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Unformatted text preview: Lecture Note 6: Ramsey Taxation Part 2B: Paper 1. Dr. T.S. Aidt University of Cambridge Michaelmas 2010 1 Introduction We know from the Diamond-Mirrlees production e ciency result that a gov- ernment in need of revenue with access to a full set of tax instruments should maintain production e ciency and raise the revenue by distorting consumer prices (i.e., the price facing each buyer of a &nal good and each seller of a pri- mary factor of production). This is an important benchmark statement about the structure of taxation. Yet, it remains to be seen how the tax burden should be allocated across di/erent commodities and factors of production. In other words, how does the optimal tax structure look like in a Diamond-Mirrlees world. The answer is called Ramsey taxation after another famous Cambridge economist. The sorts of questions we have in mind include: should the tax on bread and butter be the same as the tax on sports cars and designer cloths? Should all &nal consumption goods be taxed at the same rate (e.g., by a uniform and comprehensive sales tax or VAT) or is there a case for excepting books, baby cloths and food? 2 Ramsey Taxes To study how the government should levy taxes on di/erent commodities and factors of production, we assume from the outset that producer prices are &xed. This implies that the entire tax incidence is borne by consumers, as recom- mended by the production e ciency result. The general question, we are seeking an answer to is the following: suppose the government needs to raise a certain amount of revenue to &nance its spending plans (on public services and goods) or to undertake redistribution, how should taxes on commodities (including pri- mary factors of production such as labour) be levied to minimize the deadweight cost of taxation. 1 2.1 The baseline model The model which we shall study is based on the following assumptions: 1. There are two commodities x 1 and x 2 and one factor of production, labour (hours of work), l . [You can add more goods and factors of production (and most text books do) but this is the minimum you need to get the main insights]. 2. For now, we ignore redistribution (this is the subject of the next lecture), and assume that there is only one consumer. She is endowed with T units of time which can be divided between leisure L and hours of work l , i.e., T = L + l : (1) 3. The direct utility function of the consumer is U ( x 1 ;x 2 ;l ) and is increasing in consumption of the two goods and decreasing in hours of work. 4. Consumer prices are q , q 1 and q 1 . The budget constraint is q 1 x 1 + q 2 x 2 = q l (2) or q 1 x 1 + q 2 x 2 + q L = q T ; (3) where q T is the market value of the endowment of time, sometimes called full income....
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