Consider two firms with the following marginal abatement costs (MAC) as a function of emissions (E):

MAC_1 = 22 - 2E_1

MAC_2 = 10 - E_2,

and assume marginal external damages (MED) from the aggregate emissions of both firms (E_Agg = E_1 + E_2) is:

MED = .5E_Agg.

To achieve the socially efficient level of aggregate emissions (E*_Agg), the government institutes a per unit tax on emissions.The per-unit tax on emissions is $____.