Chapter Notes

Determination of Income and Employment

In macroeconomics, our goal is to understand the big picture: what determines a country's national income, the overall price level, or the unemployment rate? To do this, we use theoretical tools called models. These models help explain complex situations like economic recessions, rising prices (inflation), or unemployment.

It's very difficult to study all economic variables at once. So, we often use a technique called ceteris paribus, a Latin phrase meaning "other things remaining equal." This means we focus on one or two variables while assuming all other factors stay constant. This allows us to see the relationship between our chosen variables more clearly.

In this chapter, we will explore how National Income is determined using a model based on the theories of John Maynard Keynes. We will make two key assumptions for now:

1. The price of final goods is fixed.
2. The rate of interest is constant.

Aggregate Demand and its components

In national income accounting, terms like consumption and investment refer to the actual, measured values for a specific year. We call these ex post measures, meaning "after the fact."

However, in economics, we are often more interested in what people plan to do.

• Ex ante consumption is what households plan to spend.
• Ex ante investment is what producers plan to invest.

These planned values are called ex ante measures, meaning "before the fact." Understanding the difference between what was planned (ex-ante) and what actually happened (ex-post) is crucial.

To understand how income is determined, we must first look at the planned components of aggregate demand.

Consumption

The most important factor influencing a household's consumption demand is its income. The relationship between consumption and income is described by a consumption function.

The simplest consumption function has two parts:

1. Autonomous Consumption ($\bar{C}$): This is the minimum level of consumption that occurs even if income is zero. People need to consume to survive, so they might use past savings or borrow money. This spending is "autonomous" because it is independent of income.
2. Induced Consumption ($cY$): This part of consumption depends directly on income. As income increases, people spend more.

The consumption function is written as: $C = \bar{C} + cY$ Here:

• C is total consumption expenditure.
• $\bar{C}$ is autonomous consumption.
• c is the Marginal Propensity to Consume (MPC).
• Y is the level of income.

The Marginal Propensity to Consume (MPC) is the rate at which consumption changes when income changes. It tells us what fraction of an extra rupee of income will be spent on consumption. $MPC = \frac{\Delta C}{\Delta Y} = c$ The value of MPC is always between 0 and 1.

• If MPC = 0, it means a person doesn't spend any of their extra income.
• If MPC = 1, it means a person spends their entire extra income.
• Typically, 0 < MPC < 1, meaning people spend a part of their extra income and save the rest.

• Its autonomous consumption ($\bar{C}$) is 100. Even with zero income, its citizens consume goods worth ₹100.
• Its MPC (c) is 0.8. This means for every extra ₹100 of income, consumption will increase by ₹80.

Savings is the part of income that is not consumed. $S = Y - C$ The Marginal Propensity to Save (MPS), or s, is the rate at which savings change when income changes. It's the fraction of an extra rupee of income that is saved. $MPS = \frac{\Delta S}{\Delta Y} = s$ Since every extra rupee of income is either consumed or saved, the two must add up to one. $s = 1 - c \quad \text{or} \quad MPS + MPC = 1$

Some Definitions

• Marginal Propensity to Consume (MPC): The change in consumption per unit change in income (c = ΔC/ΔY).
• Marginal Propensity to Save (MPS): The change in savings per unit change in income (s = 1-c).
• Average Propensity to Consume (APC): The ratio of total consumption to total income (C/Y).
• Average Propensity to Save (APS): The ratio of total savings to total income (S/Y).

Investment

Investment is the addition to the stock of physical capital (like machines and buildings) and changes in a producer's inventory of finished goods.

Investment decisions often depend on factors like the market rate of interest. However, to keep our model simple, we will assume that firms plan to invest a fixed amount every year, regardless of the level of income. This is called autonomous investment.

We can write the ex ante investment demand as: $I = \bar{I}$ Where $\bar{I}$ is a positive constant representing the fixed, autonomous investment in the economy.

Determination of Income in Two-sector Model

In a simple economy with only households and firms (a two-sector model), the ex ante Aggregate Demand (AD) is the sum of planned consumption and planned investment. $AD = C + I$ By substituting the functions for C and I, we get: $AD = \bar{C} + cY + \bar{I}$ We can group the autonomous parts together: $AD = (\bar{C} + \bar{I}) + cY$ Let's call the total autonomous expenditure $\bar{A}$, where $\bar{A} = \bar{C} + \bar{I}$. The equation then becomes: $AD = \bar{A} + cY$

The economy is in equilibrium when the planned supply of final goods (Y) equals the planned demand for them (AD). $Y = AD$ So, the equilibrium condition is: $Y = \bar{A} + cY$

Determination of Equilibrium Income in the Short Run

In macroeconomics, we determine equilibrium in two stages. First, we assume the price level is fixed. Later, we relax this assumption and allow prices to change.

We assume a fixed price level in the short run for two main reasons:

1. We assume the economy has unused resources (labor, machines). This means firms can produce more output without increasing their marginal costs, so they don't need to raise prices.
2. It is a simplifying assumption that helps us build our initial model.

Macroeconomic Equilibrium with Price Level Fixed

(A) Graphical Method

We can represent the components of aggregate demand graphically.

• Consumption Function: The equation C = C̄ + cY can be drawn as an upward-sloping line. The line starts at C̄ on the vertical axis (the intercept) and has a slope equal to c (the MPC).
• Investment Function: Since investment is autonomous (I = Ī), it is represented by a horizontal line parallel to the income axis.
• Aggregate Demand Function: The AD curve is found by vertically adding the consumption and investment functions. It will be a line parallel to the consumption curve, but starting from a higher intercept (C̄ + Ī).

Supply Side With fixed prices and unused resources, firms are willing to supply whatever is demanded. This is represented by a 45° line from the origin. Every point on this line has the same horizontal and vertical coordinate, meaning that total income/output (Y) equals aggregate supply.

Equilibrium The equilibrium level of income is found where the ex ante aggregate demand (AD) curve intersects the aggregate supply (45°) line. At this point, planned spending exactly equals the planned level of output in the economy.

(B) Algebraic Method

We can find the equilibrium income algebraically by setting aggregate supply equal to aggregate demand: $Y = AD$ $Y = \bar{C} + \bar{I} + cY$ Now, we solve for Y: $Y - cY = \bar{C} + \bar{I}$ $Y(1 - c) = \bar{C} + \bar{I}$ $Y = \frac{\bar{C} + \bar{I}}{1 - c}$ This equation tells us the equilibrium level of income in the economy.

Effect of an Autonomous Change in Aggregate Demand on Income and Output

Equilibrium income depends on aggregate demand. If any component of autonomous spending (C̄ or Ī) changes, the equilibrium level of income will also change.

Let's say autonomous investment increases. This will shift the entire AD curve upwards. The original equilibrium point is no longer valid because at that level of income, demand now exceeds supply (excess demand). To meet this demand, producers will increase their output. This process continues until a new, higher equilibrium level of income is reached.

Interestingly, the increase in equilibrium income will be greater than the initial increase in autonomous investment. This magnified effect is known as the multiplier.

The Multiplier Mechanism

An initial change in autonomous expenditure (like investment) leads to a much larger change in the final equilibrium income. This is because of the multiplier mechanism.

Here's how it works as a chain reaction:

1. Round 1: Suppose autonomous investment increases by ₹10. This directly increases aggregate demand by ₹10. To meet this demand, firms increase output by ₹10. This extra output becomes ₹10 of new income for households (as wages, profit, etc.).
2. Round 2: Households receive this extra ₹10 of income. They will spend a fraction of it, determined by the MPC. If MPC is 0.8, they will spend ₹8 (0.8 x 10) and save ₹2. This new spending of ₹8 increases aggregate demand again.
3. Round 3: To meet this new demand of ₹8, firms produce ₹8 of extra output, which creates ₹8 of new income. Households then spend 0.8 of this, which is ₹6.40.
4. And so on...: This process continues in successive rounds, with each new round of spending being smaller than the last.

The total increase in income is the sum of all these rounds: $10 + (0.8 \times 10) + (0.8^2 \times 10) + (0.8^3 \times 10) + \dots$ This is an infinite geometric series. The total increase in income (ΔY) can be calculated using a formula. The ratio of the total change in income to the initial change in autonomous expenditure is the investment multiplier.

$\text{The investment multiplier} = \frac{\Delta Y}{\Delta \bar{A}} = \frac{1}{1 - c} = \frac{1}{s}$ Where ΔĀ is the initial change in autonomous spending, and c is the MPC.

Paradox of Thrift

Common sense suggests that if everyone saves more, total savings in the economy should increase. However, the Paradox of Thrift shows that this may not be true. If everyone in the economy becomes more thrifty (i.e., their MPS increases and MPC decreases), the total value of savings may not increase; it might even remain the same or decline.

Here's why:

1. Suppose people decide to save more. This means their MPC decreases (e.g., from 0.8 to 0.5).
2. A lower MPC means that for any given level of income, consumption spending will be lower. This causes the aggregate demand (AD) curve to shift downwards (or swing downwards, as its slope c decreases).
3. With lower aggregate demand, there is now an excess supply of goods. Firms find their inventories piling up.
4. In response, firms cut production, which leads to a decrease in national income.
5. This process continues until a new, lower equilibrium level of income is reached.

At this new, lower income level, people are saving a larger proportion of their income, but their total income is smaller. The net result can be that the total amount of savings remains unchanged. In our model, savings must equal planned investment (I) in equilibrium. Since we assumed I is autonomous and constant, total savings must return to its original level.

Some More Concepts

The equilibrium level of income determined in our model does not necessarily correspond to the full employment level of income. Full employment is a situation where all factors of production (like labor) are fully utilized.

• Deficient Demand: If the equilibrium level of output is less than the full employment level, it means aggregate demand is not high enough to employ all available resources. This leads to unemployment.
• Excess Demand: If the equilibrium level of output is more than the full employment level, it means aggregate demand is higher than what the economy can produce with its available resources at full employment. This situation leads to a rise in prices (inflation) in the long run.