Suppose the government imposes a tax on each unit of output produced of $t. What is the firm’s new profit maximizing level of output?
The question suggests the use of comparative to determine how a change in tax affects a change in output. The firm would operate under perfect competition conditions.
I started to answer it this way.
Before Tax:
π = revenue - costs
π = pq - C(q)
dπ/dq = p - C'(q)
Set dπ/dq for profit-maximisation
0 = p - C'(q)
p = C'(q)
p = MC
After Tax:
π = revenue - costs - tax
π = pq - C(q) -tq
dπ/dq = p - t - C'(q)
Set dπ/dq for profit-maximisation
0 = p - t - C'(q)
p = t + C'(q)
p = t + MC
Next I would try to find out how quantity changes with tax t by taking derivates? Any ideas?