Tax and Spend 2

 Tax and Spend version 2

  

   Back in July 2016, I wrote a piece on this blog titled "Tax and Spend" [1]. I remarked at the surprising fact that neither the 'Deficit

Spending' school of macroeconomists (Keynes, Klugman, Chick & Pettifor, etc.), nor the 'Austerity' school (Hayek, Friedman, etc.) seemed to be able to convince the other school. Each could see the power of their own argument but not that of the other school. The issue was left in the hands of the politicians,  who were ill equipped to understood either argument.    I could understand parts of each school, but hoped there was a simpler way of revealing the logic. I tried to build a simplified model of the national economy; crude but robust. It illuminated very clearly the so-called 'multiplier' whereby money injected into the system goes round and round, doing more good, to more people, than you might at first expect. I ended, not as a 'Deficit Spender' but a 'Tax and Spender'. 

     I have gone over the argument again, improving and correcting. Let me show you. 

     Imagine a country that neither imports nor exports, neither goods nor services. Suppose that, in a certain fiscal year, the aggregated income (AI) of its citizens is 1 trillion pounds sterling (AI=1,000B£). Imagine that every citizen pays income tax (IT) at a flat rate (ITR) of 20p in the pound on all income (ITR=0.2), saves (S) 18% of net income (S=0.18), and spends the remainder. 

     (To estimate the fraction saved I shall consider incomes of greater that £200,000 p.a. to be saved and not spent. Clearly these super-rich will spend a little; but, equally clearly, some of the merely-rich will save a little. HMRC figures for 2022/3 suggest that total national income was 1347 B£, while that earned by the super-rich (so saved in this model) was 244 B£. So 18.11% of the total. For convenience I count as saved 18% of net income.)

     (I note that approximately 1/3 of UK government revenue comes from VAT and that governments use VAT as a fine-grained  way of directing our spending patterns. (Thus, food is exempt, but ice-cream and crisps are VATed). I shall initially assume that 1/4 of the purchases are VAT-free, and that VAT is charged on 3/4 of the  purchases at a rate of 20% (VATR=0.2).)

     Both the VAT-free and the VATable 'spend' is spent in this notional country, so it forms the gross takings of some of the citizens. If spent on bread, part will buy flour and fuel for the baker, but part will constitute income for the baker. Suppose (initially) that, for every business (or for businesses in aggregate), half the gross taking is spent on raw material (RMr=0.5) and half constitute wages (W). (I.e. Wages/net income = Wr = 1-RMr).   

     Looking now at the income of the government we can see that it is the sum of the income-tax takings (ITT) , and the VAT takings (VATT). What will the government do with the Total Tax (TT)? It will spend a fraction on wages (FW), a fraction on benefits (FB), a fraction on infrastructure (FI) and will waste a fraction (FW). Let us, rather arbitrarily, set these as follows: FW=0.5; FB =0.33; FI=0.1; FW=0.07. Note, however, that benefits constitute the income of a fraction of the population. Also that infrastructure includes roads, schools, libraries, the army, etc., while a fraction of tax inevitably produces no benefit, and is essentially wasted. (I am told that 'Benefits' comprise  roughly 10% of GDP, while wages comprise c. 75% of the cost of  the NHS.)

     All these quantities (see Table 1) enter the model as constants but are initial values only, and the simulation can be re-run with different values. 

     

The Results Table (Table 2) is like a 'Bagatelle Board'. We put 1 T£ in at the top. Some is spent by the citizenry and some is routed to the Treasury. At the end of 'round one' a sizeable fraction (c. 60%) of both tax money and private spending emerges as more income, so that part goes round again. And that again produces more income, repeatedly until the sums get too small to bother with.    

     What we want to know is the final result, in terms of final GDP (fGDP), final saving (fS), final tax (fTT), final infrastructure (fI), final private spend (fPS), and final Waste (fW). (See Table 3.)

Conclusions

(1) The multiplier effect is striking; varying from 2  to 2.5. Seeding with 1 trillion and ending with 2.0 trillion.

(2) A surprising result is that GDP increases 10% when taxes are raised from 20p to 30p in the pound. Presumably because government spending recycles more than private spending.

(3)  Infrastructure benefits by a striking 58% when taxes are raised from 20p to 30p in the pound. The government has 58% more money for roads, schools, army etc. 

(4)  The downside of raising taxes from 20p to 30p in the pound, is that the money for private spending is reduced, but only by some 13%. It need not fall at all for the poorer half of the population, if the tax system is suitably 'progressive'. Tax rises are difficult to sell to the public, but perhaps not impossible, if we need a better army, better roads, and better schools. 

References:

[1] https://occidentis.blogspot.com/2016/07/tax-and-spend.html 

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