The market for good Q has the demand and supply curves: QD = 40-2P Qs = P-6 The marginal external cost associated with the production of good Q is: MEC = 4+0

Given that Q_D = 40 - 2P and Q_S = P - 6

at equilibrium, Q_D  = Q_S

So, by equating both we get the value of Equilibrium Price P and Equilibrium Quantity Q as -

40 - 2P = P - 6

or, 3P = 46

or P = 46/3

P = 15.33

similarly from Supply Equation, putting value of P,

Q = P - 6

or, = 15.33 - 6

Q = 9.33

Now, MEC = 4 + 0.5 Q

or, MEC = 4 + 0.5 * 9.33

or, MEC = 4 + 4.66

or, MEC = 8.66

This causes negative externality that the Government is trying to remove. Thus the production of each unit of output will cost an extra charge of 8.66; which results in reduction of net benefit of the economy.

Difference between the Equilibrium price P and MEC is ( 15.33 - 8.66) = 6..67

Thus the government must introduce a Tax equal to 6.5 to bring down the effectiveness of the externality. ( not a tax of 9 as then the producers will not be able to pay that amount of tax, they might have to stop production in near future.)

The goverment must imply tax and not subsidy as this is a case of negative externality that the government is trying to solve or reduce its impact. The Tax implied will help them in controlling the degree of effectiveness of the MEC which is faced by the economy as a whole. Subsidy must be provided only when there is a case of positive externality.