STAPLES manufactures bookcases. The firm's total cost of production is as follows, where TC(q) denotes the firm's total cost of production and q denotes the number of doors produced. If the firm produces 500 bookcases or less, then TC(q)=20q. If the firm produces more than 500 bookcases but no more than 1000, then TC(q)=10,000+40(q-500). If the firm produces more than 1000 bookcases, then TC(q)=30,000+80(q-1000). Assume the firm can sell as many bookcases as it wants at a price of 60 per bookcase.

i) What is the firm's profit maximizing level of output? Explain your reasoning and

show work.

In answering ii) and iii) assume everything is the same as above except the firm's total

cost of production is now given as follows. If the firm produces 500 bookcases or less,

then TC(q)=20q. If the firm produces more than 500 bookcases but no more than 1000,

then TC(q)=30,000+40(q-500). If the firm produces more than 1000 bookcases, then

TC(q)=50,000+80(q-1000).

ii) What is the firm's profit maximizing level of output? Explain your reasoning and show work.

iii) Same question as in ii), except now assume the government imposes an avoidable

lump sum tax on the firm. To be precise, the firm must pay the government 15,000 if it

sells a positive number of bookcases, but pays zero if it sells zero. Explain your reasoning

and show work.