Some Taxation Theorems in the Hotelling Model

In this paper, we investigate the relationship between the demand ad valorem, cost ad valorem and unit taxes in terms of price, quantity and tax revenue. In particular, we prove that the Musgravian transformation holds in the Hotelling model. In addition, we show that the Suits‐Musgrave theorem must be revised as output in the Hotelling model remains invariant in the presence of different taxes. That is, for a given price instead of a given output, the tax revenue under demand ad valorem tax exceeds that under the corresponding unit tax as long as profit levels for both stores are positive, a very general assumption. The exception is when the two stores are located close to each other and transportation cost is zero. Only in this case, are tax revenues and price under both tax regimes the same. If both stores are symmetrically located, the superiority of the ad valorem tax holds true except when the two stores are located back to back. Finally the farther away the location of a firm from the end point is, the smaller the difference in tax revenues between demand ad valorem and unit tax will be: the effect of the Suits‐Musgrave theorem weakens in the presence of location clustering