10-23-09 - Economics 448 Class Notes GET A BETTER...

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Economics 448 – Class Notes – 10/23/09 GET A BETTER DEFINITION OF WAGE CONTRACT Reservation level of utility – the level utility needed to get the worker to accept the contract Wage will be a function of the work effort MODEL #1: In the example on the handout: How much would the worker need to be paid in order to ACCEPT THE CONTRACT and also PUT IN THE LOW LEVEL OF EFFORT, and: How much would the worker need to be paid in order to ACCEPT THE CONTRACT and also PUT IN THE HIGH LEVEL OF EFFORT, and: o Asking for the participation constraint LOW LEVEL OF EFFORT: A = 0 U(w, aL) = w^(1/2) – 0 = 9 I have to construct my contract so that the utility received from putting in the low level of effort is GREATER than the reservation level of utility Reservation level of utility = 9 Thus, w >= 81 If I want the worker to put in the low level of effort, you have to pay the worker $81 This is the level of effort where it doesn’t matter if the worker comes to work and puts in low effort or not come to work at all This is a simple contract: worket is paid $81 to come to work and do the low level of effort PROFIT TO FIRM (low level) Profit = TR – TC Profit = 70 – 81 = (-11) NOT WORTH IT TO THE FIRM if you only get the worker to put in a low level of effort How much do I have to pay the agent (worker) to put in the high level of effort? U(w, aH) = w^(1/2) – 5 >= 9 w^(1/2) >= 14 W(H) = $196 (high level of effort wage) Firm’s profit: Profit = $270 - $196 = $74
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We want the worker to put in the high level of effort, so I need to structure the contract so that
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