An alternative way to model merit good arguments

tax rates, t^c , say. Since all substitution effects are proportional to supernumerary
income, (21) reduces to

On the other hand, because the income effects are independent of income,
(23) can be written as β^hr(t^c) = r(t), where r(∙) denotes the net increase in gov-
ernment revenue from a marginal increase in the lump sum grant to a consumer.
Combining both results gives:

rr(⅛ ^tc =^{t                               (44)}

If then r(t) > (<) r(t^c) then t^c À (≪) t.  Because both income effects are

positive, this implies that r(t^c) > (<) r(t), a contradiction. Therefore t^c = t and
β^h =1 (all h).

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