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$Distribution Exercise #3 Answers (
points)
Please limit your answers to the spaces provided. If necessary, write on the back of the page.
Do not attach printout or additional pages. All questions pertain to the $Distribution module in
the SimEcon® software package.
Make sure that you have read the “$Distribution Manual” and “SimEcon® Operation
Instructions.” These materials may be found at the Class Web site prior to beginning the
exercise. For many of the exercise’s questions, it will be necessary to refer to those instructions.
For many of the exercise’s questions, it will be necessary to refer to your text.
Open the $Distribution module. You will see the “Initial Income Distribution.” Print out or
copy this table for future reference. Look at the quintile distribution. What percent of income is
earned by the bottom 40% of the population? 14.2%. What percent of income is earned by the
top 40% of the population? 70.2%. What is the total GDP of the society? $10,000. What is the
Gini coefficient? The Gini coefficient is 0.598
Click “Continue.” You will arrive at the table entitled, “How Do You Want to Change the
Distribution?” Select the button entitled, “Economic Policy.” The program will respond
automatically. Select “Change Income Tax Rates.” You will arrive at a table of the tax rate
schedule, which is shown below. Before proceeding, answer the questions in the next paragraph.
Current Tax Rate Schedule
Bottom 20%
0.12
2nd 20%
0.15
3rd 20%
0.20
4th 20%
0.25
Top 20%
0.35
What is meant by a progressive tax system? A progressive tax system is one in which those
with high incomes pay a greater proportion of their income than those with lower incomes.
What is meant by a regressive tax system? A regressive tax system occurs where those with
lower incomes pay a greater portion of their income than those with higher incomes. What
is meant by a proportional tax system? A proportional tax system occurs where everyone
pays the same proportion of their income. Is the current tax rate schedule a progressive,
regressive or proportional tax system? This is a progressive tax system.
Suppose the current administration gets its political support from those in the upper income
brackets. Considering the last paragraph, would the administration want a progressive, regressive
or proportional tax system? The administration would want a regressive tax system.
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$Distribution Exercise #3 Answers
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Now, enter the following tax rate schedule.
Current Tax Rate Schedule
Bottom 20%
0.35
2nd 20%
0.25
3rd 20%
0.20
4th 20%
0.12
Top
0.08
Is this a progressive, regressive or proportional tax system? This is a regressive tax system.
Click “Results.” What percent of income is earned by the bottom 40% of the population?
11.8%. What percent of income is earned by the top 40% of the population? 73.7%. What is
the total GDP of the society? $9,334. What is the Gini coefficient? The Gini coefficient is
0.619. Has the distribution of income become more equal or more unequal? The distribution
of income has become more unequal. Has the total income of this society increased or
decreased? The total income of society has decreased. On a positive economic basis, i.e.
considering only the total benefit to society, does this tax system represent sound economic
policy? No (Yes, No). Why or why not? This policy is not sound because it has caused a
net decrease in total GDP. Do the upper classes benefit more from this tax system than do the
poor? Yes (Yes, No). Is the total income received by the top 20% higher or lower? Lower.
How much has that income changed—show your calculations. Before the top 20% received
47.4% of $10 trillion. After the change they receive 50.5% of $9.334 trillion. Their income
has dropped from $4.74 trillion to $4.71 trillion.
Click the “Back” button twice. When you see “How Do You Want to Change the Distribution?”
select “ Economic Disturbance.” Suppose that we could compare this country to another nation
which is identical in every way except for the initial distribution of wealth. Suppose this other
nation had a more unequal distribution of wealth. First, what is the difference between wealth
and income? Wealth is the net value of everything that a person possesses at a given point
in time. Income represents the flow of revenues that a person enjoys over a period of time.
Select “Change Wealth Distribution.” Fill in the amounts below for the current wealth
distribution in this nation.
Current Wealth Distribution
Bottom 20%
-0.05
2nd 20%
0.25
3rd 20%
4.50
4th 20%
11.90
Top 20%
83.4
The figure for the bottom 20% is negative. What does this mean? This means that the typical
person in the bottom 20% owes more than he or she owns (more debts than assets). The
typical net worth of this group is negative. Fill in the following new amounts for a revised
wealth distribution on the next page and click “Results.”
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$Distribution Exercise #3 Answers
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New Wealth Distribution
Bottom 20%
-0.05
2nd 20%
-0.05
3rd 20%
-0.05
4th 20%
0.00
Top 20%
100.15
Look at the quintile distribution. What percent of income is earned by the bottom 40% of the
population? 14.1%. What percent of income is earned by the top 40% of the population?
71.6%. What is the total GDP of the society? $10,000. Click See Graph and look at the Gini
Coefficient. What is the Gini coefficient? The Gini coefficient is 0.612. Compared to the
initial distribution that this module started with, has the distribution of income become more
equal or more unequal? The distribution of income has become more unequal. Has the total
GDP of society changed, compared with the initial situation? No (Yes, No). Thus, from a
positive economic standpoint, i.e. concerned only with facts and only with maximizing total net
benefit, would an economist support, oppose or be indifferent to this policy (Give reasons for
your answer)? The economist would be indifferent to this policy because it results in no
change in total income. However, what might be some of the normative (value judgment)
arguments against this policy? A normative analysis would include consideration of equity.
If there were reason to think that the greater degree of inequality was caused by unfair
means, that would be a reason to change it. One theory of justice (Rawls) requires
everyone to ask if this degree of inequality would be acceptable to them if they did not
know whether they would be among the wealthy or the poor. If a distribution would not be
acceptable, that distribution would be considered unjust.
Click the “Back” button twice. You will see “How Do You Want to Change the Distribution.”
At this point, lets take a different approach. Suppose that the government of this nation had great
concern for the plight of the poor. Select “Economic Policy.” Select “Change Welfare Budget.”
Given this government’s new intentions, how should it change the size of the welfare budget?
The government should increase the welfare budget. Which group of people do welfare
programs primarily benefit? They primarily benefit those in the bottom portion of the
income distribution. Enter a value of 8% and click “Results.” You will see the table entitled,
“Results of Setting the Welfare Budget.” Click “Quintile Results.” What percent of income is
earned by the bottom 40% of the population? 20.90%. What percent of income is earned by the
top 40% of the population? 63.05%. What is the total GDP of the society? $9,735. What has
happened to the Gini coefficient? It is now 0.55.
Compared to the initial distribution that this module started with, has the distribution of income
become more equal or more unequal? The distribution of income has become more equal.
Has the total GDP of society increased or decreased, compared with the initial situation? Total
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$Distribution Exercise #3 Answers
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GDP has decreased. Why would this policy decrease GDP? This policy may decrease real
GDP because it reduces the incentives to produce. A poor person who now receives more
welfare benefits is less desperate for a job and may work less (produce less). Taxpayers
who are paying for these benefits may reduce their efforts also since they are being
“forced” to share their production with welfare recipients. Thus, from a positive economic
standpoint, i.e. concerned only with maximizing total net benefit, would an economist support,
oppose or be indifferent to this policy? (give reasons for your answer)? The economist might
be opposed to this policy because of this cost. However, what might be a normative (value
judgment) argument in favor of this policy? Some might argue that this policy is more
humane and “fair” and “just.” Click “See Graph” and draw the resulting graph on the next
page. Indicate the old Lorenz Curve, the new Lorenz Curve, the 45-degree line, and label all
axes.
Percent of
Families
0
20
Percent of Income
40
60
80
100
Dashed Line = 45-Degree Line; Thick Line = New Lorenz Curve; Thin Line = Old Lorenz Curve
What is the Lorenz Curve and what is it purpose? The Lorenz Curve is a plot of the quintile
distribution. The purpose of the Lorenz Curve is to graphically depict the equality or
inequality of the distribution of income in a given economy. What does the 45-degree line
depict? The 45-degree line indicates an exactly equal distribution of income, where
everyone gets an equal share of the income pie. If the Lorenz Curve is stretched out further
away from the 45-degree line, does that indicate a more equal or more unequal distribution of
income? That indicates a more unequal distribution of income. If the Lorenz Curve is
located closer to the 45-degree line, does that indicate a more equal or a more unequal
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$Distribution Exercise #3 Answers
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distribution of income? That indicates a more equal distribution of income. Look at the
new Lorenz Curve that you drew above. Considering the first three quintiles, has the distribution
of income become more equal? Yes (Yes, No).
Click the “Back” button three times. You will arrive at the table entitled, “How Do You Want to
Change the Distribution.” Select “Economic Disturbance.” Suppose that this government
wanted to affect the unemployment rate. Given its concern for the poor would it seek to
increase, leave unchanged or decrease the unemployment rate? (Give reasons for your answer.)
This government would want to decrease the unemployment rate because joblessness
primarily affects the lower and middle-income groups. Lowering the unemployment rate
would increase their earnings and would result in a larger proportion of income going to
them even though the absolute incomes of those in the upper income group could even rise
as profits, rents, etc. increase.
Select “Change Unemployment Rate” and enter a rate of 2%. Click “Results.” What percent of
income is earned by the bottom 40% of the population? 15.70%. What percent of income is
earned by the top 40% of the population? 68.90%. What is the total GDP of the society?
$10,371. Has the total income of the top 40% increased, decreased, or remained the same?
Total income for this group has gone up. What was the income of this group before and after
the change? Before the change the top 40% received 70.2% of $10 trillion, or $7.02 trillion.
After the change this group received 68.9% or $10.371 trillion, or $7.146 trillion, an
increase of $126 billion. What is the Gini coefficient? It is 0.59.
Compared to the initial distribution that this module started with, has the distribution of income
become more equal or more unequal? The distribution of income has become slightly more
equal. Now, compare these results with the very last example where the welfare budget was
changed. Are the results of changing the unemployment rate stronger or weaker compared to
changing the welfare budget? The results of changing the unemployment rate are weaker.
However, has the total GDP of society increased or decreased as a result of reducing
unemployment? Total GDP has increased. Why has this occurred? Total GDP has increased
because more resources, including workers, are being used.
From a positive economic standpoint, i.e. without concern for fairness, would an economist
support, oppose or be indifferent to this policy (Give reasons for your answer)? The economist
would support this policy because it results in an increase in total income. To some extent,
does reducing the unemployment rate represent the best of both worlds in terms of redistributing
income and increasing total GDP? Yes (Yes, No).