Econ 4620 Seminar assignment for week 39
Problem 1. Taxes on labour and social efficiency effects. Assume that some measure taken by the government induces further labour supply. Analyse the social gain due to labour supply responses in each of the following cases. i. A group of persons facing a marginal tax rate equal to 1/3 increase their income by 150 000. ii. A group of persons with a wage-rate equal to 150 and facing a marginal tax rate equal to 1/3 increase their labour supply by 100 hours. iii. A group of persons with a wage-rate equal to 300 and facing a marginal tax rate equal to 1/3 increase their labour supply by 100 hours. iv. A group of persons with a wage-rate equal to 300 and facing a marginal tax rate equal to 1/2 increase their labour supply by 100 hours. v. Compare and comment on the results in ii.- iv . vi. A group of persons, initially not working, enter the labour market to earn an income of 180 000 facing an average tax rate equal to ¼ and a marginal tax rate equal to 1/3. Problem 2 Interpreting optimality conditions for a linear income tax. The optimum linear income tax can be characterised by -ncov( ,Z) or by
t cov(b, Z ) 1 wi sit n i
i
i
( Z -G’(t))=0,
where Z is gross income Z is the average gross income G’(t) is the change in the per capita lump sum transfer when the marginal tax rate is increased is the social marginal utility of income b is the net social marginal valuation of income n is the number of taxpayers i is an index identifying individual wi is the wage rate of individual i sit is the compensated tax derivative of individual i’s labour supply Explain verbally the economic content of the conditions.
Problem 3 Distributional effects of commodity taxes. Consider a marginal change in a commodity tax rate. Let us assume (A) that there is an equivalent change in the consumer price. i. Explain in what sense the (private) real income loss incurred by a consumer can be measured by her consumption of the good in question. Make use of the tables of expenditure shares handed out during lectures. ii. Discuss the distributional effects of a tax on jewellery (smykker) when you compare income groups for a given household size, and when you compare households of different size for a given income bracket. iii. Compare the distributional effects of a tax on electricity and a tax on restaurant meals, hotel accommodation etc. iv. How would you assess a proposal to subsidise children’s clothes from the perspective of distribution between households with different number of children and with respect to distribution across income groups. Suppose that instead of granting a commodity subsidy the child allowance (lump sum transfer per child) is being increased. v. What difference would that make in terms of distributional effects, and efficiency effects. vi. Discuss critically assumption (A). vii. Explain why the additional tax burden imposed on the taxpayers is not exactly captured by the measure introduced in #i. Problem 4 Income tax design. Consider a range of people from those with very low income to those with a very high income. i. Discuss conceivable arguments of relevance for the choice of marginal income tax in the various income brackets. It is sometimes argued that it is unfair to face people with ‘ordinary income’ with high marginal tax rates. ii. Comment on this argument from a tax theory perspective.