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What value of Y1 makes the consumer indifferent between these two jobs? How does a change in the tax rate affect this level of income?
In a state-contingent income space, each person's indifference curves are generally bowed in toward origin. Why does this imply that the person is risk averse?
Provide an expression for the optimal value of X. For F = ½ and p = ½ show that the declaration X is an increasing function of t.
Use the parameter values from the previous exercise with the modification that pay in the occupation permitting. How is this value affect by an increase in t?
What level of income would you announce? Once declarations are made, will the revenue service act according to its announced auditing plans?
What are the advantages and disadvantages of categorical grants relative to negative income tax?
Provide an argument to establish that the optimal allocation must be Pareto-ancient. What assumptions have you placed upon the social welfare function?
How is the deadweight loss affected by changes in a and b? How does a change in b affect the elasticity of demand at the equilibrium without taxation?
And a poverty line of z = 6, calculate the Sen poverty measure. Explain the values obtained for the two distributions.
Explain how Mr. A and Mrs. B must have very different views about income sharing within a family to end up with such different answers.
Draw the Lorenz curve for this income distribution. What is the approximate value of the Gini coincident?
Should we be concerned with inequality if it is due to differences in ability? What if it is due to differences in effort levels?
What is the Gini index, and how can it be used to determine the impact of taxes and transfers on income inequality?
If children provide utility for their parents, show on a diagram how an equivalence scale can decrease as family size increases.
What economies of scale are there in family size? Are these greater or smaller at low incomes?
Let the utility function be U = 40d½ log(M), where d is family size. Construct the equivalence scale for value of U = 10. How is the scale changed if U = 20.
Show that if t3 > 0, then the measure of welfare loss in part a overestimates the welfare loss. What is then the correct measure of the welfare change?
The production process has decreasing returns to scale. Explain the derivation of the optimal commodity tax when profit is not taxed.
Any firm purchasing a good to use as an input can reclaim the tax it has paid. Assess this tax structure using the Diamond-Merles Production Exigency Lemma.
Show that the optimal allocation with commodity taxation is unchanged when the consumption good becomes the untaxed nume´raire.
Suppose that to overthrow the status quo, an alternative requires 70 percent or more of the vote. Which property of voting is violated?
Show that unidimensional median voting wth single-peaked preferences satisfies the conditions of theorem 5.
What are the relative merits of private insurance compared to coverage of costs from general tax revenues?
Explain why an automaker's willingness to offer a resale guarantee for its cars may serve as a signal of their quality.
What kind of argument based on asymmetric information could support the claim that free meals (an in-kind transfer) are better than the cash handout?