Notes on the Basic Model I: Consumers, Producers, and Government

Unit 2: The Basic Model I: Consumers, Producers and Government

Presented By Dr. R. Nishimwe-Niyimbanira (Senior Lecturer)
University of Mpumalanga

Introduction to the Basic Model I

After studying this chapter, the learner should be able to:

• Construct a basic model of production and income determination.
• Use the model to explain fluctuations in total income in the economy over the course of the ‘business cycle.’
• Compare and explain the behavior of primary components of expenditure in an open economy:
  • Consumption
  • Investment
  • Government expenditure
  • Imports
  • Exports
• Compose chain reactions or ‘chain reasoning’ to analyze changes in economic variables (taxation, interest rates, etc.) or external disturbances dynamically through the economy.
• Use graphical aids to support and critically evaluate economic reasoning.

Simple Keynesian Model

• The Simple Keynesian theory of income determination is essential for understanding the economy's operations.
• Originally designed to explain recessions and prolonged unemployment, this model focuses on fluctuations in real national income and employment.
• It emphasizes the real sector (goods sector) of the economy, where activities like production, consumption, saving, investment, imports, and exports take place.
• Understanding this theory can aid in comprehending the South African economy, particularly regarding GDP fluctuations.
• In more modern Keynesian theory, the price level is crucial for inflation analysis; however, in the simple version, it is assumed constant.

The Basic Framework

• Key Aspect: The changes in production and income alterations are tied to fluctuations in total expenditure in the economy.
• Total expenditure is central to understanding the macroeconomic state of the economy.
• Therefore, the Keynesian model is characterized as an expenditure- or demand-determined model.
• Assumption: The average price level remains constant.

Types of Transactions in the Economy

• There are three main types of transactions:
  • Goods Market Transaction
  • Labour Market Transaction
  • Financial (Capital) Transaction
• A labour market and financial market are constituents of the factor market.

Circular Flow Model

Figure 2.2: Circular Flow of Goods and Services

• Firms: Producers of goods and services.
• Households: Consumers purchasing goods and services.
• Factors of Production: Inputs used to produce goods and services.
• Factor Payments: Payments made to factors of production (income).
• The circular flow illustrates the transactions between firms and households where total expenditure and production are interconnected.

Figure 2.3: Basic Circular Flow

• Expenditure Flow: Payments for goods circulating from households to firms.
• Income Flow: Factor payments (wages, profit, etc.) flowing from firms to households.
• Economic Activity: Shows interaction of spending and income between firms (producers) and households (consumers).

Macroeconomic Equilibrium

• A key observation: an increase in total expenditure likely leads to an increase in production to meet this demand, adjusting sales and real income (Y).
  • Chain Reaction Example:
  • Total expenditure increases → Stocks deplete → Production increases → Real GDP and real income increases.
• Equilibrium occurs when total expenditure equals total production:
  $ext{Total Expenditure} = ext{Total Production}$

Income-Expenditure Diagram

Figure 2.5: Equilibrium Income Determination

• Displays a 45° line representing total income and expenditure equilibrium:
• Where aggregate expenditure intersects the 45° line suggests equilibrium income (Yo).

Components of Total Expenditure

• Total Expenditure (TE) formula:
  $ext{Total Expenditure} = C + I + G + (X - M)$
• Where:
  • C = Consumption expenditure
  • I = Investment expenditure
  • G = Government expenditure
  • X = Exports
  • M = Imports

Real Consumption (C)

• Refers to household expenditure on consumable items and services, including:
  • Clothing
  • Entertainment (sport, movies)
  • Medical services
• It constitutes the largest component of total spending in the economy and is typically the most stable element of aggregate expenditure.

Determinants of Real Consumption

• Function:
  $C = f (Y_D, ext{Wealth}, ext{Expectations}, ext{Habits}, ext{Demographic Factors}, etc.)$
• Important factor: Level of real disposable income (Y_D).
• Definition: Disposable income is the income (Y) remaining after taxation (T):
  $Y_D = Y - T$
• An increase in taxation will reduce disposable income.

The Consumption Function

• It represents the relationship between real consumption and real income:
  $C = a + bY$
• Where:
  • C = consumption
  • a = autonomous consumption
  • b = marginal propensity to consume
  • Y = level of income
• The consumption function's positive slope indicates a direct relationship between real consumption and real income.

Figure 2.7: Keynesian Consumption Function

More Complex Relations Between Consumption and Income

• Concepts influencing consumption:
  • Relative Income: Consumption varies based on an individual’s income distribution position (James Duesenberry, 1949).
  • Permanent Income: Consumption is based more on expected lifelong income than current income (Milton Friedman).
  • Life-Cycle Income: Spending plans align with expected income over a lifetime (Franco Modigliani).
  • Distribution of Income: Different households have varying Marginal Propensities to Consume (MPC) depending on whether they are poor, middle-income, or rich.

Real Investment (I)

• Defined as the purchase of production or capital goods such as factories and machinery, expecting returns from sales.
• Investment is typically a more unstable component within the economy.
• It consists of:
  • Gross Fixed Capital Formation
  • Inventory Investment
• Simplified assumption:
  $I = I<em>{ ext{private firms}} + I</em>{ ext{public corporations}}$

Determinants of Real Business Investment

• Function:
  $ext{Investment} = f ( ext{Real Interest Rate}, ext{Expectations}, ext{Business Confidence}, ext{Regulation}, etc.)$
• Investment has a negative correlation with real interest rates:
• An increase in the real interest rate discourages capital formation, while a decrease stimulates it.
• Definition: Real interest rate is the effective interest rate adjusted for inflation effects.
• Nominal interest rate is the routine rate charged by banks to customers (e.g., prime rate).

Real Investment Function

The Investment Function:

$I = I_a - h imes r$

• Where:
  • $I_a$ = autonomous investment
  • $h$ = sensitivity of investment to changes in the real interest rate (r).
• The inverse relationship: Higher real interest rates deter investment; conversely, lower rates encourage it.

Figures: Investment Functions

Figure 2.8: The Investment Function

Figure 2.9: Investment in the 45° Diagram

Macroeconomic Equilibrium: The Basic Idea

• Analyzing Consumption and Investment leads to deriving the equilibrium condition in a two-sector model:
• At equilibrium:
  $ext{Total Expenditure} = ext{Total Production}$
  $Y = C + I$
• Substituting yields:
  $Y = a + bY + I_a - h imes r$
• Rearranging gives:
  $Y - bY = a + I_a - h imes r$
• Finally, we arrive at:
  $Y = \frac{1}{1 - b}(a + I_a - h imes r)$
• The expression $rac{1}{1 - b}$ represents the multiplier (K_E).

Changes in the Equilibrium: Multipliers

• A fall in interest rates reduces opportunity costs for investment, promoting planned investment projects.
• Resulting chain reaction:
  • If investment (I) increases, total expenditure rises, leading to inventory reduction.
  • This inventory reduction signals and incentivizes increased production.
• Overall effect: Increased production aligns with higher expenditure, raising GDP and real income ($Y$).
• Equation for this chain reaction:
  $r o ext{decrease} o I o ext{increase} o ext{total expenditure} o ext{increase} o ext{production} o Y o ext{increase}$

Expenditure Multiplier

• The expenditure multiplier indicates that any change in expenditure ($ riangle ext{Exp}$) leads to a disproportionately larger change in equilibrium income ($ riangle Y$).
• The multiplier size (K) is defined as:
  $K = \frac{ riangle Y}{ riangle ext{Exp}}$
• The multiplier process consists of multiple rounds of respending following an initial expenditure injection.
• Each expenditure is income for another party, with a portion respent dependent on the marginal propensity to consume (MPC).

Figure 2.12: The Multiplier Effect Diagram

Cumulative Income Change

• The cumulative change in income (sum of increases) is significantly higher than the initial expenditure injection.
• The initial injection undergoes multiplication.
• This cumulation's size is contingent on spending portion العودة تساهم 김添خ回 Programmierbability's habitual return cycle will reduce over time, inversely linking to leakage percentages (savings, taxation, imports).

Expenditure Multipliers and Leakage

• Relationship of multiplier value to leakage percentage:
  $K<em>E = \frac{1}{ ext{marginal leakage rate}} ext{ (Open Economy)}$$K</em>E = \frac{1}{1 - b} ext{ (closed economy with C and I)}$
• Since MPC + MPS = 1, we derive:
  $K_E = \frac{1}{ ext{MPS}}$
• The multiplier is applicable for any expenditure injection (leakage) caused by government spending, taxation changes, exports, etc.

Government Expenditure and Taxation

• Government expenditure refers to goods and services purchases by the general government, including:
  • Central government
  • Provincial governments
  • Local governments
• For this study, government expenditure defined as a sum of general government consumption and investment.

Government Expenditure and Fiscal Policy

• Government expenditure (G) and taxation (T) are crucial elements of fiscal policy.
• Government expenditure (G) is a substantial element of total expenditure, impacting it directly.
• In the 45° diagram, G is represented as a horizontal line, being added vertically to C and I:
  $Y = C + I + G$
• The eventual change in Y exceeds the initial change in G multiplied by K_E.

Figure 2.14: Macroeconomic Equilibrium with Government Expenditure

Taxation Effects on Consumption

• Function:
  $C = a + bY_D$
• Where YD represents after-tax disposable income: $Y</em>D = Y - T$
• As tax rate (t) rises, $(1-t)$ decreases, increasing the denominator of the multiplier and reducing its value.
• Hence, the larger the tax rate, the smaller the effective multiplier from consumption.

Tax Multiplier Effects

• Taxation indirectly influences equilibrium income through its effect on disposable income and consumption patterns:
• A decrease in T typically causes an increase in C and S, however:
• Increase in Government expenditure follows the normal multiplier process:
• Defined as:
  $K<em>T = ext{MPC} imes K</em>E$

International Trade: Exports and Imports

• Introduction of the fourth economic sector (open economy).
• The South African economy relies significantly on international trade for export and import transactions.
• Thus affecting expenditure and production patterns meaningfully.

Total Expenditure in an Open Economy

• Open economy formula:
  $ext{Total Expenditure} = C + I + G + (X - M)$
• Total production equilibrium defined as:
  $C + I + G + (X - M) = ext{Total Production}$
• Therefore:
  $C + I + G + (X - M) = Y$
• Increased exports $(X - M) o ext{increased total expenditure} o ext{induced production} o ext{GDP increase} o Y increase.

Complete Real Sector: Expenditure Multiplier with Exports and Imports

• Assume that exports (X) are exogenous.
• Imports modeled as:
  M = m_a + mY
• Where: m = marginal propensity to import.
• Full expenditure formula:
  Y = C + I + G + (X - M)
• Substituting yields:
  Y = a + b(1 - t)Y + Ia - hr + G + X - ma - mY
• Rearranging gives:
  Y = rac{1}{(1 - b(1 - t) + m)} (a + Ia - hr + G + X - ma) $$

More Complete Circular Flow Model

• The circular flow includes all economic sectors:
  • Households (Consumers)
  • Firms (Producers)
  • Government
• Incorporates all aspects like consumption, investment, government spending, saving, and taxation.

Conclusion

• The relationships among consumers, producers, and government spending are crucial for understanding the basic model and its implications for income determination and economic cycles.