Question

Suppose the government imposes a profit tax. Prove that the profit maximizing condition is MR=MC

Answer 1

Profit function is

(x) = R(x) - C(x)

where x = output

R(x) = Total Revenue

C(x) = Total cost

Now government imposes a profit tax of t per unit

Profit function after profit tax would be

(x) = (1 - t)[R(x) - C(x)]

'(x) = (1 - t)[R'(x) - C'(x)]

put '(x) = 0  

(1 - t)[R'(x) - C'(x)] = 0  

[R'(x) - C'(x)] = 0

R'(x) = C'(x)

MR = MC  

SOC  

''(x) < 0

Therefore profit maximizing condition is MR = MC