Question

How to find a tax that maximizes government tax revenue?

Suppose the market can be described by the following equations:

Demand: P = 10 - Q

Supply: P = Q - 4

Using the given equations find the value of tax per unit that maximizes the government's total tax revenue.

Answer 1

Demand: P = 10 - Q

Q = 10 - P

Supply: P = Q - 4

Let the government imposes $t taxes on sellers

New price that sellers have to receive for their good = Ps + t

at equilibrium, Ps + t = Pd

Q - 4 + t = 10 - Q

2Q = 14 - t

Q = 7 - 0.5t

Total Tax Revenue = Q(t)*t

TR = 7t - 0.5t^2

First order condition,

dTR/dt = 0

7 - t = 0

t* = 7

value of tax per unit that maximizes the government's total tax revenue.= $7

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