A Theory of Piecemeal Policy Recommendations

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The theory of the second best, first formally presented by Lipsey and Lancaster [16], maintains that the abolition of an arbitrarily chosen distortion in an economy with multiple distortions may reduce the welfare of the economy. The main objective of the present paper is to formulate some piecemeal policy recommendations which would definitely result in a move towards efficiency. In particular, we will prove the following: (a) a policy which reduces all price distortions uniformly will improve the welfare of the economy, if it is stable in the Marshallian sense. (b) a policy which brings the highest distortion to the level of the next highest will improve the welfare of the economy, if the good with the highest distortion is substitutable for all the other goods and if the economy is stable in the Marshallian sense. Our results integrate the characterization of the second best solution by Green [9], the analysis of the uniform reduction of tariff and excise tax by Foster and Sonnenschein [8] and Bruno [4], and the demonstration by Kemp [15] that the welfare effect of the tariff reduction in the two commodity world is related to the stability of the economy. In the present paper, an extensive use of the compensated demand function enables us to reveal the underlying relationship among these seemingly unrelated works.' In Section 2, we will define the compensated demand function, and will present its properties used in this paper. The model will be presented in Section 3. In Section 4 we will establish that in an economy with constant-cost technology a uniform reduction in excise tax rates improves welfare provided that the aggregate of income terms weighted by marginal costs (AIM) is positive. We will also show that a reduction of the highest tax rate to the level of the next highest rate improves the welfare if the AIM is positive and if the good with the highest tax rate is substitutable for all other goods. In Section 5 the main theorems will be proved by establishing that the positivity of AIM in the propositions of Section 4 can be replaced by another condition if the economy is stable under the Marshallian adjustment mechanism (which is defined in the text). Section 6 will re-evaluate the theory of the second best from our framework. (This section can be read independently of Section 5.) Throughout this paper, a matrix will be denoted by an upper-case letter; a lower-case bold-faced letter will represent a column vector; its transpose will be shown by a prime; and the ith element of the vector is denoted by the same letter with subscript i, unless stated otherwise.