GEE - Problem set 6

What mechanism do classical economists believe will return the economy to potential GDP in the long run?

In a recession, firms reduce prices due to low demand. In an open economy, lower domestic prices boost exports and reduce imports, increasing output and triggering a multiplier effect that helps the economy recover—assuming the global economy is not also in recession.

1. Classical view (no active policy)

   • ●  Long run mechanism: Price ↓ → Real exports ↑ → Demand ↑

     → Output ↑ via multiplier effect.

   • ●  Assumption: external conditions are favourable

Why do some economists support active fiscal policy?

Because the long run may take years, and the economy might not return to full employment on its own. Activists advocate for expansionary fiscal or monetary policies to speed up recovery and reduce suffering.

1. Active policy (Keynesian view)

   • ●  Economy may return to potential GDP in the long run... BUT it

     takes too long

   • ●  Expansionary fiscal or monetary policy can reduce suffering

     and speed recovery

What are the two main arguments against active fiscal policy?

1. Policy lags: Recognition, implementation, and impact delays can make policy counterproductive.

2. Deficits: Expansionary policies usually increase the public deficit in the short term.

Why do some economists prefer monetary policy over fiscal policy?

• ●  Faster to implement

• ●  Investment reacts more strongly to interest rate changes

• ●  “Costless” compared to fiscal policy (no direct budget impact)

• ●  Easier to reverse or fine-tune

In 2019, with G = 25, Z = 10, INT = 2, and desired public debt = 20, how much should taxes (T) be?

T = 27. The deficit must be 10 to keep debt at 20, so T must rise by 7 units from the previous year.

1. 2018: G=20, Z=10, T=20, Debt_start=0 → DEF=10 → Debt_end=10

2. 2019 Goal: Debt_end = 20 → DEF=10

3. NewINT=20%of10=2→Solve for T:25(G)+10

   (Z) + 2 (INT) = T + 10 → T = 27

What was Santa Clara’s public debt at the beginning of 2013 if 2012's debt was 10, G = 3, Z = 1.5, T = 2, and INT = 0.5?

New debt = 10 (old) + 3 (deficit) = 13 units.

4. G=3,Z=1.5,T=2,Debt_start=10,INT=0.5(5%of10) b. DEF=3+1.5+0.5–2=3→Debt_end=13

If a government wants to increase transfers (Z) but keep debt at zero, can disposable income increase?

No. Since any increase in Z must be matched by an equal increase in T (∆Z = ∆T), disposable income Yd = Y − T + Z remains unchanged.

1. Yd = Y-T+Z

2. IfG isfixed&debt=0→changeinZmustbematchedbychangeinT→no change in Yd

3. Conclusion: Transfers cannot increase disposable income without raising debt

Does a tax rate drop increase government revenue?

Generally false. A lower tax rate increases output (Y), but not enough to offset the lower rate, especially if the country is on the left side of the Laffer curve.

• Although Y increases due to higher multiplier, T = T0 + t’Y usually still drops

• ●  Revenue increases only if the country is on the right side of the Laffer curve - rare in practice

Can increased G increase revenue more than spending?

No. Even with high multipliers and tax rates, increased revenue from higher Y is typically less than the spending increase, so the budget deficit increases.

Example:G↑=300→Y*↑=500→T↑=250→Deficit

increases by 50
● Even with high t′ or c′, deficit increases in short run.

Why can the budget deficit fall over time after an initial spike?

Improved expectations can boost autonomous consumption/investment, increasing Y and thus T, reducing the deficit. Governments may also gradually cut G or raise T as recovery takes hold.

What does it mean to “jump-start” the economy?

A large enough fiscal effort to shift expectations positively, avoiding the need for permanent government spending increases.

Why is rising public debt concerning?

Not due to its size, but its potential to become unsustainable, triggering investor fears and raising borrowing costs.

→ market panic→ rising r → default risk

Is high public debt always a sign of default risk?

No. Defaults often happen in countries with low debt-to-GDP ratios (20–40%).

What defines sustainable public debt?

A constant or slowly growing debt-to-GDP ratio. If the ratio accelerates, the debt may become unsustainable.

(r – g)(PD/Y) = D/Y

What condition must hold for debt sustainability?

If:

(g−r)⋅PD/Y=D/Y

Then the debt-to-GDP ratio is stable. If r>gr > gr>g, the government needs a budget surplus to prevent the ratio from rising.

If not feasible, debt grows explosively.

Why did PIIGS' debt become unsustainable?

Because interest rates (r) rose significantly above growth (g), causing the debt-to-GDP ratio to accelerate.

Why is Japan’s high debt sustainable?

Its growth is low, but interest rates are even lower, allowing for deficits without growing the debt ratio.

Is Mexico’s public debt sustainable if r = 8.36%, g = 2.2%, and debt-to-GDP = 52%?

No. Mexico needs a 3.2% surplus to keep the ratio constant, but it’s running a 4.6% deficit, so debt is growing.

Why might reducing the budget deficit fail? Austerity

Logic: cut G / raise T → deficit will decrease → r decreases → debt becomes sustainable

Reality: Cuts to G or increases in T can lower GDP, decreasing T further, and potentially increasing the deficit instead. This worsens debt sustainability and market confidence.

In Sufrolandia, if G increases by 300, c′ = 0.8, t′ = 0.5, what is ∆Y*?

ΔY∗=1−c′+c′t′1​⋅ΔG=35​⋅300=500

Given:

C = 180 + 0.8(Y – T) T = 100 + 0.5Y
ΔG = 300
i. Multiplier:

ΔY*=1/(1–c′+c′t′)*ΔG =1/(1–0.8+0.4)=5/3 → ΔY* = 500

What is the increase in T?

ΔT=t′⋅ΔY∗=0.5⋅500=250

What happens to the deficit?

It increases by 50 (G ↑ 300, T ↑ 250). Economists should be fired — not jailed — for the poor recommendation.

Is it ever possible for increased G to pay for itself via increased T?

No. Algebra shows that for ∆T > ∆G, the tax rate t′ would have to be greater than 100%, which is impossible. Budget deficits always increase from fiscal expansions in the short run.

Budget constraint

G+Z+INT=T+DEF

• G = Government spending

• Z = Transfers

• INT = Interest payments on public debt

• T = Tax revenue

• DEF = Budget deficit

The deficit DEF is what needs to be financed, typically through borrowing.

Disposable Income

Yd​=Y−T+Z

• Yd​ = Disposable income

• Y = Total income

• T = Taxes

• Z = Transfers

Disposable income is the income households have after paying taxes and receiving transfers. This is the income available for consumption or savings.

sustainability condition for public debt

(g−r)× Y/PD ​= D/Y

• g = Growth rate of the economy

• r = Interest rate on government debt

• PD = Public debt

• Y = GDP

• D = Public debt as a percentage of GDP

If the difference between the growth rate ggg and the interest rate rrr is negative, it can indicate that public debt might become unsustainable over time.

multiplier with taxes

ΔY∗ =1 /1 −c′+c′t′ ×ΔG

• ΔY∗ = Change in national income

• c′ = Marginal propensity to consume

• t′ = Tax rate

• ΔG = Change in government spending

calculates the change in national income (GDP) resulting from a change in government spending, accounting for the marginal propensity to consume and the tax rate. The multiplier effect shows how government spending can ripple through the economy.

change in taxes

ΔT = t′×ΔY∗

• ΔT = Change in tax revenue

• t′ = Tax rate

• ΔY∗ = Change in national income

how much tax revenue changes in response to a change in national income. The higher the tax rate, the larger the change in tax revenue.