Question

5. a) Say the Marginal Cost of Public Funds (MCF) associated with a tax on good 1 is $1.75 and the MCF associated with a tax on good 2 is $1.50. Is this tax system optimal from a pure efficiency perspective? Explain your answer. (10)

b) Say that a tax of $10 per unit is levied on a good and at that tax the equilibrium demand for the good is 1000 units. Now say the tax increases from $10 to $11 per unit, and as a result equilibrium demand for the good falls to 950 units. What (approximately) is the MCF associated with the tax (show your work, and explain the steps you are taking)? (10)

Answer 1

5a) It shall be noted that at optimal tax system, the marginal cost of public funds equals to 1.

Since, the marginal cost of public funds associated with tax on good 1 and good2 are each not equal to 1. Hence, the tax system is not optimal from a pure efficiency perspective.

b)

Tax0 = $10 per unit; Equilibrium Qd* = 1000 units

Tax1 = $11 per unit; Equilibrium Qd'* = 950 units

The utility function of the consumer is not provided. Assume, the utility derived is equal to units of goods demanded.

Hence, loss in the welfare due to increased tax = 1000 - 950 = 50 utils

Change in tax collected = ($11*1000 - $10 * 950) = $1500

Thus, the marginal cost of funds associated with the tax is: 50/1500 = 1/30 = 0.033