An alternative way to model merit good arguments

Appendix

• Derivation of the first best tax rules.

The first order conditions for an interior maximum are given by:

Performing ∣L — ^dLx and ∣L — ^dLy gives:
'ɔ Otx     OT          Oty ∂T & 'ɔ

where a^denotes a compensated price effect and 7 =^f ~. Using the homogeneity
condition on the compensated price effects, (31) may be rewritten as

Because the substitution matrix (Oqx O q^y ) is negative definite, (32) reduces to

Oq x Oq_y

^u.           ^U2     A /           ^ug                      /99 A

7tχ = qx--g , and γty = q_y--_y.                   (33a)

^u1                  ^u1

Inserting these conditions back in the FOC for T, shows that 7 = 1.

Since q_x = u² and q_y = uɪɪ, the first best tax rates are as in the text.

• Derivationof u^g(z,x,y)

By definition of F(∙)

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