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PCP Microeconomics Session 12

PCP Microeconomics Session 12. Takako Fujiwara-Greve. Homework 10. Real-world Externalities Noise, pirating music CDs, blocking sunlight of neighbors, land price near a new railway Recycling may be positive externalities to future generation Studying with highly motivated friends.

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PCP Microeconomics Session 12

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  1. PCP MicroeconomicsSession 12 Takako Fujiwara-Greve

  2. Homework 10 • Real-world Externalities • Noise, pirating music CDs, blocking sunlight of neighbors, land price near a new railway • Recycling may be positive externalities to future generation • Studying with highly motivated friends

  3. Kreps 14.1 • (a) commute time via the bridge = 30 + nB/20k • = commute time via the tunnel = 40 + (400k - nB)/5000 • <=> nB = 360,000 nT = 40,000 • 30 + nB/20k = 48 minutes • (b) total commute time = nB ·48 + nT · 48 = 400 k · 48 =19.2 million minutes

  4. 14.1 (c ) • Minimize nB (30 +nB/20k) + (400k - nB) (40 + (400k - nB)/5000) • By differentiation -170 + nB/2000 = 0 • n* B = 340,000 • n*T = 60,000 • Commute time • Bridge 30 + 340k/20k =47 min. • Tunnel 40 + 60k/5k =52 min. • (d) impose toll of 0.5 for the bridge

  5. Kreps, 15.2

  6. EU approach • Jo: EU from the gamble = 0.25 ·1 + 0.75 · 0.49 = 0.615 • Utility from sure $7500 ≈ 0.65 • Jack: EU =0.25 √45,000 + 0.74 √5000 ≈ 106.066 • Utility from sure $7500 = √12500 ≈111.68 • Jim: EU = 0.25 √90,000 + 0.75 √50,000 ≈242.705 • Utility from sure $7500 = √57500 ≈239.79

  7. Solving for Certainty Equivalent • Jack • x + 5000 = (106.066) => CE ≈ 6250 < 7500 • Jim • x + 50,000 = (242.705) => CE ≈ 8905>7500 2 2

  8. Kreps, 15.3 (a) • 40,000 - 0.05· 750,000 = 2500

  9. Moral Hazard • Insured factory owner: will she take care of dangerous things well? • Workers: will they work hard when they are not supervised? • Partnership: will partners work hard to increase the joint profit? • Actions of one party affects the welfare of others, where the interests of the parties are not the same

  10. Incentives • Direct financial incentives • If you work hard, I pay you more • Reciprocity, reputation • If you are nice to others, others will be nice to you later • Intrinsic motivation, social norm • Feel proud or feel guilty for being bad

  11. Solution 1: write a contract • Determine the “correct” action • Write it in the contract • Problem • How can we monitor/measure/prove?

  12. Solution 2: Put all responsibility on the person who takes actions • No insurance • Tie payment to the worker’s sales • Problem • No risk sharing • Simultaneous moral hazard

  13. Fundamental problems with incentives • The desired actions cannot be specified contractually • Measurement, monitoring, enforceability • Even if the desired action is taken, there is uncertainty about the consequences • Loading the full consequences on the party taking actions is undesirable • Could share the risk and improve all

  14. Salesperson Compensation • Sale --> you (employer) get $60,000 • No sale -->you get $0 • Salesperson’s choices disutility • Kills himself: sale with prob. 0.5 40 • Works hard: sale with prob. 0.4 20 • Not hard: sale with prob. 0.25 10 • Loafs: sale with prob. 0.05 0 • S’s utility √wage - disutility • Outside opportunity: $10,000 w/ no disutility • Employer must give at least utility 100 • Employer: risk neutral

  15. If you can specify an effort level in a contract • “S chooses effort level A and be paid X if a sale is made and Y if not” • Efficient risk sharing: X = Y • No effort is ok: √w - 0 ≥100 <=> w = $10,000 • Employer’s profit = (0.05)(60,000) - 10,000 = - 7000 • Let him try: √w - 10 ≥100 <=> w = $12,100 • Profit = (0.25)(60,000) - 12,100 = 2900

  16. Work hard: √w - 20≥100 <=> w = 14,400 • Profit = (0.4) (60,000) - 14,400 = 9600 • Kill himself: √w - 40 ≥100 <=> w = 19,600 • Profit = (0.5)(60,000) - 19,600 = 10,400 • Optimal action for the employer = killing level

  17. If effort is not contractable • If S is risk neutral, put all risk on him • But S is risk averse… • Shall the employer take all risk? • No! Then S will not make any effort • C.f: pride, reputation, promotion…

  18. Try a bonus contract • Base wage = 9500 • Bonus = 15,000 if and only if a sale is made 100 quit loaf 0.95 √9500 + 0.05 √ 245,000 = 100.421 try 0.75 √9500 + 0.25 √ 245,000 -10= 102.232 hard 0.6√9500 + 0.4 √ 245,000 - 20= 101.091 kills 0.5 √9500 + 0.5 √ 245,000 - 40= 86.996

  19. For this bonus contract • Salesperson will try but not hard • Profit = 0.25 · 60,000 - 9500 - 0.25 · 15,000 = 1750 • Trade-off • Efficient risk sharing => put risk on the employer • Motivation => tie the wage to outcomes (risky) • Optimal solution: compromise of these

  20. To find “optimal” contract • That maximizes the profit • Step 1: For each of possible effort level (action), what is the cheapest way to motivate him to do? • Step 2: Which effort level (with the cheapest contract) maximizes your profit?

  21. Problem 19.1: Let’s solve! • Find the cheapest (wage, bonus) to induce “try but not hard” level of effort • b= utility from base wage • x= utility from base wage + bonus 100 quit loaf 0.95 b + 0.05 x try 0.75 b + 0.25 x -10 hard 0.6 b + 0.4 x - 20 kills 0.5 b + 0.5 x - 40

  22. Only two binding constraints • To maximize your profit we only need to satisfy • Participation constraint • 0.75 b + 0.25 x - 10 = 100 • > would also work, but why pay more? • Incentive constraint (not to choose easier action) • 0.75 b + 0.25 x - 10 = 0.95 b + 0.05 x • Check later that other effort levels are not better

  23. Solution b=97.5, x=147.5 => base wage =9506.25, bonus = 12,250 • 0.5 b + 0.5 x - 40 < 0.6 b + 0.4 x - 20 < 0.75 b + 0.25 x - 10 ok • Your profit 0.25 (60,000 -21,756.25) + 0.75 (- 9506.25) = 2431.25

  24. To “induce”? loafing • Participation constraint only • No need to give him a bonus • Base wage = 10,000 bonus =0 • Your profit = 0.05· 60000 - 10000 = -7000

  25. To induce hard work • Participation constraint • 0.6 b + 0.4 x - 20 = 100 • Incentive constraint • 0.6 b + 0.4 x - 20 = 0.75 b + 0.25 x - 10 • Check others of course • Solution: b = 93.33.., x = 160 • Base wage = 8711.05, bonus = 16,889 • Your profit = 8533.37

  26. To induce killing level • Participation constraint • 0.5 b + 0.5 x - 40 = 100 • Incentive constraint • 0.5 b + 0.5 x - 40 = 0.6 b + 0.4 x - 20 • =>b = 40, x = 240 • Base wage = 1600, bonus = 56,000 • Your profit = 400

  27. Therefore… If the action can be specified in a contract, killing level was optimal and your profit = 10,400

  28. Suggested Exercises • Kreps, Problem 19.3 • Answers to the above will be posted in my website on Friday 15th • For a limited time, probably until early August • You can pick up your homework 11 anytime at my office from 15th (I hope). Answers are posted asap.

  29. Summary of the Course • Optimization • Marginal X, supply, demand, price discrimination … • Market equilibrium • Efficiency, surplus • Externalities • Risk and expected utility • Hidden information (Adverse selection) • Moral hazard

  30. Towards the final… • 1 sheet of A4-size paper, EJ, JE dictionary (incl. electronic ones) • You all did fine in homeworks • Review concepts • Review computations • But it will not be very complex (like opening a root) • What is important?

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