Question - Consider a perfectly competitive market for natural gas. Price taking natural gas consumers (electricity plants, industrial producers, and residential users) have an iso-elastic demand function given by: P=100(Q(1/Nd)), where Nd < 0 is the elasticity of natural gas demand.
Price taking natural gas suppliers have an iso-elastic supply function given by P=5(Q(1/Ns)), where Ns>0 is the elasticity of natural gas supply. Suppose the government is considering an ad valorem tax on producers of 10% of the sale price.
a. For Nd between -5 and -1.1 (increments of 0.1) and Ns=2:
i. calculate the change in consumer and producer surpluses due to the tax relative to the no-tax competitive equilibrium.
ii. Calculate the change in deadweight loss due to the tax.
b. For Ns between 1.1 and 5 (increments of 0.1) and ND=-2
i. Calculate the change in consumer and producer surpluses due to the tax relative to the no-tax competitive equilibrium.
ii. Calculate the change in deadweight loss due to the tax.
c. Suppose that Nd=-1.5 and Ns=2. The government when setting the tax argued that producers would not bear the brunt of the tax incidence.
i. Was the government correct in making this assessment?
ii. What were the implications of the government's choice for the efficiency costs of the tax?