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profit maximizing output level

A meat company located upstream from a bourbon distillery, dumps waste into the stream, so that the distillery must incur the costs of cleaning the water to the quality standard advertized on the bottle.

PB is price of bourbon, PB=$7/unit
PM is price of the meat, PM=$5/unit
B is units of bourbon production
M is units of meat production
TCB is the total cost of producing bourbon TCB=0.005B^2 + 0.1B+M
TCM is the total cost of producing meat, TCM=0.005M^2 + 0.15M

a) Asuming the bourbon producer cannot control the actions of the meat producer, so that meat enters the bourbon distillery's cost function as an externality, what is the bourbon-producer's profit maximizing output level of bourbon?

b) What are the bourbon producer's profits at this output level?

c) What is the meat producer's profit maiximizing output level of meat?

d) What is the meat producer's profits at this level?

e) What is total of the 2 firm's profits (sum of answer b and d)

f) Now assume the firm's merge becoming one company with 2 divisions. In this context, the costs of meat will be internal to the production decisions for both bourbon and meat. What is the profit maximizing level of bourbon production in this context? (Note: Meat enters the bourbon cost function as a fixed cost)

g) What is the profit maximizing output level of meat?

h) What now are the total profit from producing meat and bourbon?

i) Explain the reasoning behind the difference in answer in (h) and (e)

Please see attachment towards the end of the pdf file for background write up on this problem.

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Solution Summary

Find the profit maximizing output level.