Tax competition and the efficiency of "benefit-related" business taxes

We consider a model in which business public services must be financed with either a source-based tax on mobile capital, such as a property tax, or a tax on production, such as an origin-based VAT and assess which of the two tax instruments is more efficient. In general, both a capital tax and a production tax are inefficient. However, the production tax is efficient if the production function belongs to the knife-edge case between log sub- and log supermodularity with respect to capital and public services (e.g., a Cobb-Douglas production function), while the capital tax results in underprovision of public services in this case. Similarly, if the production function is log submodular with respect to capital and public services (e.g., a CES production function with an elasticity of substitution greater than 1), a production tax is again less inefficient than a capital tax, although both taxes result in underprovision of the public service. Finally, if the production function is log supermodular (e.g., a CES production function with an elasticity of substitution smaller than 1), a production tax results in overprovision of the public service, while the effects of a capital tax - and thus the relative efficiency properties of the two taxes - are theoretically ambiguous.