Macro Notes: AD, SRAS, Gaps, and Fiscal Policy — Spending vs Tax Changes

Overview: AD and SRAS, Gaps, and Fiscal Policy

• Aggregate demand (AD) is all spending in the economy by the four major sectors: households (consumers), government, businesses (investments), and foreigners (net exports). Expenditures approach to AD:
  • AD = C + I + G + NX (or AD = E = ext{consumer spending} + ext{government spending} + ext{business investment} + ext{net exports}).
• Short-run aggregate supply (SRAS) is the total production by all firms in the economy in the short run. It shows how much the economy can produce given input costs and price levels in the short run.
• The short-run equilibrium occurs where AD intersects SRAS. This equilibrium tells us the current real GDP output (Y) and the price level (P).
• Long-run aggregate supply (LRAS) is vertical and represents potential real GDP output, denoted as Y_f (full employment). When the economy is at full employment, we are at the potential level of output.
• The price level rising over time is inflation.

Potential Output, Full Employment, and Gaps

• Y_f (potential real GDP) is the level of output achievable when the economy is at full employment.
• If the economy is producing below potential (Y < Y_f), we are in a recessionary gap. This is associated with higher unemployment than the natural rate.
• If the economy is producing above potential (Y > Y_f), we are in an inflationary gap. This is associated with rising price levels (inflation).
• Relationship between real GDP and unemployment: as real GDP rises (more output), unemployment tends to fall (inverse relationship) on the axis representing unemployment versus real GDP.
• The natural rate of unemployment is around 4%. For example, an observed unemployment rate of 6% indicates unemployment above the natural rate, consistent with a recessionary gap.
• Types of unemployment: structural, frictional, and seasonal are natural unemployment components; cyclical unemployment arises from the business cycle (higher in a recession) and tends to disappear as we move toward Yf. In a recession (Y1 < Yf), cyclical unemployment exists; at Y_f, cyclical unemployment is zero.

Fiscal Policy: Stimulating the Economy in a Recession

• Two primary tools: (1) Increase government spending (G) and (2) Lower taxes (tax cuts). Raising taxes would reduce AD (contractionary policy).
• A rise in government spending directly increases AD (since G is a component of AD). In a recession, expansionary policy aims to shift AD to the right to raise real GDP and reduce unemployment.
• Fiscal policy effects can also influence the price level: as AD shifts right, the price level tends to rise (inflation) if there is a positive output response.
• Crowding out: Government borrowing to finance higher spending can raise interest rates, which can crowd out private investment. This is a potential offset to the increase in AD, particularly in the long run. This effect is typically discussed in later units (unit five in this course), but the basic idea is that higher interest rates discourage private spending and investment.

How the Economy Responds to Spending Increases (The Spending Multiplier)

• Money can be used in two ways: consumption (C) or saving (S). The marginal propensity to consume (MPC) is the fraction of extra income that is spent, and the marginal propensity to save (MPS) is the fraction saved. By definition:
  • MPC + MPS = 1
  • Everything else equal, the higher the MPC, the larger the multiplier effect.
• Spending multiplier (also called the spending multiplier) is:
  • k = rac{1}{1 - ext{MPC}} = rac{1}{ ext{MPS}}
• Example 1 (direct government spending):
  • Suppose the government spends ext{Δ}G = 1000 and the MPC is 0.9.
  • Multiplier: k = rac{1}{1 - 0.9} = 10
  • Change in GDP: ext{Δ}Y = k imes ext{Δ}G = 10 imes 1000 = 10{,}000
  • This arises because the initial $1000 circulates through the economy: recipients save 10% (MPS = 0.1), spend 90%, that spend is re-saved/spent by others, etc., producing a total impact of $10{,}000.
• Example 2 (spending with a smaller ΔG):
  • If instead ext{Δ}G = 100 and the MPC is 0.8, then
  • k = rac{1}{1 - 0.8} = 5
  • ext{Δ}Y = 5 imes 100 = 500
  • This shows how a smaller initial government outlay still produces an amplified effect on GDP via the multiplier, but the size depends on MPC.
• The chain-like reasoning behind the multiplier: each round of spending produces fewer dollars as recipients save a portion, but the total across all rounds sums to a geometric series. If $MPC = 0.8$, the total spending multiplier is 5, and the sum of the series $100 + 80 + 64 + 51.2 +
  …$ equals 500.

Tax Policy and Its GDP Impact (Tax Multiplier vs Spending Multiplier)

• A tax cut (a reduction in taxes) leaves people with more disposable income. The amount of the tax cut that is actually consumed depends on MPC.
• If the initial stimulus is a tax cut of size ext{Δ}T, and the MPC is the same as above, the overall effect on GDP is:
  • ext{Δ}Y = ext{Δ}T imes rac{ ext{MPC}}{1 - ext{MPC}} = ext{Δ}T imes ext{MPC} imes ext{multiplier}
• Example (tax cut):
  • Suppose the government reduces taxes by ext{Δ}T = 1000 and the MPC is 0.9.
  • Multiplier for spending would be 10, but since only a portion of the tax cut is spent (MPC < 1 on the tax cut), the tax multiplier is ext{Δ}Y = 1000 imes rac{0.9}{1 - 0.9} = 1000 imes rac{0.9}{0.1} = 9000
  • Compare this to an equivalent $1000 increase in G, which would raise GDP by 10{,}000 with MPC = 0.9. The tax cut has a smaller impact because not all of the tax savings are spent.
• Key takeaway: For the same policy size, government spending generally has a larger positive effect on GDP than an equivalent tax cut, because spending directly injects money into the economy, while tax cuts rely on consumers to spend a portion of the extra income.
• If the MPC were lower (e.g., 0.8 or 0.75), the tax multiplier would be even smaller relative to the spending multiplier, further widening the gap between the effectiveness of spending versus tax cuts.

Practical Implications and Real-World Relevance

• In a recession, expansionary fiscal policy (increasing G or cutting taxes) is used to raise AD, boost real GDP, and reduce unemployment.
• However, higher government spending can lead to higher deficits and debt, which must be financed by taxes or borrowing. If debt increases significantly, it can push up interest rates (crowding out), potentially reducing private investment and offsetting some gains from fiscal expansion.
• The composition of financing matters for the economy's response: debt-financed spending can have long-run implications for inflation and interest rates, while taxes affect the economy through discretionary policy choices about consumer behavior.
• The AP-style exam questions commonly test understanding of: (i) the direction of AD shifts from fiscal policy, (ii) the concept of the spending multiplier and how to compute it using MPC/MPS, (iii) the difference between spending multipliers and tax multipliers, and (iv) the relationship between output gaps and unemployment.

Quick Practice Prompts (Apply what you’ve learned)

• Suppose MPC = 0.75 and the government increases spending by ΔG = 200. What is the change in GDP (ΔY)?
  • Multiplier: k = rac{1}{1 - 0.75} = rac{1}{0.25} = 4
  • ΔY = 4 imes 200 = 800
• Suppose the government cuts taxes by ΔT = 300 with MPC = 0.75. What is the change in GDP (ΔY)?
  • Tax multiplier: rac{ ext{MPC}}{1 - ext{MPC}} = rac{0.75}{0.25} = 3
  • ΔY = ΔT imes 3 = 300 imes 3 = 900
• If you want a larger impact on GDP while using a fixed policy size, which tool is typically more effective: a direct increase in G or a tax cut? Why?
  • Answer: Direct government spending generally has a larger impact on GDP than an equal-sized tax cut because the entire amount of the government outlay is spent into the economy immediately, whereas a tax cut is only partially consumed depending on the MPC.

Key Terms to Remember

• AD: Aggregate demand; components: C + I + G + NX
• SRAS: Short-run aggregate supply
• LRAS: Long-run aggregate supply; vertical at potential output Y_f
• Y_f: Potential real GDP; full employment output
• Price level and inflation: persistent rise in the price level
• Recessionary gap: Y < Y_f; unemployment above natural rate
• Inflationary gap: Y > Y_f; prices rise
• MPC: Marginal propensity to consume
• MPS: Marginal propensity to save; MPC + MPS = 1
• Multiplier: k = rac{1}{1 - ext{MPC}} = rac{1}{ ext{MPS}}
• Tax multiplier: ext{Δ}Y = ext{Δ}T imes rac{ ext{MPC}}{1 - ext{MPC}}
• Crowding out: When higher government borrowing raises interest rates and reduces private investment
• Debt financing: Government borrowing through bonds/treasuries; sources include taxes and debt; foreign and domestic holders
• Four sectors of AD (recalled): households, government, businesses, foreigners; imports/exports influence NX
• Policy tradeoffs: short-run stimulus vs long-run debt and crowding out effects