The tax has been proposed because, apparently, when people buy products from supermarkets, less of the money circulates within the city and more is spent outside by the supermarket than when the people buy products from small shops.
Let us illustrate this by considering two towns – Hull and Carlisle. Hull is surrounded by pig farming areas and Carlisle by sheep farming areas. Both areas have a strong natural relative advantage in rearing the respective animals. Assume that, in both Hull and Carlisle, small shops buy lamb and pork from local areas because of the cost of sourcing on a non-local basis, and also assume that large shops in both towns buy pork from East Yorkshire and lamb from the Lake District. For the purposes of illustration, let’s say that an acre of land in East Yorkshire can husband 200 pigs or 100 sheep and, in the Lake District, 90 sheep can be reared on an acre or 50 pigs. In other words, East Yorkshire has a strong comparative advantage in pigs and the Lake District in sheep – though East Yorkshire is better at producing both.
If there is a Tesco established in both Carlisle and Hull, it does both areas a great favour by sourcing lamb and pork from the cheapest place. An acre under pasture in both places, with the pigs being reared in East Yorkshire and the sheep in the Lake District will yield the two shops 200 pigs and 90 sheep to share between the residents of Hull and Carlisle.
Now, let us assume that the modern-day protectionists come along and impose a tax on Tesco, purely on the ground that it is not buying local produce and let us assume that such a tax does, indeed, lead to the Tesco being replaced by local butchers who buy everything locally because the expense of setting up a national buying network is too great. From each acre of Lake District land we are now able to obtain 45 sheep and 25 pigs (or other combination as appropriate) and, from each acre of East Yorkshire land, the Hull butchers will obtain 100 pigs and 50 sheep. The total production of pigs has fallen by 75 although 5 more sheep are produced. It is impossible for the 5 sheep to be worth more than the 75 pigs given the rate at which pigs and sheep can be exchanged for each other in the production process. There is a huge potential welfare loss here.
Of course, things will not work out exactly as suggested in this stylised example, but the effect will be the same. The council in Derby (one of the towns that wants the tax) will tax Tesco because it spends money on produce from Oxford (another of the towns that wants the tax) and vice versa. A classic tariff on goods going from Oxford to Derby and in the other direction would reduce trade and force people to produce things they were less efficient at producing. This proposal is slightly different because the tax will not vary with the actual amount of goods imported by Tesco from Oxford to Derby – it is merely levied because supermarkets tend to import goods from where they can be produced most efficiently. As such, the effect will be different from that of a tariff but detrimental in similar ways. The tax will raise the cost of operation for large shops and thus make it less likely that large and efficient shops that use large and efficient distribution networks will establish themselves. If the tax reduces the number of large shops, it will not help the local economy – it will simply lead the local economy to produce things less efficiently.
If the tax does not reduce the number of large shops, it simply redistributes money from shoppers in large shops to the local authority.
These proposals are essentially based on the economic reasoning of the early eighteenth century. It is assumed that it is better if we all buy locally rather than buy things from where we prefer to buy after taking into account the explicit costs and the subjective benefit of buying from a local trader. If we are all forced to buy locally (or taxed into such a decision), it reduces specialisation and trade. Instead of working as an academic, I should really be growing turnips for my own personal consumption whilst turnip farmers teach their children actuarial mathematics at home. In other words, we should all go back to a subsistence economy.
When people teach creationism in schools (or if people were to try to teach that the earth is flat) they are publicly ridiculed. However, the very same chattering classes who do the ridiculing wish to enshrine flat-earth economics into public policy.
 The welfare loss can be illustrated by assuming that, in East Yorkshire, 110 pigs and 45 sheep are produced. The total production of pigs has fallen by 65 and the total production of sheep is now the same.