Question

In a comparative market model
Qd = a - bp ( a,b>0
Qs = - c + dp ( c,d>0)
Qd = Qs what should be the rate of tax per unit of output that the government should impose in order to maximize its tax revenue?

Answer 1

Qd = a - bp, so pd = (a - Q)/b,

Qs = - c + dp, so ps = (Q + c)/d.

The tax revenue is maximized, when:

t = pd - ps = Q.

(a - Q)/b - (Q + c)/d = Q,

a/b - c/d = Q×(1 + 1/b + 1/d),

$Q = \frac{a/b - c/d} {1 + 1/b + 1/d}.$