Exercises: Deficit, public debt, and the shadow economy

Define federal budget deficit and national debt, and explain their relationship: why is the deficit said to be a flow and debt a stock? Use the analogy of the faucet and the bathtub.

A state spends $500,000$ million dollars and receives revenue of $470,000$ million.

1. a) Calculate its annual deficit.
2. b) Explain where the state can get the difference from.

Explain what the shadow economy is and classify these situations depending on whether or not they belong to it: a plumber who charges cash without an invoice to avoid reporting the income, a teenager who babysits their brother without pay, and a street vendor working without a license and without reporting income.

Distinguish between a budget surplus, balance, and deficit. Calculate the balance of a state that receives $200,000$ million and spends $190,000$ million, and of another that receives the same amount and spends $215,000$ million. Which of the two will have to borrow?

Who lends money to the federal government? Explain what a Treasury bond or bill is, who usually buys them (banks, funds, individuals, other countries) and what the buyer receives in return (interest and repayment of the principal).

What is the risk premium? Explain in simple words what it measures (the extra interest investors demand from one country compared with the safest one) and what it indicates if it rises sharply.

What is the federal budget and who approves it in the United States? Explain what it contains (the forecast of revenue and spending for the year) and why it is the most important economic law of the year.

Distinguish between a cyclical deficit (it appears with the recession and disappears with the recovery) and a structural deficit (it exists even in the good years). Give an example of each and explain why the second is more worrying.

A country accumulates a debt of $1,000,000$ million dollars at an average interest rate of $3\ \%$.

1. a) Calculate annual interest expenditure.
2. b) Compare that figure with an education budget of $40,000$ million and draw a conclusion about the "cost" of the debt.

The figure shows the annual public deficit of an imaginary country over six years, as a percentage of GDP.

1. a) State in which years the government spent more than it received and in which years it saved.
2. b) Explain what happens to the country's total debt during those years even if the deficit is decreasing.

Analyze the causes and consequences of the shadow economy: why it arises (taxes, paperwork, habit) and what effects it has on tax revenue, business competition, and informal workers themselves.

A country's public debt rises from $80\ \%$ to $100\ \%$ of its GDP, which is $1,200,000$ million dollars.

1. a) Calculate the debt in dollars at each moment.
2. b) Explain why the debt-to-GDP ratio can rise even if the annual deficit is falling: what role do the denominator (GDP) and the accumulated stock play?

A state has a debt of $100,000$ million dollars at an average interest rate of $2\ \%$.

1. a) Calculate the annual interest expenditure.
2. b) If each year it pays that interest by borrowing new debt and repays nothing, explain what happens to the debt in the long run (the snowball effect) and why interest rates matter so much.

European fiscal rules ask countries to keep the deficit below $3\ \%$ of GDP and debt below $60\ \%$.

1. a) What do those rules seek (market confidence, sustainability, common discipline in a shared currency)?
2. b) What problem do they have in the middle of a recession (forcing cuts when the economy is weak: a pro-cyclical effect)? Reason through the debate.

Fictitious headline: "The federal government breaks its revenue record and still closes the year in deficit."

1. a) Explain how this is possible (spending grows even faster than revenue).
2. b) What data do you need to judge whether that deficit is worrying (the size of GDP, the cost of the debt, economic growth, what it is spent on)? Justify each one.

Debt sustainability depends on the race between the growth of the economy and the interest rate the federal government pays.

1. a) Explain in simple words why a debt is easier to sustain if the economy grows faster than the interest it pays (the denominator grows faster than the debt).
2. b) Reason what happens if rates stay above growth for years and what options the federal government has left.

A city report reveals that in a tourist town, $25\,\%$ of home renovation work and hospitality services is paid in cash without being declared. The spokesperson of a merchant association states: "In reality, this benefits the town: the client saves $21\,\%$ in sales tax, the self-employed worker survives with lower costs, and that money is spent in local shops, boosting the economy."

1. a) Refute this argument from an economic standpoint: demonstrate what negative externalities and failures this practice generates regarding the sustainability of the welfare state, public accounts, and businesses operating legally.
2. b) One political party proposes reducing the underground economy by lowering general tax rates, while another proposes tripling inspections and penalties. Predict the effects of both measures on the public deficit and tax compliance in the short and long term.
3. c) Design a fiscal measure based on conflicting interests between buyer and seller to bring undeclared activity to light voluntarily, justifying its feasibility.

Observe the budgetary data of a country during the first year of an economic recession:

• Real GDP falls by $3.2\,\%$.

• Tax revenue (federal income tax and sales tax) decreases from $120,000$ to $106,000$ million dollars.

• Spending on unemployment benefits increases from $14,000$ to $21,000$ million dollars.

• The remaining public spending items remain frozen at $110,000$ million dollars.

• The federal government has not passed any tax laws or discretionary budgetary changes.

1. a) Demonstrate, using these data, how the automatic stabilizers have operated and calculate the change in the budget balance (deficit or surplus). What macroeconomic function do they serve regarding aggregate demand during the fall in GDP?
2. b) Suppose that the Secretary of the Treasury, alarmed by the resulting deficit, decides to implement a procyclical policy by cutting public spending on healthcare and infrastructure to force an immediate budget balance. Predict the impact this decision will have on GDP, unemployment, and future tax revenue (paradox of thrift / paradox of austerity).
3. c) Distinguish between cyclical deficit and structural deficit in this scenario. Why can trying to eliminate the cyclical deficit through spending cuts worsen the crisis?

A country's Treasury announces a record issuance of public debt to finance its negative budget balance. Analyze the impact of this measure in two different macroeconomic contexts:

• Scenario A: The economy operates close to full employment ($4\,\%$ unemployment), private savings remain stagnant, and the Federal Reserve pursues a restrictive monetary policy to curb inflation.

• Scenario B: The economy goes through a deep recession ($19\,\%$ unemployment), there is high precautionary savings stagnant in banks, and the Federal Reserve maintains interest rates at $0\,\%$ with bond-buying programs.

1. a) Predict in which of the two scenarios a "crowding out" effect on private investment is highly likely to be triggered and in which one it is not. Justify the financial mechanism by explaining what will happen in each case to interest rates and credit to small businesses.
2. b) A commentator states: "Every public deficit automatically reduces private investment." Refute this statement drawing upon the concept of "crowding in" for Scenario B.
3. c) If you were the director of analysis at the Department of the Treasury, what three financial variables or indicators would you monitor to confirm whether public debt is crowding out the productive sector or not?

The federal government must address two extraordinary spending needs of $12,000$ million dollars each:

• Project A: Emergency aid campaign and direct subsidies to households and small businesses to cushion the temporary loss of income caused by a health or war crisis over six months.

• Project B: Construction of a railway infrastructure network and freight logistics hubs with an estimated useful life of $50$ years.

Congress debates whether each project should be funded through an extraordinary tax hike in the current year or through the issuance of $30$-year government bonds.

1. a) Apply the principle of intergenerational equity and the "golden rule of public finance" (which links debt to investment) to justify which of the two financing methods is economically and ethically most suitable for each of the projects.
2. b) A member of Congress argues that financing Project A with debt "costs current citizens nothing because the money is provided by voluntary investors." Refute their argument by explaining two real economic costs that the massive issuance of debt immediately transfers onto the current economy.
3. c) Based on the Ricardian equivalence theorem, predict how household saving and consumption will react if the federal government decides to finance Project A with debt instead of taxes, and what consequences this response has on the effectiveness of fiscal policy.

Unit challenge. Advise the Ministry of Finance: how to balance public accounts while protecting the welfare state? Imagine that you are part of a fiscal expert committee; your mission is to draft a brief executive report with realistic proposals to restore the health of the country's public finances.

1. Diagnosis with real data: Go to the website of the Banco de España or the INE and extract the latest official public debt-to-GDP figure (around $105.5\%$) and the fiscal deficit for the most recent closed fiscal year.

2. Shadow economy and tax revenue: Find out the standard estimate of the size of the shadow economy in Spain (between $18.0\%$ and $22.0\%$ of GDP). In a simple table, calculate the potential tax revenue that would be obtained if $3.0\%$ of GDP were brought to light with an average tax burden of $38.0\%$.

3. Reasoned proposal: Design two progressive tax measures to safeguard public healthcare or education, along with an expenditure control measure that cuts the deficit without harming social cohesion.

Evaluation criteria:

• Rigor in obtaining and citing official data from the INE or Banco de España.

• Coherent connection between deficit, public debt, tax fraud, and the welfare state.

• Economic feasibility, progressivity, and sense of equity of the proposed measures.

• Clarity of presentation, correct terminology, and ability to synthesize.