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→Question B1: Work contracts with a continuum of workers
A firm is hiring from a continuum of workers with unit mass. Workers are heterogenous in their cost of effort. A typical worker has a private cost type <math>c\,</math> where <math>c\,</math> is uniformly distributed on the interval <math>[\frac{1}{2},1]\,</math>. A worker of type <math>c\,</math> who puts in effort <math>e\,</math> pays a personal cost of effort <math>ce^2\,</math>. All workers are risk-neutral so their payoffs are simply:
<math>\pi_w = m -ce^2\,</math>
where <math>m \,</math> is the compensation paid to the worker by the firm,
The firm's objective function is to maximize the sum of the efforts on the part of the workers. Effort is observable; however the worker's cost type is not. Furthermore the workers are protected by limited liability, so the firm cannot pay negative amounts to the workers. That is, the total expenditure of the firm on wages can be, at most, <math>\frac{1}{2}\,</math>. A firm derives benefit only from effort - not from any unspent portion of its budget.
