Archive for May, 2010

May 18 2010

The role of taxes in income re-distribution – another preview of my textbook

Inequality in the distribution of income is an inevitable result of an economic system that rewards the households with the highest skills, best education and most access to capital with higher wages and incomes in the marketplace.

The existence of poverty, both relative and absolute, poses several obstacles to the improvement of well-being for a nation’s people. Social unrest among the poorest members of society can lead to political and economic instability for a nation as a whole. The hardships experienced by society’s poorest members are ultimately felt by the rest of society as the needs of the poor must be met in one way or another, and in extreme circumstances may lead to a violent struggle between economic classes.

The existence of absolute poverty poses the greatest obstacle to national economies and society as those who experience it are unlikely to contribute whatsoever to national output and economic growth given the desperate state of their health and education. Without promoting some degree of equality in the distribution of income, governments run the risk of undermining their accomplishment of other social and economic objectives. So how do governments achieve more equal income distribution? Before we look at the modern mechanisms by which this objective is achieved, it is important to examine the historical ideology that frames modern economic policy.

For centuries the role of government has been debated among economists. The extent to which it is the government’s job to assure equality in the distribution of income has never been fully agreed upon by policymakers, whose opinions differ depending on the school of economic ideology to which they prescribe. On the far left of the economic spectrum is Marxist/socialist ideology, which believes that households’ money incomes should be made obsolete and each household’s level of consumption should instead be based on the “use-value” of the output which it produces. In a pure Marxist or socialist economy, money incomes do not matter since the output of the nation will be shared equally among all those who contribute to its production. Private ownership of resources and the output those resources produce is wholly abolished in a socialist economy and the ownership and allocation of resources, goods and services is in the hands of the state and production and consumption is undertaken based on the principle of equality.

The slogan “from each according to his ability, to each according to his need”, made populate by Karl Marx, summarized the view that a household’s consumption should be based on its level of need. To take this idea to its logical conclusion, all households in a nation have essentially the same basic needs therefore household incomes should be equal across the nation.

On the other extreme of the economic spectrum is the laissez faire, free market model which argues that the only role the government should play in the market economy is in the protection of private property rights, which assures that the private owners of resources, including land, labor and capital, are able to pursue their own self-interest in an unregulated marketplace where their money incomes are determined by the “exchange-value” of the resources they control. In a laissez-faire market economy, the level of income and consumption of households varies greatly across society as the exchange-value of the resources owned by households determines income, rather than the principle of equality underlying socialism. Each individual in society is free to pursue his monetary objectives through the improvement of his human capital and the subsequent increase in its exchange-value in the labor market.

In today’s world, there exists neither a purely socialist economy nor a purely laissez fair free market economy. In reality, all modern national economies are mixed economies in which governments do much more than simply protect property rights, but do not go so far as to own and allocate all factors of production. The role of government in the distribution of income in today’s economies is relegated to the collection of taxes and the provision of public goods and services and transfer payments.

A tax is simply a fee charged by a government on a person’s income, property, or consumption of goods and services. Taxes can be broken into two main categories: direct and indirect.
  • Direct taxes: These are taxes paid directly to the government by those on whom they are imposed. An income tax is a direct tax because it is taken directly out of a worker’s earned income. Corporate and business taxes are also direct taxes based on the revenues or profits of firms. Direct taxes cannot be legally avoided since they are based on the earned income of each individual. The burden of direct taxes is born entirely by the households or firms paying them.
  • Indirect taxes: These are the taxes paid by households through an intermediary such as a retail store. The consumer pays the tax at the time of his purchase of a good or service and the amount of the tax is usually calculated by adding a percentage rate to the price of the item being purchased. Indirect taxes include sales taxes, value added taxes (VAT), goods and services tax (GST) as well as ad valorem taxes (or excise taxes) which are placed on specific goods such as cigarettes, alcohol or petrol. Indirect taxes can be avoided simply by not consuming certain products or by consuming less of all products. The burden of indirect taxes is born by both households and firms, the proportion born by each is determined by the price elasticities of demand and supply (as demonstrated in chapter 4).

Taxes can be either progressive, regressive or proportional in nature, meaning that different taxes place different burdens on the rich and the poor.

Proportional tax: A tax for which the percentage of income taxed remains constant as income increases is a proportional tax. The rich will pay more tax than the poor in absolute terms, but the burden of the tax will be no greater on the rich than it is on the poor. A household earning 20,000 euros may pay 10% tax to the government, totaling 2,000 euros. A rich household in the same country pays 10% on its income of 200,000 euros, totaling 20,000 euros in taxes, but the burden is the same on the rich household as it is on the poor household. Proportional taxes are uncommon in advanced economies, although some “payroll taxes”, which are those collected to support social security or welfare programs, are payed by employers based on a percentage of employees’ incomes up to a certain level. For instance, the US social security tax is 6.2% of gross income up to $108,000. Regardless of a person’s income below $108,000, he or she will pay 6.2% to the government to support the country’s social security program.

Regressive taxA tax that decreases in percentage as income increases is said to be regressive. Such a tax places a larger burden on lower income households than it does higher income earners since a greater percentage of a poor household’s income is used to pay the tax than a rich household’s. You may be wondering what kind of government would levy a tax that harms the poor more than it does the rich, but in fact almost every national government uses regressive taxes to raise a significant portion of its tax revenues. Most indirect taxes are actually regressive, which may not make sense at first, since a sales tax is a percentage of the price of products consumed consumed. The regressiveness is apparent when the amount of the tax is compared to the income of the consumer, however.

To demonstrate how a sales tax is regressive, imagine three different consumers who purchase an identical laptop computer for 1,000€ in a country with a value added tax of 10% added to the price of the computer.
Income of buyer Amount of tax paid % of income taxed
10,000€ 100€ 1%
50,000€ 100€ 0.2%
100,000€ 100€ 0.1%

The higher income consumer pays the same amount of tax as the lower income consumer, but the the tax makes up a lower percentage of her income than it did the lower income consumer’s. Although they appear to be fair since everyone pays the same percentage of the price of the the goods they consume, indirect taxes such as VAT, GST and sales taxes are in fact regressive taxes, placing a larger burden on those whose ability to pay is lower and a smaller burden on the higher income earners whose ability to pay is greater.

Progressive tax: This is a tax for which the percentage of income taxed increases as income increases. The principle underlying a progressive tax is that those with the ability to pay the most tax (the rich) should bear a larger burden of the nation’s total tax receipts than those whose ability to pay is less. Lower income households not only pay less tax, but they pay a smaller percentage of their income in tax as well. Most nation’s income tax systems are progressive, the most progressive being those in the Northern European countries which, not surprisingly, also demonstrate the most equal distributions of income. Of the various types of taxes, a progressive income tax aligns most with the macroeconomic objective of increased income equality.

A progressive income tax typically consists of a marginal tax bracket in which the increasing tax rates apply to marginal income, rather than to total income. In such a system, the average tax a household pays increases less rapidly than the marginal tax, since the higher marginal rate only applies to additional income beyond the upper range of the previous bracket.

Income range Marginal tax rate
Tax paid by someone
at top of bracket
Average tax rate
$0-$8,375 10%
$8,375-$34,000 15%
$34,000-$82,400 25%
$82,400-$171,850 28%
$171,850-$373,650 33%
$373,850 -$500,000
(and above)
(on $500,000)

Notice in the table above that the total tax paid by Americans at the top of each income bracket is NOT the simply the tax rate times income. Rather, the tax rate for each income bracket only applies to income earned above and beyond the upper boundary of the previous bracket. An American worker earning $8,000, for instance, will pay $800 in income tax. But if his income increases to $10,000 he will NOT pay 15% of the full $10,000, or $1,500. Rather, he will pay 15% on the income earned above $8,375. Such a worker would therefore pay 10% of his first $8,375 ($837.50) plus 15% on the additional $1,625 he earned, which is another $243.75. The marginal rate of taxation (MRT) is the change in tax (t) divided by the change in gross income (yg). His total tax would therefore equal $1,081.25.

The marginal rate of taxation between the first and second income brackets above is found using the equation:

The average rate of taxation (ART) is equal to the tax paid (t) divided by the gross income (yg):

The average rate for workers who fall in the second income bracket above can be found using the equation:

For workers in each of the income brackets above, the average rate of taxation is always lower than the marginal rate of taxation, since tax increases only apply to additional income earned beyond the previous bracket. The graph below shows the marginal (in blue) and the average (in red) rates of taxation for individuals earning between $0 and $500,000 in the United States in 2010.

Marginal and average tax rates in the US

The main argument against progressive income taxes is that taxing higher incomes at higher rates creates a disincentive to work, in effect punishing any increase in productivity or effort among the nation’s workers. However, the fact that higher rates only apply to marginal income, rather than total income, assures that a worker’s after tax income will always be an increasing function of gross income; therefore there will always be an incentive to increase income by working harder, longer, or more efficiently since the increase in taxes will always be less than the increase income.

A progressive income tax system provides governments with an effective means of re-distributing the nation’s income since those with the greatest ability to pay (the rich) provide the nation with far more of its tax revenue than those with the least ability to pay (the poor). The graph below shows the total amount of tax revenue generated by each of the five quintiles of income earners in the United States in 2006. While the lowest 20% of income earners accounted for around 1% of total tax receipts, the top quintile contributed nearly 70% to America’s tax revenues.

Progressive income tax burden:data source:

In other Western economies, progressive income taxes typically account for the largest proportion of total tax receipts by the government. America’s neighbor to the north, Canada, has an even higher top marginal tax rate than the US, and rather than applying to people earning above $370,000, as it does in the US, Canada’s top tax rate kicks in for workers earning just $100,000 per year. In Canada, personal income taxes account account for around 50% of total federal tax revenues, while the corporate tax and the national goods and services tax make up the next largest portions.

As mentioned, the highest marginal tax rates tend to exist in the social democratic nations of Northern and Western Europe. Denmark, a country with a Gini index of 29, has the highest tax rate on top income earners. More significant than the high rate, however, is the fact that it kicks in at such a low income level, around $50,000 per year. This means that a large number of Danish workers are paying a high marginal and average tax rate. The burden of the income tax in Denmark is born not by only the rich, but by the middle class as well. In contrast, Germany’s top marginal tax rate of 47% is only reached when a worker’s gross income exceeds $300,000 per year, meaning the income tax burden in Germany will be born more by the rich than those earning lower incomes, as is the case in the United States.

Marginal tax rates in OECD countries,3343,en_2649_34533_1942460_1_1_1_1,00.html#pir

Arguments against progressive income taxes – the Laffer Curve:

The primary argument against the use of progressive income taxes as a means to redistribute national income comes from the “supply-side” school of macroeconomic thought. Supply-siders, whose views are formed by the classical theory of macroeconomics based on the belief that a free market economy left entirely to its own devices will always gravitate towards a level of production corresponding with full employment of the nation’s resources, believe there is a certain level of taxation at which a nation’s total tax receipts will be maximized. Beyond this point, further increases in the tax rat actually lead to a decline in the amount of taxable income due to the disincentive created by the higher tax rate. The Laffer Curve demonstrates the relationship between tax rate and tax revenue graphically:

At a tax rate of 0% households and firms will keep 100% of their gross income and there will be no tax revenue for the government. At a tax rate of 100%, however, there will also be no tax revenue since no rational individual will choose to work if the government takes everything he or she earns. The supply of labor falls as the tax rate increases since fewer individuals will be willing to work as the government collects higher percentages of their earned income. Therefore there will be no income for the government to tax when the tax rate is 100%.

Since both 0% tax and 100% create zero tax revenue, the Laffer Curve theory holds that at some tax rate (m) in between 0% and 100% the government’s total tax receipts will be maximized.The Laffer Curve is often cited by supply-side advocates as an argument for reducing marginal income tax rates on the top income earners. If, for instance, the tax rate is at y, it is possible that a lower tax rate could lead to higher tax revenue if the falling taxes incentivize individuals to join the labor force and existing workers to work harder and longer hours, creating more taxable income. In addition, entrepreneurs may be more inclined to start businesses and firms to increase their investments in physical and human capital, both activities contributing further to increases in national output and taxable income. At lower tax rates, argue the supply-siders, the level of taxable income may increase leading to higher tax revenues for the government.

It is not clear from the Laffer Curve at what precise level of taxation tax revenues are maximized. The model is most commonly employed by supply-siders to justify their desire for lower income and corporate taxes and a general reduction in the interference of the government in the functioning of the free market. The supply-side argument holds that lower taxes lead to an increase in the supply of labor and capital as households and firms are incentivized to become more economically active, leading to increases in the nation’s aggregate supply and thereby promoting the accomplishment of the macroeconomic goals of full employment and economic growth.

Practice calculating marginal and average rates of taxation in France (2010)

Marginal Income Brackets Marginal rate of taxation Worker’s gross income Tax paid Average rate of taxation
0-€5,875 0% €5,000
€5,876 – €11,720 5.5% €10,000
€11,721 – €26,030 14% €20,000 €1,480.675 7.4%
€26,031 – €69,783 €50,000 19%
€69,783 and above 40% €100,000 €27,537.575
  1. Calculate the total amount of tax paid by a French worker earning €10,000 per year.
  2. Calculate the average rate of taxation the same worker pays. Which is greater, the marginal rate of taxation or the average rate of taxation? Explain.
  3. What will a French worker earning €50,000 pay in taxes?
  4. Calculate the marginal rate of taxation for for a worker whose income increases from €20,000 to €50,000.
  5. What is the average rate of taxation for a French worker earning €100,000 per year?
  6. Evaluate the claim that a progressive income tax decreases the incentive among workers to work harder improve their productivity.

7 responses so far

May 05 2010

Facts and the Phillips Curve: new evidence of the short-run trade-off between unemployment and inflation

Introduction: The following is a selection of a chapter from my new Economics textbook project, the Pearson Baccalaureate Economics text, which will be available to IB Economics teacher for the 2011-2013 school year.

It should be noted that the original Phillips Curve theory did not distinguish between the short-run and the long-run. In fact, the original Phillips Curve itself was a long-run model demonstrating a trade-off between unemployment and changes in the wage rate over a span of 52 years in the United Kingdom.

Up until the early 1970s, the Phillips Curve was treated as a generally accurate demonstration of the relationship between two important macroeconomic indicators. Throughout the 60’s data for the United States showed in most cases that increases in unemployment corresponded with lower inflation rates, and vis versa.

Year 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969
UR 5.5 6.7 5.5 5.7 5.3 4.5 3.8 3.6 3.5 3.7
IR 1.46 1.07 1.2 1.24 1.28 1.59 3.01 2.78 4.27 5.46

As can be seen above, between almost every year of the decade a fall in the inflation rate corresponded with a rise in unemployment. The only exceptions were between 1962 and 1963, when both unemployment and inflation increased slightly, and between 1968 and 1969, when again both variables increased. Phillips’ theory of the trade-off between unemployment and inflation was generally supported throughout most of the decade, as the downward slope of the line in the graph above demonstrates.

Beginning in 1970, however, data for the US began to point to a flaw in the Phillips curve theory. Throughout the decade, both unemployment and inflation rose in the US, as oil exporters in the Middle Ease, united under the Oil Producing and Exporting Countries (OPEC) cartel, placed embargoes on oil exports to the US in retaliation for America’s support of Israel in a war against its Arab neighbors. The resulting supply shock in the US led to energy and petrol shortages and rising costs for US firms, forcing businesses to reduce costs by laying off workers, while simultaneously raising output prices. Several other macroeconomic variables contributed to rising unemployment and inflation in the late 1970s, including the return of tens of thousands of troops from the Vietnam War who entered the labor market and found themselves unemployed as firms reduced output in the face of rising energy costs. The Phillips Curve for the 1970s told a somewhat different story about inflation and unemployment than that of the 1960s.

Year 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
UR 4.9 5.9 5.6 4.9 5.6 8.5 7.7 7.1 6.1 5.8
IR 5.84 4.3 3.27 6.16 11.03 9.2 5.75 6.5 7.62 11.22

Between 1973 and 1974, both the unemployment rate and the inflation rate increased significantly, and even as unemployment increased by almost 3% between 1974 and 1975, the inflation rate fell by less than 2% but still remained at nearly 10%. Unlike the 1960s, the 1970s was a decade of both high unemployment AND high inflation. By the end of the decade, unemployment was at approximately the same level as it was in 1963 (5.8%) but inflation was nearly 10 times higher (11.22% in 1979 versus just 1.24% in 1963). The Phillips Curve theory was apparently busted, as the seemingly random scattering of data in the graph above points to no discernible trade-off between unemployment and inflation throughout the 1970s.

Several prominent economists in the 1970s, including Nobel Laureate Milton Friedman, revived the classical view of the macroeconomy which held that policies aimed at managing aggregate demand would ultimately be unsuccessful at decreasing unemployment in the long-run, since a nation’s output and employment would always return to the full-employment level regardless of the level of demand in the economy. Friedman, whose theory of the macroeconomy would come to be known as monetarism, believed that changes in the money supply would lead to inflation or deflation, but no change in unemployment in the long-run. Monetary policy and its effects on aggregate demand and aggregate supply will be explored in more depth in a later chapter in this book. The basic premise of the monetarists, however, was that in order to maintain stable prices and low unemployment, the nation’s money supply should be allowed to grow at a steady rate, corresponding with the desired level of economic growth. Any increase in the money supply aimed at stimulating spending and aggregate demand would result in an increase in inflationary expectations, an increase in nominal wages, and a leftward shift of aggregate supply, resulting only in higher inflation and no change in real output and employment. Therefore, monetary rules were needed to assure that policymakers would not manipulate the supply of money to try and stimulate or contract the level of aggregate demand in the economy.

By the late 1970s, our current interpretation of the Phillips’ theory as including both a short-run and a long-run model became widely adopted. The short-run Phillips Curve may accurately illustrate the trade-off between unemployment and inflation observed in the period of time over which wages and prices are relatively inflexible in a nation’s economy. For instance, during the twelve month period between July 2008 and June 2009, the level of consumption and investment in the US fell as the economy slipped into recession. Unemployment rose and inflation decreased and eventually became negative in the final three months of the period. The graph below shows the relationship between unemployment and inflation during the onset of the recession in 2008 and 2009.

A clear trade-off appears to have existed in the twelve month period above. At the time of writing, it is yet to be seen whether the unemployment rate will return to its pre-recession level in the United States. Although in the short-run it seems likely that the downward sloping Phillips Curve holds some truth, a look at a longer period of time for the same country tells a different story. The graph below shows the unemployment / inflation relationship during the twelve years leading up to the onset of recession in 2008.

Looking at data for a longer period of time shows that even as inflation fluctuated between 0.5% and 4%, US unemployment remained in a relatively narrow range of between 4% and 6%. Year on year unemployment and inflation often increased together, while at other times demonstrated an inverse relationship as Phillips’ theory predicts it should. The narrow range of unemployment portrayed in the data above is evidence that the Long-run Phillips curve for the US between 1997 and 1998 was more like a vertical line than a downward sloping one. It appears that during the period above the natural rate of unemployment for the United States was around 5%; meaning that even as AD increased and decreased in the short-run, the level unemployment remained relatively steady around the natural rate of 5% in the long-run.

The 1970’s represented a turning point in the mainstream economic analysis of the relationship between inflation and unemployment. Demand-management policies by governments may be effective at fine-tuning an economy’s employment level and price level in the short-run, but as data from the 1970’s and early 2000s shows, in the long-run a nation’s level of unemployment tends to be independent of the inflation rate, and is likely to remain around the natural rate of unemployment once wages and prices have adjusted to fluctuations in aggregate demand. In response to supply shocks such as the oil shortages of the 1970’s, both inflation and unemployment may increase at the same time, calling into question the validity of the original Phillips Curve relationship. Despite the breakdown in the relationship between unemployment and inflation in the long-run, the evidence from the recession of 2008 and 2009 seems to support the theory that an economy in which aggregate demand is falling will experience a short-run trade-off between the rate of inflation and the rate of unemployment.

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