Suppose you manage a factory with ten workers. Each worker’s output is determined by the equation q = e. Output sells in the market for a price of 40. The firm has fixed cost equal to 800, and variable costs aside from labor are 8 per unit of output. Worker utility is U = w – e2. Suppose you are paying workers a wage equal to bq. What is the profit- maximizing value of b? Suppose that the probability of worker error increases as the worker increases effort, and that worker error results in unusable output. Suppose that the probability of worker error is Pr[Error] = e/10. Then for worker effort level e, expected (usable) output is now determined by the equation E[q] = (1-Pr[Error]) x e. However, the problem is that you cannot detect errors until after the product is shipped to customers, meaning you pay workers for output before you know whether it is usable or not, and you have to refund your customers for unusable output. Demonstrate why you should not pay your workers the same piece rate you calculated in part a under these conditions. Identify a compensation scheme that would result in higher profit to the factory than w = bq, where b = the value you identified in part a. Why does your scheme result in higher profit?
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Suppose you manage a factory with ten workers. Each worker’s output is determined by the equation q = e. Output sells in the market for a price of 40. The firm has fixed cost equal to 800, and variable costs aside from labor are 8 per unit of output. Worker utility is U = w – e2.
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Suppose you are paying workers a wage equal to bq. What is the profit- maximizing value of b?
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Suppose that the probability of worker error increases as the worker increases effort, and that worker error results in unusable output. Suppose that the probability of worker error is Pr[Error] = e/10. Then for worker effort level e, expected (usable) output is now determined by the equation E[q] = (1-Pr[Error]) x e. However, the problem is that you cannot detect errors until after the product is shipped to customers, meaning you pay workers for output before you know whether it is usable or not, and you have to refund your customers for unusable output. Demonstrate why you should not pay your workers the same piece rate you calculated in part a under these conditions.
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Identify a compensation scheme that would result in higher profit to the factory than w = bq, where b = the value you identified in part a. Why does your scheme result in higher profit?
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