A simple model for merit good arguments

Journal of Public Economics 43 (1990) 127-129. North-Holland

A SIMPLE

MODEL

FOR MERIT GOOD

ARGUMENTS

A Comment

James P. FEEHAN* Memorial University of Newfoundland, St. John’s, Newfoundland, Canada AIC X37

Received May 1989, revised version received March 1990

In a recent contribution, Besley (1988) derived first-best and second-best subsidy rules for merit goods. This focus on policy formulation in the presence of merit goods may be considered quite desirable in light of, on the one hand, the merit good arguments which often underlie actual policy and, on the other hand, the limited attention paid to merit goods in the theoretical literature. Unfortunately, Besley’s first-best subsidy rule is inaccurate. This note identifies the source of the problem and provides the correct rule. The key feature of the Besley model is a divergence between the state’s and the individual’s assessment of the individual’s utility. The hth person ranks utility according to

Uhbh, Yh), where U”is an increasing, strictly quasi-concave, able function, x is an n-dimensional vector of quantity of a single merit good. The distinction goods follows from the state’s evaluation of differing evaluation is given by

(1) twice continuously differentinon-merit goods and y is the between merit and non-merit the individual’s utility. That

f#Jh( Xh,y")= u”(Xh,Bhyh),

(2)

where tIh> 1 (0” c 1) corresponds to a merit (demerit) good. There are no other sources of distortion or market failure and there is a standard utilitarian social welfare function, W( .), defined over individual utilities. In this setting, to achieve social optimum, state intervention may be *The piece was written while the author was visiting at the University of Western Ontario. Helpful discussions with Nicolas Schmitt and Ronald Wintrobe are gratefully acknowledged. 0047-2727/90/$03.50 0 199&-Elsevier Science Publishers B.V. (North-Holland)

128

J.P. Feehan, Merit good arguments

limited to lump-sum redistribution and the establishment of person-specific subsidies for the merit good. Besley (equation 3.8, p. 376) gives the formula for these subsidies as

Th= (1 - Oh)/P.

(3)

This is not, however, generally correct. An example is su~cient to illustrate this contention. Consider the case of a single merit good and a single nonmerit good in which utility functions are of the Cobb-Douglas type:

Uh(Xh, Y”)=(~*~(h)(yh)~(h). These are-re-interpreted

(4)

by the state as

(5) This simply amounts to changing the weights on individual utilities as they enter the social welfare function. If social welfare is maximized over (5) rather than (4), then a different income distribution is required and, contrary to (3), no subsidies on the merit good are called for. It is a mis-interpretation of the relationship between the partially indirect utility functions associated with (1) and (2), which is the source of the problem in Besley’s analysis. These partially indirect utility functions are written, respectively, as

gh(p3 YhYmh)

(6)

g”(P, ohyh,

(7)

and mh),

where p denotes the price vector for the non-merit goods, and nzh denotes the lump-sum transfer to the hth person. In deriving (3) Besley takes the following to be true:

and $P.

BhYh, m”) = 3

(p, yh, mh).

(9)

J.P. Feehan, Merit good arguments

129

Neither of these hold in general. The reader may readily confirm this by using the example of Cobb-Douglas preferences. The correct specification of the person-specific subsidies may be obtained by following Besley’s procedures and adjusting for the above problem. The result is:

Zh,

ati(P, @yh, mh)

$P>Y”, mh)sakT b, Yh, m”) $(P,

b-hehYhv m”) a

I$

OhYh,m”)

(P, ehyh, mh)

Reference Besley, T., 1988, A simple model for merit good arguments, 371-383.

Journal of Public Economics

35,