ECO102: Business Cycles & Aggregate Expenditure

• Lecture 6 discusses business cycles and aggregate expenditure in ECO102: Principles of Macroeconomics, taught by Tyler Paul in Winter 2025.
• The lectures objectives outline defining short-run fluctuations and business cycle features, introducing planned aggregate expenditure as a demand measure, using the Keynesian Cross and algebraic solutions to analyze short-run output, and considering countercyclical fiscal policy.

Long-Run Growth and Potential Output

• Growth economics studies determinants of living standards over 5+ years, considering physical capital, human capital, and technology.
• Potential output (Y) is the output level an economy can produce when using all resources sustainably.
• The natural rate of unemployment is associated with potential output, including frictional and structural unemployment.
• The long-run real interest rate is the price of loanable funds associated with potential output.

Short-Run Fluctuations: Output Gap

• Short-run economics studies deviations from potential output over 1-2 years.
• The output gap (Ỹ) is the difference between actual and potential output.
• Output gap = (Actual output - Potential output) / Potential output × 100.
• Ỹ = (Y - Ỹ) / Ỹ × 100 is the equation for the output gap.
• A recessionary gap occurs when Y < Ỹ, and an expansionary gap occurs when Y > Ỹ.
• GDP trend of 1.9% per year

Output Gap and Business Cycles

• Business cycles involve frequent fluctuations in the output gap, but are not actual cycles.
• These cycles have irregular timing and duration, and the size of Ỹ varies considerably.

Key Features of the Business Cycle

• A recession is a period of significantly below-normal output growth, not necessarily two quarters of negative GDP growth.
• A depression is an extremely severe or protracted recession.
• An expansion is a period of significantly above-normal output growth.
• A peak is the high point of economic activity, marking the start of a recession.
• A trough is the low point of economic activity, marking the end of a recession.

Causes of Short-Run Fluctuations

• Potential output is determined by supply factors, including physical capital, technology, and labor.
• The output gap is determined by demand factors, such as spending decisions by consumers, firms, government, and foreign entities.
• Demand does not affect potential output in the long run.
• If demand rises but potential output remains constant, prices must increase.
• In the short run, prices are sticky and cannot adjust immediately to demand changes.
• Demand determines output in the short run

Key Assumptions of the Short-Run Model

• Prices do not adjust immediately to changes in demand due to menu costs, incomplete information, and contracts.
• Prices change every 4.5 months on average.
• Firms preset prices and meet demand at those prices.
• High demand leads firms to increase production, and low demand results in reduced production and built-up inventories.
• The Keynesian theory suggests that the output gap is driven by changes in aggregate demand combined with market frictions.

Representing Aggregate Demand

• Total output (Y) must equal total spending (C + I + G + NX).
• Planned aggregate expenditure (PAE) is the amount that households, firms, government, and foreigners want to spend, represented as PAE = C + IP + G + NX.
• Planned investment (IP) is the desired level of investment spending by firms, including business fixed investment and residential investment.
• Firms expect inventory investment to be 0.
• Unplanned inventory investment occurs when actual sales are less than expected, leading to increased inventories, or when actual sales are more than expected, leading to more inventories sold.

Keynesian Consumption Function

• The lecture transitions from defining PAE to creating a model for aggregate demand.
• Disposable income (income - taxes + transfers) determines household spending.
• Aggregate consumption is expressed as C = C + mpc × (Y – T).
• "C" autonomous consumption, driven by non-income factors like wealth and expectations.
• mpc, marginal propensity to consume, measures how much C increases when Y increases by $1, with 0 < mpc < 1.

Graphing Consumption and PAE

• The slope of the consumption function is mpc.
• The consumption function is used in the PAE equation: PAE = C + IP + G + NX.

Shifting Versus Moving Along PAE

• Movement along the PAE curve indicates changes in Y.
• Shifts in the PAE curve are due to changes in C, IP, G, NX, or T.
• Rotation of the curve is due to mpc.

Short-Run Equilibrium: Spending = Production

• PAE differs from actual spending due to unplanned inventory investment from firms producing too much or too little.
• Short-run equilibrium occurs when planned spending equals actual output: Y = PAE.
• When Y = PAE, firms have no incentive to change production.
• The equilibrium corresponds to the 45° line in a graph, where all points on this line satisfy Y = PAE.

Keynesian Cross Diagram

• Short-run equilibrium output (YSR) is where Y = PAE, indicated by the intersection of the PAE line crossing the 45° line
• If Y > YSR, then Y > PAE, I > IP leading to excess inventories, excess inventories, which prompts firms to cut production.
• If Y < YSR, then Y < PAE, I < IP, which prompts diminishing inventories, leading firms will raise production,
• The economy tends toward YSR.

Algebraic Representation of Short-Run Model

• The definition of planned aggregate expenditure: PAE = C + IP + G + NX.
• The representation of a behavior assumption about aggregate consumption: C = C + mpc × (Y − T).
• The condition for short-run equilibrium: PAE = Y.
• Exogenous variables: determined outside the model : (C, IP, G, NX, T)
• Parameters: variables measured from outside data (mpc)
• Endogenous variables: determined inside the model (PAE, Y, C).

Algebraic Solution of Short-Run Model

• The way to write endogenous variables as functions of exogenous variables and parameters..
• Three equations and three unknowns: PAE, Y, C
• PAE = C + IP + G + NX
• C = C + mpc × (Y – T)
• PAE = Y

Keynesian Multiplier

• YSR = (1 / (1 - mpc)) [C + IP + G + NX - mpc × T]
• Multiplier = 1 / (1 - mpc)
• Because 0 < mpc < 1 , the multiplier will always > 1, and thus amplifies changes in spending.
• A drop in government spending lowers PAE, leading to lower income, lower consumption spending, and further lower PAE through repeat cycles.

PAE with Income Tax: Government and Revenue

• Made simple assumptions for G and T in our model: Where T is a lump-sum tax
• Suppose tax revenues depend on income: Τ = τY for a multiplier (0 < τ < 1)
• Plug into PAE curve: PAE = C + mpc(Y − τY) + IP + G + NX
• Now find a new Multiplier Y = (1 / (1 - (1 - τ)mpc)) [C + IP + G + NX]
• New income tax multiplier is now generally smaller, meaning before → less amplification!

Countercyclical Government Spending

• Fiscal policy is concerned with how to determine the type or the amount of spending, taxation, and transfer payments
• The aim of countercyclical policy is to reduce severity of recessions
• The are three fiscal policies that occur in response to a recession:
• Decline/Increase in taxes or direct transfer payments: T
• Government purchases financed by debt: G
• Government purchases financed by taxes: G and T
• Each of these options will shift PAE up

Fiscal Policies: Decline in T vs Increased G

• Assume net taxes are lump-sum:
• YSR = (1 / (1 - mpc))[C + IP + G + NX - mpc × T]
• When G ↑ by $1, YSR ↑ by: (1 / (1 - mpc))
• When T ↓ by $1, YSR ↑ by: (mpc / (1 - mpc))

Fiscal Policies: Increased G Funded by Increased T

• Assume all government spending is financed by increased taxes, so ΔG = ΔT
• YSR = (1 / (1 - mpc)) [C + IP + G + NX - mpc × T]
• Government spending financed by debt increases YSR the most, but balanced budget spending still increases YSR