# VAT revenues, where to tax? Portuguese case

Currently in Portugal we all know government has to reduce the fiscal deficit, that’s something taken as given (the end). What we don’t know is the best way to achieve it (the means). The ways to achieve a given outcome are based on political decisions, we might reach the agreed budget deficits by cutting more expenditures, putting more efforts on economic growth or increasing taxes. This article focuses on the latter.

When we talk about taxes’ increases too criteria come: efficiency, equity. Efficiency relates to social welfare that is lost by imposing a tax and equity is how spread is the cost or loss coming from a tax among economic agents.

Regarding efficiency, taxes as VAT, that have a direct impact on markets (supply and demand of a given product), originate distortions and these distortions are the loss of efficiency or welfare by introducing a tax. Basically they are measured as the difference between the quantity the market wants to consume of a given product (aggregate demand) and the quantity actually consumed due to the tax (VAT will increase price paid by the final consumer so the quantity demanded is expected to be lower). In economic terms there is a deadweight loss (DWL) – transactions that have an economic value could have taken place if it wasn’t the tax in place. The key question now is to know what determines the extent of the DWL?

In a simplified model of linear supply and demand, the DWL is characterized by the triangle on the graph below:

The amount of the distortion is determined by the tax increase and the variation in the quantity demanded. This means that for the same tax rate the distortion is higher for larger price elastic products, i.e. when consumers are more sensitive to prices imposing a tax (which is the same of saying the consumer pays more for each unit) will result in a bigger wedge between the desired and the actual quantity demanded.

Where “e” is the price elasticity of demand – the percentage change on the quantity demanded by one per cent increase in price paid, on average, ceteris paribus. The derivative of the DWL on elasticity is positive meaning that the more sensitive the consumer is the larger the market distortion or inefficiency generated. Graphically:

For the same tax rate (and let’s assume for the same government revenue, i.e. the quantities on both graphs are equal to generate the same revenue t*Q), we are better off by taxing the inelastic good. If we need to tax (as the Portuguese case mirrors), we ought to tax more inelastic markets, where distortions will be lower.

Take this small model to the Portuguese reality. For my surprise last week, when I was travelling from Coimbra to Lisbon by bus, the VAT charged was 6%. The government budget for 2012 predicted a VAT increase to 23% on restaurants and cafés (increased 10pp). Was this the best political choice? First the financial argument, second the economic argument.

Let’s assume the government needs a given revenue (say T). In order to get T, government will impose a tax (t) on the market price which will affect the quantity consumed. The larger the market, the same tax (t) yields higher revenue. According to Portuguese Statistical Bureau (INE) the gross-added value for transports and restaurants was 3,464 and 1,8 billion € (American billions) in 2004. To get T government will need a lower tax (t) on transports compared to restaurants and cafés. If this is so the distortion caused is lower.

Furthermore from the economic view, we have different price elasticities for both goods. Fouquet (2012) estimates an elasticity of -0,6 for transports and Anderson et al. (1997) -2,3 for restaurants. Transportation is more inelastic than restaurants meaning that if VAT had increased on transports instead of restaurants, the distortions and inefficiencies would have been lower.

When the analysis seems to be more macro it might be the case where the answers are on the micro details. The government needs to save, however if it can save causing less inefficiencies the better for the society and for government itself, because inefficiency means loss in GDP.

References:

IMTT; Fouquet, Roger, Trends in income and price elasticities of transport demand (1850-2010), BC3 Working Paper Series 2012-01;

Anderson, Patrick, McLellan, Richard, Overton, Joseph and Wolfram, Gary, Price Elasticity of Demand, 1997;

INE;

Barómetro, Departamento Económico e Estudos, edição nº 2, 2007.

Gustavo Almeida