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Practice with simple calculations related to Fiscal Policy:
Question 1: According to Paul Krugman, the complex multiplier
for the United States is about equal to 2. The American
Recovery and Reinvestment Act of 2009 earmarked $787B in
deficit spending, of which $330.4B was spent in 2009. (Total
government deficits for 2009 were $1251.7B.) The increase in
nominal GDP from 2009 to 2010 was $541.2B (3.8%). If we
assume that this growth resulted from the ARRA stimulus
package, what was the implied multiplier associated with the
stimulus package?
Question 2: Look at disposable income, personal consumption
and personal savings. What was the personal savings rate in the
United States in 2011? (Use savings/disposable income, i.e.
Average Propensity to Save.)
Question 3: What proportion of GDP was our federal
government sector in 2010? (Divide federal government
spending by GDP.) Per dollar of government spending, how
much government spending was financed by government debt
(negative savings) in 2010 at the federal level? (Divide negative
federal government savings by federal government expenditure.)
Question 41: One popularly reported statistic for national
economies is the Debt/GDP ratio. Total US Federal Debt in
2010 was $13.562 Trillion. What was our Debt/GDP ratio in
2010?
Question 5: Refer to Graph Set #2, the first picture entitled
“Eurostat News Release.” How does the EU compare in the size
of its public sector? (What percentage of GDP is government
spending?) Are its government deficits larger or smaller than
those of the US as a percentage of GDP in 2009?
Question 6: Government stimulus can take the form of
increased spending or reduced taxes, or both. It creates
government debt in both cases, but that debt affects the larger
economy by different pathways. Can you answer each the
following questions in one short sentence?
· The government increases spending without increasing taxes,
and a deficit is generated:
· Where does the money to finance the deficit come from?
· How does this affect affordable credit for Investment and
Consumption?
· How does it affect National Incomes? Who is the government
paying money to when they make an expenditure?
· The government decreases taxes without decreasing spending,
and a deficit is generated:
· Where does the money to finance the deficit come from?
· How does this affect affordable credit for Investment and
Consumption?
· How does it affect personal savings rates (if personal taxes are
lower)? How does it affect business savings rates, i.e. retained
earnings, if profits taxes are lowered? How does it affect the
cost of borrowed funds for businesses?
Monte-Carlo Option Pricing
This exercise uses observation that an option price can be
calculated as a discounted risk-neutral expectation.
Context
This observation suggests that we could value an option by
sampling many thousands, say, of possible asset prices, at ,
calculating the payoffs, taking their expected value and
discounting this at the risk-free rate to today in order to
estimate the option’s current value. This game of chance does in
fact work and in this task you will see how. It is an example of
a simple Monte Carlo method: so-called because games of
chance form an important part of that part of Monaco’s
economy.
You have seen in lectures that the asset price It process, for
with and , has at expiry, with the solution exp((r- In what
follows we let be the payoff function for a plain vanilla
European-style option written on a non-dividend paying
underlying asset. In particular, if S is the underlying’s price at
expiry then V(S) will give the value of the option at the same
time.
Task:
· First make sure you know what the central limit theorem says.
Then complete the following task.
Let... be a sequence of independent and identically distributed
(i.i.d.) random variables each with mean and variance Define
the sample mean,
Explain why, as M gets large, we have:
and
· The statement for the estimated option price becomes more
accurate as (the central limit theorem). Explain why you can
infer from this that the standard deviation of the estimate
decreases with. Explain how and why we can expect that,
And show that this may also be written as,
And hence, explain why is an approximate 95% confidence
interval for the true option price.
Where is the mean and is the variance of the current option
price.
is the price and a standard deviation.
CONSUMPTION, INVESTMENT and GOVERNMENT
STIMULUS (Graph Set #2)
Different Perspectives on the Composition of US Government
Debt:
Decomposed According to Categories Used by the Treasury
Department: 3rd Quarter 2010
Decomposed with All Pensions (SSA, State and Local
Government, Corporate, Union and Private) Shown Separately:
3rd Quarter 2010
Decomposed to Show Foreign Owners by Country
“To Whom Does the U.S. Government Owe Money?” Business
Insider Magazine, January 14, 2011.
http://articles.businessinsider.com/2011-01-
14/markets/29973919_1_national-debt-public-debt-oil-exporters
The foreign-owned debt in the pie chart above sums to 31.8% of
all public debt. This is a fairly significant upward manipulation
of actual Treasury Department Data. Here are the proportions
provided by Treasury to Commerce and reported in the
Economic Report of the President to Congress, 2011, Appendix
B.
2007 25.5%
2008 28.8%
2009 29.9%
2010 (as of 3rd Quarter) 21.9%
Fed & SSA
Banks
State/Local Govt
Other Private
Foreign
Fed
Banks
All Pensions
State/Local Govt
Other Private
Foreign
CONSUMPTION, INVESTMENT and GOVERNMENT
STIMULUS (Data Set #2)
In Billions of Current Dollars unless otherwise noted
Source: Economic Report of the President to Congress, 2011;
Appendix B, Department of Commerce [1]
DateNominal PersonalGross PrivateNet Private
GDPConsumptionDomesticDomestic
InvestmentInvestment
2007 14,601.8 9,806.3 2,266.1 984.2
2008 14,369.1 10,104.5 2,137.8 743.0
2009 14,119.0 10,001.3 1,716.4 231.5
2010 14,660.2 10,351.9 1,752.8 464.2
DateGovernmentGovernmentGovernmentGovernment
Government
ExpenditureExpenditureSavingsSavings Debt (Federal)
(Federal)(State & Local)(Federal)(State & Local)
2006 $ 8,451.4
2007 2,674.2 1,697.9 -245.2 12.2 $
8,950.7
2008 2,878.3 1,798.5 -616.2 -47.4 $
9,986.1
2009 2,914.9 1,775.3 -1251.7 -20.1
$11,875.9
2010 3,002.3 1,788.0 -2,080.0 [2] not available
$13,528.8
NET PRIVATE SAVINGS CONSUMER
DEBT
Date DisposablePersonalPersonalRetainedOutstandingChange
from
IncomeConsumptionSavingsEarningsDebtPrevious Year
2007 10,423.6 9,806.3 214.7 270.7 2,522.19
137.35
2008 10,952.9 10,104.5 447.9 156.7 2,561.12
38.92
2009 11,034.9 10,001.3 655.3 284.2 2,449.38 -
111.73
2010 11,378.3 10,351.9 655.1 474.2 [3] 2,403.00 -
46.40
DateNominalTotal GrossPopulation
GDPSavings & (in millions of people)
Investment
2007 14,601.8 2,013.6 302.00
2008 14,369.1 1,785.2 304.80
2009 14,119.0 1,533.8 307.44
2010 14,660.2 1,728.3 [3] 308.75
[1] Note that these data reported by the Department of Congress
differ by ± 1% from the data reported by the Bureau of
Economic Analysis and provided to you in Data Set #1
[2] US Treasury 4th quarter report; not included in the
Economic Report of the President to Congress.
[3] Based on third quarter estimates

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1Practice with simple calculations related to Fiscal Polic.docx

  • 1. 1 Practice with simple calculations related to Fiscal Policy: Question 1: According to Paul Krugman, the complex multiplier for the United States is about equal to 2. The American Recovery and Reinvestment Act of 2009 earmarked $787B in deficit spending, of which $330.4B was spent in 2009. (Total government deficits for 2009 were $1251.7B.) The increase in nominal GDP from 2009 to 2010 was $541.2B (3.8%). If we assume that this growth resulted from the ARRA stimulus package, what was the implied multiplier associated with the stimulus package? Question 2: Look at disposable income, personal consumption and personal savings. What was the personal savings rate in the United States in 2011? (Use savings/disposable income, i.e. Average Propensity to Save.) Question 3: What proportion of GDP was our federal government sector in 2010? (Divide federal government spending by GDP.) Per dollar of government spending, how much government spending was financed by government debt (negative savings) in 2010 at the federal level? (Divide negative federal government savings by federal government expenditure.) Question 41: One popularly reported statistic for national economies is the Debt/GDP ratio. Total US Federal Debt in 2010 was $13.562 Trillion. What was our Debt/GDP ratio in 2010? Question 5: Refer to Graph Set #2, the first picture entitled “Eurostat News Release.” How does the EU compare in the size of its public sector? (What percentage of GDP is government spending?) Are its government deficits larger or smaller than those of the US as a percentage of GDP in 2009? Question 6: Government stimulus can take the form of
  • 2. increased spending or reduced taxes, or both. It creates government debt in both cases, but that debt affects the larger economy by different pathways. Can you answer each the following questions in one short sentence? · The government increases spending without increasing taxes, and a deficit is generated: · Where does the money to finance the deficit come from? · How does this affect affordable credit for Investment and Consumption? · How does it affect National Incomes? Who is the government paying money to when they make an expenditure? · The government decreases taxes without decreasing spending, and a deficit is generated: · Where does the money to finance the deficit come from? · How does this affect affordable credit for Investment and Consumption? · How does it affect personal savings rates (if personal taxes are lower)? How does it affect business savings rates, i.e. retained earnings, if profits taxes are lowered? How does it affect the cost of borrowed funds for businesses? Monte-Carlo Option Pricing This exercise uses observation that an option price can be calculated as a discounted risk-neutral expectation. Context This observation suggests that we could value an option by sampling many thousands, say, of possible asset prices, at ,
  • 3. calculating the payoffs, taking their expected value and discounting this at the risk-free rate to today in order to estimate the option’s current value. This game of chance does in fact work and in this task you will see how. It is an example of a simple Monte Carlo method: so-called because games of chance form an important part of that part of Monaco’s economy. You have seen in lectures that the asset price It process, for with and , has at expiry, with the solution exp((r- In what follows we let be the payoff function for a plain vanilla European-style option written on a non-dividend paying underlying asset. In particular, if S is the underlying’s price at expiry then V(S) will give the value of the option at the same time. Task: · First make sure you know what the central limit theorem says. Then complete the following task. Let... be a sequence of independent and identically distributed (i.i.d.) random variables each with mean and variance Define the sample mean, Explain why, as M gets large, we have: and · The statement for the estimated option price becomes more accurate as (the central limit theorem). Explain why you can infer from this that the standard deviation of the estimate decreases with. Explain how and why we can expect that, And show that this may also be written as, And hence, explain why is an approximate 95% confidence
  • 4. interval for the true option price. Where is the mean and is the variance of the current option price. is the price and a standard deviation. CONSUMPTION, INVESTMENT and GOVERNMENT STIMULUS (Graph Set #2) Different Perspectives on the Composition of US Government Debt: Decomposed According to Categories Used by the Treasury Department: 3rd Quarter 2010 Decomposed with All Pensions (SSA, State and Local Government, Corporate, Union and Private) Shown Separately: 3rd Quarter 2010 Decomposed to Show Foreign Owners by Country “To Whom Does the U.S. Government Owe Money?” Business Insider Magazine, January 14, 2011. http://articles.businessinsider.com/2011-01- 14/markets/29973919_1_national-debt-public-debt-oil-exporters The foreign-owned debt in the pie chart above sums to 31.8% of all public debt. This is a fairly significant upward manipulation
  • 5. of actual Treasury Department Data. Here are the proportions provided by Treasury to Commerce and reported in the Economic Report of the President to Congress, 2011, Appendix B. 2007 25.5% 2008 28.8% 2009 29.9% 2010 (as of 3rd Quarter) 21.9% Fed & SSA Banks State/Local Govt Other Private Foreign Fed Banks All Pensions State/Local Govt Other Private Foreign CONSUMPTION, INVESTMENT and GOVERNMENT STIMULUS (Data Set #2) In Billions of Current Dollars unless otherwise noted Source: Economic Report of the President to Congress, 2011; Appendix B, Department of Commerce [1]
  • 6. DateNominal PersonalGross PrivateNet Private GDPConsumptionDomesticDomestic InvestmentInvestment 2007 14,601.8 9,806.3 2,266.1 984.2 2008 14,369.1 10,104.5 2,137.8 743.0 2009 14,119.0 10,001.3 1,716.4 231.5 2010 14,660.2 10,351.9 1,752.8 464.2 DateGovernmentGovernmentGovernmentGovernment Government ExpenditureExpenditureSavingsSavings Debt (Federal) (Federal)(State & Local)(Federal)(State & Local) 2006 $ 8,451.4 2007 2,674.2 1,697.9 -245.2 12.2 $ 8,950.7 2008 2,878.3 1,798.5 -616.2 -47.4 $ 9,986.1 2009 2,914.9 1,775.3 -1251.7 -20.1 $11,875.9 2010 3,002.3 1,788.0 -2,080.0 [2] not available $13,528.8 NET PRIVATE SAVINGS CONSUMER DEBT Date DisposablePersonalPersonalRetainedOutstandingChange from IncomeConsumptionSavingsEarningsDebtPrevious Year 2007 10,423.6 9,806.3 214.7 270.7 2,522.19 137.35 2008 10,952.9 10,104.5 447.9 156.7 2,561.12 38.92 2009 11,034.9 10,001.3 655.3 284.2 2,449.38 -
  • 7. 111.73 2010 11,378.3 10,351.9 655.1 474.2 [3] 2,403.00 - 46.40 DateNominalTotal GrossPopulation GDPSavings & (in millions of people) Investment 2007 14,601.8 2,013.6 302.00 2008 14,369.1 1,785.2 304.80 2009 14,119.0 1,533.8 307.44 2010 14,660.2 1,728.3 [3] 308.75 [1] Note that these data reported by the Department of Congress differ by ± 1% from the data reported by the Bureau of Economic Analysis and provided to you in Data Set #1 [2] US Treasury 4th quarter report; not included in the Economic Report of the President to Congress. [3] Based on third quarter estimates