Ten workers work jointly on a project.All 10 workers are equally skilled.The total value of the output produced is $70 times the sum of the number of hours worked by all 10 workers.Each worker's utility is equal to his income minus the square of the number of hours he works.Each worker is selfish.The employers have no way of keeping track of any individual's work effort, so they decide to let each person work as long as he wants to and they divide the total value of the output equally among the workers.How much income will each worker get?
A)$245
B)$2,450
C)$35
D)$260
E)None of the above.

Question

Quizplus · Accepted Answer

The correct answer is A. Each worker will get $245.The total value of the output is $70 times the sum of the number of hours worked by all 10 workers. So, if the total number of hours worked by all 10 workers is H, then the total value of the output is $70H.Each worker's utility is equal to his income minus the square of the number of hours he works. So, if worker i works for h_i hours, then his utility is U_i = $7H/10 - h_i^2.Each worker is selfish, so he will choose the number of hours he works to maximize his own utility. To do this, he will set the derivative of his utility function with respect to h_i equal to zero:dU_i/dh_i = $7H/10 - 2h_i = 0Solving for h_i, we get:h_i = $7H/20So, each worker will work for $7H/20 hours.The total number of hours worked by all 10 workers is H = 10 * $7H/20 = $7H/2.So, the total value of the output is $70H = $70 * $7H/2 = $245H.Each worker will get $245H/10 = $245.

Ten Workers Work Jointly on a Project