a town. Everyone has $10000 each year to spend, and has utility function is .If someone has a crop failure, their income is only $2500. • Assume that each year, 10 people randomly have crop failure and the others do not. Suppose a crop insurance company offered a policy that pays $7500 to someone who had a crop failure (and nothing otherwise). What is the actuarially fair premium if everyone in town buys the insurance? • Show that people in town would be willing to pay this ‘actuarially fair’ premium for insurance. (Hint: do this by showing that the amount that anyone in town would be willing to pay for insurance is greater than this actuarially fair premium).

  19. Exercise • What is the expected dollar value of each of the two lotteries? • What is Jane’s expected utility from each of the two lotteries? • Which lottery would Jane prefer (or is she indifferent)? • Is Jane risk averse? Suppose that Jane is facing the second lottery. You can interpret the second lottery as the job market, Jane gets 1$ wage per hour on a bad state of the economy (p=0.5) and 9$ wage per hour on a good state of the economy (1-p=0.5) e) An insurance company offers an insurance to Jane, this insurance pays 8$ if the economy is on a bad state and 0$ otherwise. How much would Jane will be willing to pay for this insurance policy?

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