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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?
What is the minimum level of s that will achieve separation? Which kinds of job will be filled by which types of workers, and at what wages?
If there is no depreciation and risk-neutral consumers know that 20 percent of all new cars are defective, how much do the consumers value a non defective car?
New cars sell for $14,000 each, and used ones for $2,000. If cars do not depreciate physically with use, what is the proportion d of defective new cars?
A firm hires two kinds of workers, alphas and betas. One can't tell a beta from an alpha by looking at her. What is the equilibrium of this scheme?
Can the Condorcet winner lose under a transferable vote system? Show how strategic voting can affect the outcome.
Which condition does the Borda rule violate? Which condition does the Condorcet method fail? Why do we wish to exclude dictatorship?
Assume that all voters have an hourly wage of $10 and that it takes half an hour. What is the number of voters at which voting no longer becomes worthwhile?
Discuss the individual benefits that may arise from a preferred party winning. How large are these likely to be relative to the cost of voting?
Consider a scoring rule in which the preferred option is given one point and all others none. Demonstrate the scope for false voting.
Construct an example of preferences for which the majority voting outcome is not the median. Given these preferences, what is the median voting outcome?