Final answer:
The $2 tax on each 12-pack of beer sold in Rockingham County will not increase social surplus because the losses to consumer and producer surplus are not fully compensated by the tax revenue.
Step-by-step explanation:
The imposition of a $2 tax on each 12-pack of beer in Rockingham County is designed to decrease alcohol consumption. This tax will indeed increase social surplus due to the tax revenue (option A), decrease producer surplus as producers get less for each 12-pack (option B), and create a $2 wedge between what consumers pay and producers receive (option C).
However, this tax will not increase social surplus because while tax revenue goes up, consumer and producer surplus usually go down. Therefore, the statement that the tax will increase social surplus (option A) is not correct as the loss to consumers and producers is not typically completely off-set by the gain in tax revenue. Moreover, when a tax is introduced, it typically results in a decrease in consumer surplus because consumers pay more for products (option D).