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ECO 610-401

ECO 610-401. Monday, December 8 th Performance Measures Readings, Brickley et al., 16; 19:575-591 Extended Assignment 3 due. Principal-Agent Problems. Recall the principle-agent problem: Output by agent (employee) depends on her effort and some other random (and unknown) factors:

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ECO 610-401

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  1. ECO 610-401 • Monday, December 8th • Performance Measures • Readings, Brickley et al., 16; 19:575-591 • Extended Assignment 3 due

  2. Principal-Agent Problems • Recall the principle-agent problem: • Output by agent (employee) depends on her effort and some other random (and unknown) factors: • Q = ae + u • where e is effort and u is random component • Payment structure might be • C = Wo + BQ • where C is total compensation, Wo is base salary, and B is commission (piece) rate • If B < 1 then worker has incentive to shirk • But have B > 0 means that worker has risk (payment depends on risk: • C = Wo + B(ae+ u) = Wo + Bae + Bu

  3. Contractible Output • Note that we assume that contract can be written on Q, that is, Q is an objective performance measure. • Other assumptions: • Principal knows employee’s production function (Q=ae+u) • Output can be observed at zero cost • One measure of performance – output • Employee produces a single output • Employee cannot “game” the performance measure • Employee works independently; no team production

  4. Determining the Relationship between Effort and Output • How can the relationship between effort and output be determined? • Time/Motion Studies • Expensive; Need to be redone with new equipment or design changes • Past Performance • The “Ratchet Effect” • “Gaming”

  5. Relative Performance Weights • Suppose that we have a group of sales persons. • Random components consist of: • Shock common to all salespersons in a year ut • Shock to an individual salesperson vit • Then individual output in a year is: • Qit = aeit + uit + vit • Average Output is • Qt = aet + ut • Difference in Output is • Qit – Qt = a(eit – et) + vit

  6. Relative Performance Weights (2) • Can base compensation on individual performance alone: • C = Wo + BQ • Or base it on relative performance: • C = Wo + B(Q-λQ) • Why one rather than another?

  7. Relative Performance Weights (3) • Example: Salesperson (Ed). • 2 alternative payment structures • Absolute Performance: • C = 15 + .2Q • Relative Performance: • C = 21 + .2(Q-Q) • Optimal Relative Performance: λ = cov(Q,Q)/var(Q) • C = 20.1 + .2(Q - .85*Q)

  8. Ed’s Sales

  9. Ed’s Sales

  10. An Issue in Vertical Integration: Double Marginalization • Firms frequently grant firms exclusive territories. Why? • Avoids “free rider” problem in advertising? • Problem : Double Marginalization • Autocorp: Demand for automobile in a market is: • P = 55,000 – 100Q • MC = 5000 • P* = 30,000 and Q* = 250, Profits = 6,250,000

  11. An Issue in Vertical Integration (2) • Autocorp sells through SUVmart • Only MC facing SUVmart is charge from Autocorp • Autocorp needs to know how many cars SUVmart will buy. • SUVmart’s demand is the market demand • P = 55,000 – 100Q  R = PQ = 55,000Q – 100Q2 • MR = 55,000 – 200Q

  12. An Issue in Vertical Integration (3) • It’s MC is Pw the price Autocorp will sell the cars at • So Pw = 55,000 – 200Q  R = PwQ = 55,000Q – 200Q2  MR = 55,000 – 400Q • Autocorp will set MR = MC  55,000 – 400Q = 5000 • Pw = 30,000 & Q = 250 • Then SUVmart will have • 55,000 – 200Q = 30,000  P = 42,500

  13. An Issue in Vertical Integration (3) • Avoidance of “Double-Marginalization” • Company-Owned Stores • Two-Part Pricing • Franchise fee + Cars at MC • Quotas

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