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

Kreps 14.1 (a) commute time via the bridge = 30 + n B /20k = commute time via the tunnel = 40 + (400k - n B )/5000 n B = 360,000 n T = 40,000  30 + nB/20k = 48 minutes (b) total commute time = n B ·48 + n T · 48 = 400 k · 48 =19.2 million minutes

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

Kreps, 15.2

EU approach Jo: EU from the gamble = 0.25 · · 0.49 = Utility from sure $7500 ≈ 0.65 Jack: EU =0.25 √45, √5000 ≈ Utility from sure $7500 = √12500 ≈ Jim: EU = 0.25 √90, √50,000 ≈ Utility from sure $7500 = √57500 ≈239.79

Solving for Certainty Equivalent Jack x = ( ) => CE ≈ 6250 < 7500 Jim x + 50,000 = ( ) => CE ≈ 8905>

Kreps, 15.3 (a) 40, · 750,000 = 2500

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

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

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

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

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

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

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 = Let him try: √w - 10 ≥100 w = $12,100  Profit = (0.25)(60,000) - 12,100 = 2900

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

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…

Try a bonus contract Base wage = 9500 Bonus = 15,000 if and only if a sale is made quit 100 loaf0.95 √ √ 245,000 = √ √ 245, = try hard kills 0.6√ √ 245, = √ √ 245, =

For this bonus contract Salesperson will try but not hard Profit = 0.25 · 60, · 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

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?

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 quit 100 loaf0.95 b x 0.75 b x -10 try hard kills 0.6 b x b x - 40

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

Solution b=97.5, x=147.5 => base wage = , bonus = 12,250  0.5 b x - 40 < 0.6 b x - 20 < 0.75 b x - 10 ok Your profit 0.25 (60, ,756.25) ( ) =

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

To induce hard work Participation constraint 0.6 b x - 20 = 100 Incentive constraint 0.6 b x - 20 = 0.75 b x - 10  Check others of course Solution: b = , x = 160 Base wage = , bonus = 16,889 Your profit =

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

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

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.

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

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?