Aggregate Demand and Equilibrium Income in a Closed Economy, Study notes of Law

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THE SIMPLE KEYNESIAN

MODEL (SKM)

Conditions for Equilibrium Output

• (^) The central notion in the Keynesian Model is that equilibrium level of output is equal to the aggregate demand (AD). This condition of equilibrium is expressed as ……………..(i) Where is the total output and is the aggregate demand or desired expenditure on output.
• AD consists of three components: household consumption (C), desired business investment demand (I) and the government expenditure, i.e., the government sector’s demand for goods and services (G). So, in equilibrium we have ……………………..(ii)
• (^) Since closed economy is considered here, foreign trade part of aggregate demand is neglected in the analysis
• (^) It is assumed that GDP and national income are equivalent. Thus, the national output, also measures the national income. It is also assumed that the aggregate price level is fixed and all variables are real variables all changes are changes in real terms.

• (^) Thus, there are three equivalent ways to state the condition for equilibrium in the SKM
• These conditions are explained with the help of circular flow of income and output which is explained in the next slide. The explanation and the diagram will only consider the monetary flow.

• National income flow from business sector to the household sector in the form of factor payments and this national income is equivalent to the national output.
• (^) National income is distributed in the household into three flows:
• Flow of consumption expenditure that goes back to the business sector as a demand for output. The diagram shows that the firms produce output (Y), which generates equal amount of income to the household sector, which in turn generates a demand for output (C).
• (^) Apart from the consumption expenditure, there are two other flows out of the household sector – the saving flow and the flow of tax payments. These saving and tax flows are known as the leakages from the circular flow.
• This saving leakage flows into financial markets which means that the part of income that is saved is held in the form of some financial asset.
• (^) The tax flow is paid to the government sector. This tax flow is the net tax payment which is the gross tax payment minus the transfer payments from the government sector to the household sector.

Explanation of the equivalent expressions (v)

• The GDP accountant computes investment as the total volume of business spending on plant and equipment, plus inventory investment. It is assumed here that the desired spending on plant and equipment equals actual spending as recorded by the GDP accountant.
• Let us consider a situation when the total output exceeds the aggregate demand which means …………………………….(vii) Where is the unintended inventory accumulation. The amount by which output exceeds the aggregate demand will be unsold output over and above the amount of inventory investment the firm desired. This excess is untended inventory accumulation.
• (^) Again, let us consider a situation where aggregate demand exceeds total output ………………………….(viii) Where is the unintended inventory shortfall. Here, demand is greater than the output produced and firms sell more than was planned. Inventories end up at less than the desired level.
• (^) Thus, if at any given level of output, firms are accumulating unintended inventories or find their inventories getting depleted, there is a tendency for output to change. If the production exceeds demand, firms are accumulating unwanted inventories and the firms will cut production to reduce the inventories. On the other hand, if demand is more than the output produced, there is inventory shortfall and the firms increase production to prevent further fall in inventories. Thus, when the aggregate demand equals the total output produced, firms are satisfied with the level of output produced and the equilibrium is achieved.

Components of Aggregate Demand

• (^) In order to determine the level of income, the factors that affect the components of aggregate demand is considered here. There are three main components of aggregate demand in a closed economy: consumption, investment and government expenditure Consumption
• According to Keynes, the level of consumption expenditure is a stable function of disposable income, where disposable income is the national income minus the net tax payments.
• (^) Though there are variables other than income which affect consumption, but Keynes believed that income was the dominant factor determining consumption. Hence, the influences of other factors are neglected in the analysis.
• The consumption-income relationship is termed as the consumption function and is given by , , …………..(ix)
• (^) The intercept term ‘a’ which is assumed to be positive, is the value of consumption, when the disposable income is zero. It can be thought of as a measure of the effect on consumption of variables other than income.
• The parameter, ‘b’ indicates the increase in consumption expenditure due to one unit increase in disposable income. This is known as Marginal Propensity to Consume (MPC). It is given by , ……………….(x)

• (^) We have already mentioned before that ……………………..(iii) Rearranging the equation, we can write, ……………..(xi)
• Equation (xi) shows that disposable income is the summation of savings and consumption. Thus, from (xi), we can write, ………………..(xii)
• If the consumption is unit with equal to 0, then at that point,
• (^) Again, if a one unit increase in disposable leads to an increase in units of consumption, the remainder is the increase in savings. …………………..(xiii) This increment to saving per unit of increase in disposable income is known as Marginal Propensity to Save (MPS) and is represented as.

• The saving function shows the level of saving (S) at each level of disposable income. The slope of the saving function is MPS, given by. The intercept term of the saving function () is the level of saving at a zero level of disposable income and it is obviously negative - a

𝐷 S 𝑆 = − 𝑎 +( 1 −𝑏 ) 𝑌 (^) 𝐷

Government Expenditure

• Government spending (G) is a second element of autonomous expenditures.
• (^) Government spending is assumed to be controlled by the policy maker and therefore does not depend directly on the level of income.
• (^) The level of tax receipts (T) is also controlled by the policy maker and is a policy variable. A more realistic assumption is that policy maker sets the tax rate and tax receipts vary with income.

Determining Equilibrium Income

• (^) In equation (ii), we have …………………(ii)
• (^) Equilibrium income (Y) is the endogenous variable which needs to be determined from within the model. The autonomous expenditure, I and G, as well the level of T, are exogenous variables which are determined by factors outside the model and hence their values are given in this model. Consumption, as is assumed to be a function of income, is the induced expenditure determined endogenously by the consumption function , , …………..(ix)
• (^) Substituting equation (ix) in equation (ii) , where ……………(xiv)

• (^) The level of income equal to generates consumption which is shown along the consumption function. When this level of consumption is added to the autonomous expenditures (I+G), the AD exceeds income, this means that (C+I+G) schedule is above the 45 ◦line.
• (^) Equivalently, at this point (I+G) is greater than (S+T).
• In this point, there is more demand in the economy and hence leads to unintended inventory shortfall at any point below and there will be a tendency for output to rise.
• (^) Conversely, at levels of income above , output will exceed demand and leads to unintended inventory accumulation. Then, there will be tendency for output to fall.
• (^) It is only at that output is equal to aggregate demand and there is no unintended inventory shortfall or accumulation. Consequently, there is no tendency of output to change.
• (^) Let us now consider equation (xiv) which says ………(xv) The first term of the equation is called autonomous expenditure multiplier. Since, b represents MPC and lies between 0 and 1, hence, the value of the autonomous expenditure multiplier is greater than one. This is known as autonomous expenditure multiplier because every unit change of autonomous expenditure is multiplied by this factor to get its contribution to equilibrium income.

Changes in Equilibrium Income due to Change in Investment Expenditure

• (^) Let us consider the effect on equilibrium income of a change in autonomous investment demand. It is assumed that other determinants of autonomous expenditures are constant. Thus equation (xv) becomes ……………(xvi) ……………….(xvii) A 1 unit change in investment causes a change in income of units. Suppose b = 0.8, then Y changes by 5 units for each 1 unit change in investment. Reason for income change by a multiple due to one unit change in investment
• (^) The change in investment expenditure is the initial disturbance which causes the aggregate demand to rise. Some of the firms experience this increased demand as a result of this rise in investment and thus output increases. In consequence, their payments of factors of production increase leading to increase in income. As the tax amount is fixed, disposable income increases. Consumption, being a positive linear function of disposable income, increases although by less than the increase in income. This further causes increase in aggregate demand leading to unintended inventory shortfall. Thus, the output further increases. The total increase in output/income is equal to the initial increase in investment , plus, an income-induced increase in consumption.

Changes in Equilibrium Income due to Change in Government Expenditure

• (^) Let us consider the effect on equilibrium income of a change in autonomous investment demand. It is assumed that other determinants of autonomous expenditures are constant. Thus equation (xv) becomes ……………(xvi) ……………….(xvii) A 1 unit change in government expenditure causes a change in income of units. Suppose b = 0.8, then Y changes by 5 units for each 1 unit change in investment. Reason for income change by a multiple due to one unit change in investment
• (^) The change in government expenditure is the initial disturbance which causes the aggregate demand to rise and thus output increases as there is unintended inventory shortfall. As the tax amount is fixed, disposable income increases. Consumption, being a positive linear function of disposable income, increases although by less than the increase in income. This further causes increase in aggregate demand. Thus, the output further increases. The total increase in output/income is equal to the initial increase in government expenditure, plus, an income-induced increase in consumption.

Diagrammatical Explanation

• (^) Suppose initial Government expenditure is , Investment expenditure is and tax is and the equilibrium output/income is. Now let government expenditure increases to.
• The aggregate demand increases, and AD curve shifts upward by the amount. The new AD curve is. The equilibrium point shifts from A to B where the curve cuts the AS curve. Thus, the equilibrium output increases from to.
• In the lower panel diagram, the (I+G) schedule shifts upward from to. Since the remains constant, here also the equilibrium point shifts from A to B. Thus, finally, the output increases from from to. 𝑆 + 𝑇 0 𝐴𝐷 1 = 𝐶 0 + 𝐼 0 + 𝐺 1 B A B A Y Y 𝐴𝐷 0 = 𝐶 0 + 𝐼 (^) 0 + 𝐺 0 𝐼 (^) 0 + 𝐺 1 𝐼 (^) 0 + 𝐺 0 𝑌 (^) 0 𝑌 1 𝑌 (^) 0 𝑌 1