3. Consider a world in which production of a good or service consists of a number of definitive tasks, which must all be performed correctly for the product to have positive value. Each task is filled by a single worker i whose skill level qirepresents the probability the worker performs her task correctly. Mathematically, if there are n tasks in the production of a good, and average production per worker with one unit of capital is 1 when all tasks are performed correctly, the production technology can be represented as: A) Give an example of an industry for which this might be a good model of production. What does this production function imply about the tradeoff between quality and quantity of labor in a given task? In this, how does it differ from a Cobb Douglas production function? B) Find the marginal product of increasing the skill of the ith worker. Suppose now there were two firms in the same industry that will bid for workers, and can pay them differentially according to productivity (e.g. w(q)).There are a pool of workers numbering 2n available to fill jobs in these firms. Half of them have skill such that qi=.8 and the other half have qi=.9. Intuitively, what distribution of skill do you expect to find in these companies? Why? What about wage levels at the two companies? C) Now suppose there exists a computer that can do one of the tasks with q=.99 skill. This computer can be rented for r dollars. Under what conditions will a company use the computer to replace the worker at that task? Which of the two companies will be willing to pay a higher r for the computer? Why? If adopted, what effect will adopting the computer have on the salaries of the remaining workers at the company? Why? What does this model suggest about the demand for computers in production?
3. Consider a world in which production of a good or service consists of a number of definitive tasks, which must all be performed correctly for the product to have positive value. Each task is filled by a single worker i whose skill level qirepresents the probability the worker performs her task correctly. Mathematically, if there are n tasks in the production of a good, and average production per worker with one unit of capital is 1 when all tasks are performed correctly, the production technology can be represented as:
A) Give an example of an industry for which this might be a good model of production. What does this production function imply about the tradeoff between quality and quantity of labor in a given task? In this, how does it differ from a Cobb Douglas production function?
B) Find the marginal product of increasing the skill of the ith worker. Suppose now there were two firms in the same industry that will bid for workers, and can pay them differentially according to productivity (e.g. w(q)).There are a pool of workers numbering 2n available to fill jobs in these firms. Half of them have skill such that qi=.8 and the other half have qi=.9. Intuitively, what distribution of skill do you expect to find in these companies? Why? What about wage levels at the two companies?
C) Now suppose there exists a computer that can do one of the tasks with q=.99 skill. This computer can be rented for r dollars. Under what conditions will a company use the computer to replace the worker at that task? Which of the two companies will be willing to pay a higher r for the computer? Why? If adopted, what effect will adopting the computer have on the salaries of the remaining workers at the company? Why? What does this model suggest about the demand for computers in production?
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