# Profit Maximization

The Stock Corporation makes two products, paper and cardboard.

The relationship between p, the firm's annual profit (in thousands of dollars) and its output of each good is {see attachment}, where Q1 is the firm's annual output of paper (in tons) and Q2 is the firm's annual output of cardboard (in tons).

a) Find the profit maximizing production levels for paper and cardboard.

b) If the local government imposes a tax of $5,000 per year on the firm, will this alter your answer to part a? Explain.

c) Suppose the local government imposes a 1% tax on profits. Will this alter your production levels of part a? Show.

d) Compare the two tax structures and comment on how the lump sum versus the proportional profit tax affects the allocation of resources.

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#### Solution Preview

How to setup problem for profit maximizing Production

a) p = -50 + 40Q1 + 30Q2 - 5Q1^2 - 4Q2^2 - 3Q1Q2

Take partial derivatives of p with respect to Q1 and Q2 and equate them to zero to get the profit maximizing levels.

dp/dQ1 = 40 ...

#### Solution Summary

The solution explains the concept of profit maximization pretty well. It uses the data given in the question to first calculate the profit maximization production levels. Then it evaluates the impact of additional taxes on the profit maximizing levels. Based on this analysis the solution comes to a conclusion related to profit maximization levels and the tax structure.