Understanding Aggregate Demand and Equilibrium in Macroeconomics

Posted on Jul 9, 2024 in Economy

T.3: Potential and Actual Output

Potential Output

The maximum output achievable within a given period using existing technology and fully employed resources is called the potential output level.

Actual Output

Actual output reflects real-world production. It can fall below potential output due to underutilized resources or inefficient resource allocation, even with full employment.

Business Expectations

Production decisions rely on entrepreneurs’ expectations of the future rather than solely on objective data. We assume these expectations are held with certainty and treated as objective data. For instance, future sales expectations are determined by current demand.

Model Assumptions

Economic Agents

  • Domestic Economy: Labor suppliers decide consumption and savings allocations for their income. They are also the owners of companies.
  • Enterprises: These are the productive units of the economy, deciding how much and what to produce. They make investment decisions.
  • Government: Determines public spending, raises taxes, and controls the money supply as the owner of the Central Bank.

Technology

The model assumes the production of a single good. If used as a commodity, it is consumed within the period. If used as capital goods, it increases the economy’s capital stock.

Production Function

Yt = (Kt, Lt)

The national product (PN) in period t is a function of capital (K) and labor (L) in period t. K represents a stock, while L is a flow.

Types of Assets

  • Real Estate: Capital goods held by businesses but owned by families.
  • Bonds: Perpetual debt certificates issued by the government.
  • Money: Legal tender and bank deposits.

Consumer Demand and Equilibrium Output

The equilibrium output level is where the quantity demanded matches the quantity supplied at a constant price. Adjustments to imbalances occur through quantities, not prices. The model assumes production can increase at a constant cost. In an imbalance, investment adjusts. The variable level of aggregate demand determines the production level. The equilibrium condition holds for Y = DA. Companies adjust production based on inventory accumulation or depletion.

Keynes’s “General Theory” and the Consumption Function

Keynes’s theory posits that consumption is a function of disposable income. A change in disposable income leads to a change in consumption in the same direction but with a smaller magnitude.

Marginal Propensity to Consume

The marginal propensity to consume (MPC) is positive and less than one. Considering only private consumption, disposable income is consistent with total income: Y = YD.

C = CA + cY

  • C = Household consumption
  • CA > 0: Autonomous consumption
  • Y: Income in the period
  • c = dC / dY: Marginal propensity to consume
  • C / Y = CA / Y + c: Average propensity to consume

The Saving Function

Y = C + S => S = Y – C => S = -CA + Y(1 – c)

(1 – c) represents the marginal propensity to save.

Demand for Investment

Investment plays a crucial role in GDP fluctuations over the business cycle. In this model, companies make investment decisions based on future expectations. The investment decision process involves two steps:

  1. Determining the optimal capital stock based on production targets and relative factor prices.
  2. Deciding how much to produce based on product price and cost minimization objectives.

Companies invest to maximize profits, ensuring the expected profitability of a project meets or exceeds the market rate of return. A rise in the market interest rate would lower the profitability of investment projects. We assume investment is a decreasing function of the interest rate.

I = I(r), where i < 0 and i = dR / dr

Public Sector

G represents government expenditure in a given period. There are no government savings (Sb). Public spending is financed through bond issuance (deficit) or net direct taxes (T) after transfers (GT), representing the government deficit. Disposable income is calculated as Yd = Y – T.

Goods Market Equilibrium: The IS Curve

The goods market reaches equilibrium when the planned aggregate demand equals the national product (or income) supplied. This is represented by the equation:

Y = C + I + G = DA

Where:

  • C = C(Yd) = Co + cYd, with 0 < c < 1
  • I = I(r), with dI / dr < 0 (linear function)
  • G > 0 (exogenous variable determined outside the system)
  • T > 0 (exogenous variable determined outside the system)

Substituting the equations for C, I, and G into the equilibrium equation:

Y = Co + c(Y – T) + I(r) + G

Simplifying the equation:

Y – cY = Co – cT + I(r) + G

(1 – c)Y = Co – cT + I(r) + G

Y = (1 / (1 – c)) x (Co – cT + I(r) + G)

Let (1 / (1 – c)) = α (the income multiplier)

Y = αCo – αcT + αI(r) + αG

Where α > 1 and c / (1 – c) < α

This equation shows that any increase in the components of aggregate expenditure (Co, I, G) will lead to a multiplied increase in income. The income multiplier (α) is larger when the marginal propensity to consume (c) is higher.