Problem -
A company has 10 machines, each of which can produce one part per hour. A machine requires one worker to operate it and can run for at most 16 hours per day. Workers can work between 0-12 hours per day. Workers earn $10 per hour for the first 8 hours and $20 per hour thereafter. The firm can have one of two types of generators: A small generator which powers a machine at a cost of 5$ per hour; or a large generator which powers a machine at a cost of $2 per hour but has an additional daily usage cost of $180. In the short run the company cannot hire/fire workers or change its generator. In the medium run it can hire/fire workers. In the long run it can also change its generator.
a) Calculate the short run total cost function and marginal cost function for
i) A company with a small generator and 6 workers; ii) A company with a larger generator and 8 workers
b) Calculate the medium run total cost function and marginal cost function for:
i) A company with a small generator ii) A company with the large generator
c) How high does daily production have to be in order for it to make sense to use the large generator? Calculate the long run production total cost function and marginal cost function.
d) Is MC increasing/decreasing/constant as a function of q in the short run? Medium run? Long run? Explain.