## Partha Dasgupta

Print publication date: 2001

Print ISBN-13: 9780199247882

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0199247889.001.0001

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# A.10. Cross‐Country Comparisons

Source:
Human Well-Being and the Natural Environment
Publisher:
Oxford University Press

Cross‐country comparisons of GNP per head are today a commonplace exercise. The previous sections have confirmed that the practice is mistaken. So, then, how should cross‐country comparisons be made?

Imagine that we are to compare current well‐being. There is a strong case for comparing the ‘representative’ person's current quality of life in each place.28 It (p.251) is simplest to think of a continuum of closed economies, parametrized by x (a scalar).29 Economies differ in their endowments, population size, and resource allocation mechanisms. However, because we are comparing current well‐being, none of these differences is relevant for the exercise.

The representative person's current well‐being in x is U x. It is an explicit function of x if ‘cultures’ differ and culture is a direct determinant of well‐being. Replacing time by space in (A.8), we have

$Display mathematics$
(A.26)
Earlier it was argued that the constituents of well‐being (e.g. health) are independent of culture. Cultural coordinates are components of what we call resource allocation mechanisms, but they aren't determinants of well‐being in any other respect. So we set ∂ U x/∂ x = 0 in (A.26), which then implies the following.
1. Proposition 9: Current well‐being in x is higher than in any of its immediate neighbours if and only if the accounting value of the commodity determinants of current well‐being in x is greater.

Making cross‐country comparisons of intergenerational well‐being is far harder. It involves deep conceptual problems, arising out of the fact that countries differ in population size.30 I side‐step such problems and assume that the size of the population remains constant in each country and is the same everywhere. Countries differ only in their capital endowments and resource allocation mechanisms. x is now to be interpreted as a composite index of the allocation mechanism.

Let V x be the value function in x. We may then replace time by space in (A.11) to obtain

$Display mathematics$
(A.27)
If the resource allocation mechanisms are the same as well, ∂ V x/∂ x = 0, and (A.27) implies the following.
1. Proposition 10: Social well‐being in a country is higher than in any of its immediate neighbours if and only if it is wealthier than its neighbours.31

Proposition 10 corresponds to Proposition 3.

## Notes:

(28) (‘Which economy would you choose to inhabit if in each you faced an equal probability of occupying every citizen's position?’) The classic on this is Harsanyi (1955). Since the person conducting the thought‐experiment could choose to be very risk‐averse, to focus on the representative person isn't to be insensitive to distributional concerns.

(29) I assume a continuum of economies in order to make use of the calculus. It simplifies the computations. The analysis that follows can be easily adapted for the case where there is a discrete number of economies.

(30) See Sect. A.15.

(31) The structure of accounting prices differs across countries because endowments differ.