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= Effects of taxation = The expression "Effects of taxation" is used in this article to analyze the effects that taxation has on consumption choices and labour offer.

General aspects
Effects can be divided in two fundamental categories:


 * Taxes cause an income effect because they reduce purchasing power to taxpayers.
 * Taxes cause a substitution effect when taxation causes a substitution between taxed goods and untaxed goods.

Property tax
Substitution effect and income effect with a taxation of good y. If we consider two normal goods, x and y, whose prices are respectively px and py and an individual budget constraint given by the equation xpx + ypy = Y, where Y is the income, the slope of the budget constraint, in a graph where is represented good x as a function of good y, is equal to -py/px. The initial equilibrium is in the point (C), in which budget constraint and indifference curve are tangent, introducing an ad valorem tax on the y good (budget constraint: pxx + py(1 + τ)y = Y), the budget constraint's slope becomes equal to -py(1 + τ)/px. The new equilibrium is now in the tangent point (A) with a lower indifferent curve.

As can be noticed the tax's introduction causes two consequences:


 * 1) It changes the consumers' real income (less purchasing power)
 * 2) It raises the relative price of y good.

The income effect shows the variation of y good quantity given by the change of real income.

The substitution effect shows the variation of y good determined by relative prices' variation.

This kind of taxation (that causes substitution effect) can be considered distortionary.

Income lump-sum tax
Budget's constraint shift after an introduction of a lump sum tax or a general tax on consumption or a proportional income tax. Introducing an income lump-sum tax (xpx + ypy = Y - T), with a parallel shift downward of the budget constraint, can be produced a higher revenue with the same loss of consumers' utility compared with the property tax case, from another point of view, the same revenue can be produced with a lower utility sacrifice. The lower utility (with the same revenue) or the lower revenue (with the same utility) given by a distortionary tax are called excess pressure. The same result, reached with an income lump-sum tax, can be obtained with these following types of taxes (all of them cause only a budget constraint's shift without causing a substitution effect), the budget constraint's slope remains the same (-px/py):


 * A general tax on consumption: (Budget constraint: px(1 + τ)x + py(1 + τ)y = Y)
 * A proportional income tax: (Budget constraint: xpx + ypy = Y(1 - t))

When the t and τ rates are chosen respecting this equation (where t is the rate of income tax and tau is the consumption tax's rate):

the effects of the two taxes are the same.

Effects of taxes on labour offer
To analyze the effects of taxes on labour offer we can consider a model in which the consumer chose the amount of hours spent working and the amount spent in consumption. Let us suppose that only one good exists and no income is saved.

The consumer has a given amount of hours (H) that is divided between work (L) and free time (F = H - L). The hourly wage is called w and it tells us the free time's opportunity cost, i.e. the income to which the individual renounces consuming an additional hour of free time. Consumption and hours of work have a positive relationship, more hours of work mean more earnings and, assuming that workers don't save money, more earnings imply an increase in consumption (Y = C = wL). Free time and consumption can be considered as two normal goods (workers have to decide between working one hour more, that would mean consuming more, or having one more hour of free time) and the budget constraint is negative inclined (Y = w(H - F)). The indifference curve related to these two goods has a negative slope and free time becomes more and more important with high levels of consumption. It's because a high level of consumption means that people are already spending many hours working, so, in this situation, they need more free time than consume and it implies that they have to be paid with a higher salary to work an additional hour. A proportional income tax, changing budget constraint's slope (now Y = w(1 - t)(H - F)), implies both substitution and income effects. The problem now is that the two effects go in opposite ways: income effect tells us that, with an income tax, the consumer feels poorer and for this reason he wants to work more, causing an increase in labour offer. On the other hand, substitution effect tells us that free time, being a normal good, is now more convenient compared to consume and it implies a decrease in labour offer. Therefore, the total effect can be both an increase or a decrease of labour offer, depending on indifference curve's shape.

Laffer curve
Laffer curve. In this case, the critical point is at 70% of tax rate. Revenue increases until this peak, then it starts decreasing. The Laffer curve depicts the amount of government revenue as a function of rates of taxation. It shows that after a critical rate, the government revenue starts decreasing as a consequence of labour offer's fall. This theory supports that, if the system is situated after that critical point, a decrease in tax rate should imply a rise in labour offer that in turn would involve an increase in government revenue.


 * 1) Jump up^ Artoni, Roberto (2015). Elementi di scienza delle finanze. il Mulino.