Optimization Problem:
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:
Π = -50 + 40 Q1 + 30Q2 - 5Q12 - 4Q22 - 3Q1Q2
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.