# If you charge a single (indirect) tax rate, x% on all goods and services in a country, will you get x% back as tax revenues?

Assuming 100% compliance and no leakages, will charging a single tax rate of, say, 10% give us back 10% of the GDP back as tax revenues?

What could these leakages be in real life that reduce this?

• There is the trivial issue of $\frac{10\%}{110\%}$ being less than $10\%$. – Giskard Jan 26 at 19:30
• You have several answered questions with upvoted but not accepted answers. Consider accepting some? – Giskard Jan 26 at 19:44
• I'll do that! :) – WorldGov Jan 26 at 20:57

Depends on the type of tax, and on whether you assume the government gives the money to people back or just keeps them, but generally no. The exception would be any non-distortionary tax (lump-sum tax, Pigouvian tax etc). But if it is tax that is applied to all consumption then it will create distortions.

This is because while you can tax consumption of goods and services you generally can’t tax leisure (which can be viewed as another good - just sitting and enjoying yourself) so this tax will distort the marginal rate of substitution between consumption of regular goods and services and leisure. The amount of distortion will depend also on whether you assume that for leisure you need to still consume some goods but generally there will be still distortions. So the tax will induce shift from consumption of goods and services (and consequently from their production and production determines the output/income or GDP) to leisure and the government should collect less than 10% of GDP.

Leakages like the fact that some sources of consumptions are hard to tax (like consumption of home production) just make this worse.

What I described above is the substitution (Hicksian) effect. If we assume that government redistributes the money back to people this is the only relevant effect.

If the government decides to keep the money on its account there will be second effect. This is so called income (Marshallian) effect. If the taxes are not returned to people they become poorer and as a result their decision between consumption of standard goods and services (and hence production) and leisure will get affected again by this income effect. In principle, depending on the parameters we would put on utility function, the income effect could cause people to consume more standard goods and services than previously. In that case GDP could actually increase (although overall utility would be lower - but GDP only looks at consumption of standard goods and services, consumption of leisure is not measured by it). Hence in case you assume that government keeps the money it would depend on how income effect would affect consumption of goods and services and leisure and whether this effect would be stronger or weaker than substitution effect.

• If these are the only issues, would it then be fair to say that such a single tax rate, $x%$ would yield us tax revenues that is fairly close to $x * GDP$ in the real world? (Without considering leakages and compliance issues). – WorldGov Jan 26 at 20:56
• @WorldGov not necessarily, depending on the size of tax, and parameters of the model the substitution effect can be quite large. For example, my old MSc thesis advisor currently works on estimating the average excess burden of VAT in the NL and the preliminary results (it’s still unpunished) show that to raise 1€ the tax decreases output by 1,39€. Most goods in Netherlands have 21% VAT... the effect is definitely nonlinear but I would say even being generous at 10% VAT it could easily take 1,10€ to raise 1€. Only for very small % of VAT I would say that kind of approximation would be valid – 1muflon1 Jan 26 at 21:04
• @WorldGov also just to add to my comment I think the NL is good example of country where leakages are low. We have low corruption, most of the economy is cashless and formal (meaning avoiding VAT is difficult since everything leaves paper trail) and generally tax compliance is good... so the result can’t be just mostly due to leakages (although they could bias the result up a bit) – 1muflon1 Jan 26 at 21:09