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Unformatted text preview: Lecture Note 1: Introduction to Welfare Economics Part 2B: Paper 1. & Dr. T.S. Aidt University of Cambridge Michaelmas 2010 1 Introduction This lecture note provides a brisk reminder of the basics ideas, results and concepts of welfare economics. Most this is should be familiar from last year. The note sets out the details of a baseline model. We shall make use of various versions of this model to illustrate and discuss many of the major results about optimal tax policy in the lectures to come, so it is worthwhile getting familiar with it from the beginning and also to get used to the notation. It also contains a detailed discussion of the three Pareto conditions, of why they may fail, and of the Principle of Targeting which can be used to guide policy choices in a &rst best world. 2 The Baseline Model: Notation and Assump- tions The lectures draw on a (large) number of di/erent textbooks and journal articles, each of which use their own notation and symbols. These should, of course, be clear from the context. In the lectures (and the associated notes), I am aiming at using the following notation and terms consistently. 1. Consumers are indexed by h with h = 1 ; 2 ;:::H . In some contexts, where we look at a representative consumer, the index h can be drops. In other contexts, where there are two types of consumers, it can be useful to index them with letters rather than with numbers, e.g., h = A or h = B . 2. Firms or producers are indexed by j with j = 1 ;:::J . & Disclaimer: This note may contain mistakes. If you spot any, please bring them to my attention. 1 3. Commodities and factors of production are indexed by i = 0 ; 1 ::;N . In general, there can be any number of produced goods and any number of factors of production. We (mostly) consider two special cases: (a) One-factor-of-production-many-outputs case: we assume that there is only one factor of production, labour, and this factor is given the index and denoted by l , while the produced goods are then indexed i = 1 ;::;N . (b) Two-factors-of-production-two-outputs case: we assume that there are two factors of production, labour l and capital k , and two pro- duced outputs ( x 1 and x 2 ). Capital is always assumed to be in &xed supply and all variables related to capital (e.g., its price) is indexed by k . 4. Consumption of commodity i by consumer h is denoted by x h i . 5. The supply of labour by consumer h is denoted by l h and the (total) supply of capital (if any) is denoted k . The total amount of time available for work by consumer h is T h and the amount of leisure consumed is then L h = T h & l h . 6. The output produced of commodity i by &rm j is denoted by y j i . 7. The consumer prices of the N commodities are denoted q = ( q ;q 1 .... q N ;q k ) and the producer prices are denoted p = ( p ;p 1 .... p N ;p k ) . Consumer and producer prices may di/er if the government levies taxes on the commodi- ties. We denote the vector of commodity taxes by t = ( t ;t 1 ::::;t N ;t k ) . If....
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