The employer will design a compensation scheme for the employee in the following way: for each of the three possible characteristics the employee can have, the employer will identify a value of e that he wants to induce the employee to choose. That is, the employer will determine an e(1) (the e he wants the employee to choose if = 1), an e(2), and an e(3). He will then design the employee's compensation in a way that gets the employee to make the choices of e that the employer wants, and that does so at the lowest cost to the employer. This will involve making the wages for the three relevant choices of e, w(e(1)), w(e(2)), and w(e(3)), satisfy certain features, which you are asked about next: (b) The employer will choose wage w(e(1)) so that, if an employee who has = 1 chooses e(1), that employee's utility will be zero (i.e., just enough to get that employee to agree to work). Write down an equation showing that condition., The employer will design a compensation scheme for the employee in the following way: for each of the three possible characteristics the employee can have, the employer will identify a value of e that he wants to induce the employee to choose. That is, the employer will determine an e(1) (the e he wants the employee to choose if = 1), an e(2), and an e(3). He will then design the employee's compensation in a way that gets the employee to make the choices of e that the employer wants, and that does so at the lowest cost to the employer. This will involve making the wages for the three relevant choices of e, w(e(1)), w(e(2)), and w(e(3)), satisfy certain features, which you are asked about next: (b) The employer will choose wage w(e(1)) so that, if an employee who has = 1 chooses e(1), that employee's utility will be zero (i.e., just enough to get that employee to agree to work). Write down an equation showing that condition., 2. An employer wants to hire an employee to work for him. If the employee agrees to do that, she, the employee, will make a choice about how to perform her work. That choice will generally be called e, which can be any positive number. The employee's choice of e will determine (exactly) the amount of money y that the employer makes from his operation, not including any payments made to the employee. The relationship between e and y is y(e) = 2Ine + 100. If the employer gets y from his operation and pays the employee an amount of money w the employer's profit is y w. The employee's preferences over e depend on a characteristic called @, which takes on one of three values, 1, 2, or 3. If the employee makes work choice e and is paid amount of money w by the employer, her utility is w . The employee knows the value of 6, before she decides to work for the employer, and before she chooses e. This employee has no other work opportunities, and so will agree to work for the employer as long as the utility she expects to get is at least zero. The employer does not know the employee's characteristic #; however, the employer knows that the probability that 8 =1 is %; the probability that =218 %; and the probability that = 3 is ;. |