Answer to Question #210681 in Math for Jadi

Question

Suppose the following market model for sugar in Pakistan.

Qd = 18 - 2P, and Q s= -2 + 2P

If Govt. wants to levy a tax upon this product, what is the optimal tax rate at which she can achieve

maximum tax revenue?

Answer 1

If Qd = 18 - 2P and Qs = -2 + 2P, then in equilibrium Qd = Qs, so:

18 - 2P = -2 + 2P,

4P = 20,

P = 5,

Q = 18 - 2×5 = 8 units.

Pd = 9 - 0.5Q,

Ps = 0.5Q + 1,

Ps + t = 0.5Q + t + 1.

If Govt. wants to levy a tax upon this product, then the optimal tax rate at which she can achieve maximum tax revenue is:

Ps + t = Pd,

0.5Q + t + 1 = 9 - 0.5Q,

Qt = 8 - t.

Tax revenue is:

$TR(t) = Qt×t = 8t - t^2.$

Tax revenue is maximized, if TR'(t) = 0, so:

8 - 2t = 0,

t = 4.