Comments on “The Efficiency of ‘Benefit-Related’ Business Taxes” By Elisabeth Gugl and George Zodrow Timothy J. Goodspeed Hunter College and Graduate Center – CUNY, CESifo

Type of Production Function Production Tax Capital Tax Log ModularB efficientB under-provided Log Sub- Modular B under-provided B under-provided and less efficient than production tax Log Super- Modular B over-providedB can be under-, over-, efficiently provided

 Modularity defines the relationship between K and B in the production function F(K, B, L).  Changing B changes: ◦ 1. MPK by F KB ◦ 2. F(B, K, L) by F B  If MPK/F is constant as B increases, modular  If MPK/F falls as B increases, sub-modular  If MPK/F rises as B increases, super-modular

 Max (1-t)F(K,B,L) – r*K  = Max (1-t)F(K,B,L) – (1-t) F K (K,B,L)*K  Modular Case: Since MPK/F is constant as B increases, F B is offset by F KB and the effect of the tax/B on “profits” and capital flows is nil.

 Sub-Modular: MPK/F falls with B so the effect F B raises MC more than F KB raises the MB for K, capital flees and underprovision of B MPK K r/(1-tF B ) MB=MPK+F KB *F*(1-t) MB=MPK r K*

 Super-Modular: MPK/F rises with B so the effect F B raises MC less than F KB raises the MB for K, capital flows in and overprovision of B MPK K r/(1-tF B ) MB=MPK+F KB *F*(1-t) MB=MPK r K*

 Max F(K,B,L) – (r+tau)*K  Modular, Sub-Modular: MB rises by less than MC, so capital flees and underprovision  Super-Modular: MB can rise by MC and anything can happen MPK K r + tau MB=MPK(1+F KB K) MB=MPK r K*

 1. What do we know empirically about the modality of production functions?  The literature that came to mind on this topic is the literature concerning public capital and economic growth.  While perhaps not exactly what you are after, it seems like it comes pretty close to estimating F KB

 2. While the model does not have different industries, one wonders whether city/states with different industry characteristics (e.g. different elasticities of substitution) would fare better/worse under the two tax regimes.  3. Or if residents differ in their labor/capital income shares, one wonders about a voting equilibrium. Maybe something to explore … sometime.

 4. Finally, the last simulations are presented with the choice of B instead of t. This reminded me of Dave Wildasin’s paper from a number of years ago that indicates that the strategic choice of spending versus taxes is not necessarily symmetric, so that is something to think about.