The Social Cost of Federal Financing 129 



(10) AUi = ii ^ ^Ci + h- '^ ^^^' ""^ 



(11) AUr = ii -^ ^Y^. 



We define a Social Welfare Function for all the individuals / in the 

 economy. 



(12) W = ti Ui. 

 Then 



(13) aWc = Sf ii A^i, where c refers to costs. 



We assume that is the same for all individuals and equal to 



the arbitrary constant a. Then 



(14) AW.^atiii^Yi. 



Al^c measures the costs in the analysis. The benefits are a flow of 

 future annual income accruing to various individuals, or 



(15) B = tiAB^. 



Assuming the value of marginal future income the same for bene- 

 ficiaries as for taxpayers, we have 



(16) AWj, - aSiABi. 



In order for a project to represent a favorable economic change, 

 the value of benefits must exceed the value of costs, or AlT^ > Alt',. 

 This requires 



(17) a%i ABi > aSi ii ^Y i- 



This inequality is unaflectcd by the value for a- For convenience, 

 let a = 1. Then the criterion becomes 



(18) %i AB, > v^ ,, aF^ or 



Xi ab, 



2.1 li Ai ; 



Use of the interest rate that our analysis seeks to estimate for 

 benefit-cost analysis is ecjuixalent to criterion (19). We have esti- 



