# Effect of a quantity tax in perfectly competitive market (Intermediate microeconomics)

Been stuck on this past paper question for quite some time. Doing my head in and going around in circles trying lots of different approaches...

Perfectly competitive market.

$$C(𝑦) = (0.5)y^2 + 40𝑦 + 2450.$$

where, $$𝑦$$ denotes the firm’s output. The market price, $$p = 140$$.

I have worked out optimal output to be $$y=100$$; long-run optimal output to be $$y=70$$; and long-run price to be $$110$$. (Unsure about these as do not have answers).

Question: 'In the long-run equilibrium, what are the implications of the government imposing a tax per unit on the good?'

Looking for an algebraic and graphical explanation. Thinking that price will increase, firms will exit industry, output will fall. Some sort of deadweight loss, with producer surplus/ consumer surplus falling? Not exactly sure how to represent this, especially considering it is 'long-run'.

Thank you very much.