public goods and technology of consumption: a comment

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The Review of Economic Studies, Ltd. Public Goods and Technology of Consumption: A Comment Author(s): A. Zabalza Source: The Review of Economic Studies, Vol. 44, No. 1 (Feb., 1977), pp. 193-194 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/2296987 . Accessed: 28/06/2014 10:36 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Oxford University Press and The Review of Economic Studies, Ltd. are collaborating with JSTOR to digitize, preserve and extend access to The Review of Economic Studies. http://www.jstor.org This content downloaded from 91.213.220.109 on Sat, 28 Jun 2014 10:36:50 AM All use subject to JSTOR Terms and Conditions

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Page 1: Public Goods and Technology of Consumption: A Comment

The Review of Economic Studies, Ltd.

Public Goods and Technology of Consumption: A CommentAuthor(s): A. ZabalzaSource: The Review of Economic Studies, Vol. 44, No. 1 (Feb., 1977), pp. 193-194Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2296987 .

Accessed: 28/06/2014 10:36

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Oxford University Press and The Review of Economic Studies, Ltd. are collaborating with JSTOR to digitize,preserve and extend access to The Review of Economic Studies.

http://www.jstor.org

This content downloaded from 91.213.220.109 on Sat, 28 Jun 2014 10:36:50 AMAll use subject to JSTOR Terms and Conditions

Page 2: Public Goods and Technology of Consumption: A Comment

Public Goods and Technology of Consumption: A Comment

A. ZABALZA London School of Economics

In an interesting article [2], A. Sandmo has shown how it is possible to obtain a measure of the benefits derived from public goods supply which is not based on the utility functions of the different individuals. In section 5 of [2], Sandmo assumes that the q private goods (y) and t public goods (z), all enter into each of the n final goods production functions 4(*). Given this formulation, the conditions for the efficient provision of public goods are not independent of the utility functions of the s individuals u( ). To eliminate the elements involving utility functions, Sandmo proposes in a subsequent paper [3] an additional assumption: " there is at least one commodity which does not have the property of a joint input; instead, its various uses with respect to final goods production can be identified ".

Under this extra assumption the first-order conditions for efficient provision of public goods are

i- - aF/azr (1 = 1, . ), . ..(1) = j a,ya aFlaYr

where Yr is the private good which does not enter the production functions as a joint input, and F is the transformation function. As desired, the elements involving utility functions have been eliminated. Sandmo argues that the additional assumption needed to obtain (1) is hardly a very strong one, since " it seems to be a very reasonable requirement that not all private goods have a joint input character ".

Unfortunately, the additional assumption as it stands is not sufficient. We need to assume that " there is at least one commodity which does not have the property of a joint input ", and that its marginal productivity in all production functions is positive. In formal terms, the function fj( ) must be strictly increasing with respect to yl j so that a0,/ay', > 0 for all vectors (yij, ..., yij, ..., Yi; z1, ..., zt) for which bj() is defined.

The need for this extra requirement is evident from inspection of (1). If the production of some final goods does not depend on Yr, then some r will be zero, in which case the sum of the marginal benefits derived from the provision of public goods is infinite. This extra condition, added to the original difficulty of identifying different " uses " of the same private good in his role as input, reduces considerably the scope of Sandmo's model. We need now to find a private good which has different " uses " (with positive marginal produc- tivity) in the production of all final consumption goods.

It should be noted that an apparently similar requirement is needed in Samuelson's original formulation of the conditions for provision of public goods [1].

i- - aF/a (j = 1 .., n). ... (2)

The two requirements are, however, different in character. The condition needed for

(2)-au'1/y' > 0, for all i-simply means that a good contributes to utility for all individuals. Unless there is satiation, this is perfectly reasonable. It is a natural requirement that follows from the definition of economic goods: for all individuals, more of them is always preferred to less. But the condition needed for (1)-afj/ay j>O, for allj-is much stronger,

N-44/1 193

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Page 3: Public Goods and Technology of Consumption: A Comment

194 REVIEW OF ECONOMIC STUDIES

and it is not implied by the definition of productive inputs. While the production of some final goods may need the participation of a given input, such an input may not be necessary for the production of other final goods.

First version received October 1975; final version accepted May 1976 (Eds.). I wish to thank A. Sandmo and two referees for their useful comments on an earlier draft of this note.

REFERENCES [1] Samuelson, P. A. " The Pure Theory of Public Expenditure ", Review of Economics and Statistics, 36

(1954), 387-389. [2] Sandmo, A. " Public Goods and Technology of Consumption ", Review of Economic Studies, 40

(1973), 517-528. [3] Sandmo, A. " Public Goods and Technology of Consumption. A Correction ", Review of Economic

Studies, 42 (1975), 167-168.

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