(b) Assume that a lump-sum tax is imposed on the producers of good x. What happens to the deadweight loss. Explain.
Dead weight loss is inefficiency,, in that someone (Third party) is being harmed and is not being compensated. The government steps in and (theoretically) taxes the producers causing them to internalise the cost of the externality. In theory, the costs of the producer increases and production decreases.
A lump-sum tax is viewed by producers as a fixed cost,, a cost of doing business with no connection to output. Fixed costs have to be paid if you produce or not. So, a lump-sum tax will not change or affect the variable costs (marginal costs) of a producer. Therefore, the firm who pays a lump-sum tax will not alter its amount of production. There will be no change in quantity produced and therefore would be ineffective as an incentive to get a producer to internalise the cost and produce less quantity of the negative externality.
IF marginal costs do not shift then the firm will stay at that profit max quantity.
Answer - One point is earned for stating that the deadweight loss does not change because marginal cost does not change.