Question

The government of Cloneland faces a long-standing constitutional constraint against levying lump-sum taxes. This is unfortunate because everyone in Cloneland is identical. The government must raise a given revenue of R per person to pay tribute to a foreign colonial power that conquered Cloneland many centuries ago. The citizens of Cloneland consume two goods (x1 and x2 ) and they supply labour (L) to earn enough to cover their consumption purchases. The Clones all have a wage of one; producer prices of the two consumption goods are also fixed and equal to one. The government relies on commodity taxes on goods 1 and 2 at ad valorem (percentage) rates τ1 and τ2 to raise the revenue to pay tribute to the colonial power. The Clones have identical utility functions given by U = [1/(1-1/e)]x1¹⁻⁽¹/ᵉ⁾ + [1/(1-1/n)]x2¹⁻⁽¹/ⁿ⁾ - L where e > 0 and n > 0 are constant preference parameters.

We want to determine the characteristics of the relative optimal commodity tax rates on these goods from an efficiency perspective (i.e., which maximize V (1 + τ1, 1 + τ2 ) s.t. R = τ1x1 + τ2x2 where V (·) is the indirect utility function of a representative Clonian, and x1 and x2 are determined by the demand functions which are functions of τ1 and τ2. To do this it is easier to determine the ratio (τ1/1+τ1)(τ2/1+τ2) rather than (τ1/τ2).

Answer 1

The question is about analyzing the impact of ad valorem taxes on consumption and labor supply in Cloneland to deduce the optimal commodity tax rates for achieving efficiency in raising government revenue.

Step-by-step explanation:

The student's question revolves around the determination of optimal commodity tax rates from an efficiency perspective in a hypothetical scenario for a nation called Cloneland. In this case, the focus is on the ratio between the tax rates on two different goods rather than the comparison of the two rates directly. Due to the constitutional constraint that prevents the use of lump-sum taxes, and with the citizens all having identical utility functions and constraints, the government uses commodity taxes to raise revenue. This involves understanding how these taxes would affect consumption choices for goods x1 and x2, labor supply, and the utility of the citizens. The reference information explains how the introduction of taxes impacts national income, after-tax income, and the consumption function, which becomes flatter with the inclusion of taxes due to a reduced marginal propensity to consume. Furthermore, the impact of taxes from a supply standpoint is discussed, describing how a tax can be perceived as an increase in production costs, leading to a change in market prices and quantities.