Microeconomic Theory

3. Implicit Bias Consider a task in which individuals of all genders have the same productivity. The outcome of the task depends on the productivity of the worker but also on random chance. For instance, assume that the production function of said task for a single worker looks like this: (Ii =7im+i Where q,- is the quantity produced by the worker, hi is the number of hours of work provided by worker, 7, is the productivity of the worker and 6 is a random variable that is uniformly distributed between 0 and 10. Assume that the good being produced can be sold for a dollar and that there are no other costs of production and each worker works individually. (a) Consider a rm with a single worker. Currently the wage is xed and equal to w and the worker has a 7 equals to 30. Find the optimal numbers of hours as a function of w (labor demand). If U} = $5 how many hours will be demanded by the rm? If U} = $10? (b) Assume now that there is a manager that thinks women are less productive than men. For instance, they think that women have a 7w 2 20 and men of 7m 2 40. Assume that the number of hours of work h,- is xed and equal to 9 due to some contractual obligations for all workers. Find the optimal wage that the the manager is willing to pay to a women worker versus a men worker. (c) Assume that the individual productivity 7, is a function of the wage. That is, workers are more productive when they receive a better salary. Do you think this assumption can generate a self fullling prophecy for the manager that was biased against women? (you don't have to formally prove this, just provide a convincing argument). (d) Is the outcome from part (b) socially efcient? Explain how a society can reduce inefciencies that result from implicit bias