The Effect of Inner Mobility of Shops on Tax Revenue

概要

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In this note we consider a simple model of a service sector. In this service sector there are two types of shops, each offering distinct services at differential prices with fixed cost possibly being also unequal. When the decrease of customers is experienced by one of these two types, not both, then having less profits, those shops belonging to the damaged type can shift to the other type, thus alleviating losses on the whole. This can also mitigate the effect on tax revenue. The typical sector which the authors have in mind is that of pubs and restaurants where two types are the 'first-rate (more expensive with more services)' and the 'popular' class. Based on this model, we conduct an elementary comparative statics analysis. Most results are natural consequences, which can be inferred without using equations. And yet we supply proofs based upon equations and inequalities. Our main result is that with migration between two groups, the sector may incur less loss against the decrease in customers, especially that in the first-rate class. This means the effect on tax revenue is also milder with shiftability. Our model in this note is quite restrictive because the size of customers is exogenously given and does not respond to price differentials. Moreover in the analysis of comparative statics, the number of shops is fixed with no entry and no bankruptcy. These constraints should be removed in a more general framework.
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