What you must know to pass an Economics Exam/Interview 4- The Importance of the 45° line in Income Determination Theory-

Aggregate Demand is the total amount of goods demanded in the economy. Distinguishing among goods demanded for consumption(C), for investment (I), by the government (G), and as net exports(NX), aggregate demand (AD) is determined by

AD=E=C+I+G+NX                                                                                                 (1)

Output is at its equilibrium level when the quantity of output produced is equal to the quantity demanded. Thus, an economy is at its equilibrium output when

Y=E=AD=C+I+G+NX                                                                                                 (2)

The simple form of (2) and of the identities discussed later results from neglecting some complexities in the definitions of GDP and national income.

Depreciation is neglected, so we do not need to distinguish between GDP and Net-National Product. We also assume that GDP and national income are equivalent. This means we do not include items in the model that cause a discrepancy between the two totals (primarily indirect business taxes). A final assumption relates to the units in which each of the variables is measured. We assume that the aggregate price level is fixed.All variables are real variables and all changes are in real terms.

With national product also measuring national income, we can write

YC+S+T                                                                                                              (3)

Equation 3 is an accounting definition or identity, stating that national income, all of which is assumed to be paid to households in return for factor services(wages, interest, rents, dividends) is either consumed (C), paid out in taxes (T), or saved(S).

In addition , from the fact that Y is national product, we can write

YC+I_r+G                                                                                               (4)

Equation (4) defines national product as equal to consumption plus realized investment plus government spending.

Realised investment is the total that appears in the national income accounts whether or not that investment was desired by the firms.

Using the definitions given in Equations 3 and 4, we rewrite the condition given for equilibrium income given in equation (2) in two lternative ways, which will help us understand the nature of equilibrium in the model.By 2, Y must equal C+I+G in equilibrium, and from 3 Y is defined as C+S+T; in requilibrium therefore,

C+S+TYC+I+G

Or equivalently

S+T=I+G                              (5)

From equations 2 and 4, we can see that in equilibrium,

C+I_r+GYC+I+G

Or,

By canceling terms

I_r =I                           (6)

There are then three equivalent ways to state the condition for equilibrium in the model:

Y=E=C+I+G    (2)

S+T=I+G           (5)

I_r =I                    (6)

To see how realized and inventory investment can differ, consider what happens when a level of output() is produced that exceeds AD(E=C+I+G).

In this case

YE

C+I_r+GC+I+G                         

 

Where I_r-I is the unintended inventory accumulation. The amount by which output exceeds Aggregate Demand(I_r-I) will be unsold output over and above the amount of inventory investment the firm desired. The excess is unintended inventory accumulation.

In the reverse situation, in which AD exceeds Output, we have

 

C+I+GC+I_r+G         (8)

II_r

Where I-I_r, is the unintended inventory shortfall. Demand is greater than output and firms sell more than was planned.Inventories end up at less than the desired level.The equilibrium point(I= I_r) is a level of production that, after all sales are made, leaves inventory investment at just the level desired by the firms. As can be seen from equation (7) or (8), this is the level at which output is equal to Aggregate Demand and hence is equivalent to the other two ways of expressing the condition for equilibrium.

The third way of expressing the condition for equilibrium in this model, shows clearly why there cannot be equilibrium at any other point.If at a given level of output, firms are accumulating undesired inventories or are seeing their inventories depleted, there is a tendency for output to change. I

If production exceeds demand, YE, firms are acumulatinghh unwanted inventories I_rI, and hence there is a tendency for output to fall as firms cut production to reduce the level of inventories.If alternately, demand is outstripping production, EY, there is an inventory shortfall I_r<I and a tendency for output to rise as firms try to prevent further fall in inventories.

Only when AD equals Output will firms be satisfied with their current level of output.There is neither an unintended inventory build up nor a shortfall and therefore no tendency for output to change. The situation is what is meant by equilibrium.

Graphical Determination of Equilibrium Income.

Income is measured along the horizontal axis, and the components of AD along the ve3rtical axis. The 45 line is drawn to split the positive quadrant of the graph. All points along this line indicate that aggregate expenditure equals aggregate output. The value of the variables measured on the vertical axis(C+I+G), is equal to the value of the variable on the horizontal axis, Y.C=a+bYD and Y=C+I+G, because the autonomous expenditure components I,G do not depend directly on income, the C+I+G schedule lies above the consumption function by a constant amount.

The equilibrium level of income is shown at the point where the C+I+G scheduler crosses the 45 line, and AD is therefore equal to income.

This intersection illustrates the equilibrium condition expressed in Equation 2

Y=E=C+I+G    (2)

The understanding of the 45 line and of the properties of an equilibrium level of income is aided by considering why other points on the graph are not points of equilibrium.Consider a level of income below Y, for example Y_L.

A level of income equal to Y_L generates consumption as shown along the consumption function.When this level of consumption I is added to the auitonomous expernditures I+G, aggregate demand exceeds income, the C+I+G schedule is above the 45 line. It follows that with demand outstripping production, desired investment will exceed actual investment at points such as Y_L,C+I+G>Y C+I_r+G, therefore I> I_r.There will be an unintended inventory shortfall at such points below and therefore a tendency for output to rise. Conversely, at levels of income above , output will exceed demand the 45 line is above the C+I+G schedule, and unintended inventory investment wil bev taking place(Y C+I_r+G>C+I+G; therefore I_r>I), and there will be a tendency for output to fall.It is only at that output is equal to AD; there is no unintrended inventory shortfall or accumulation, and consequently no tendency for output to change.

What you must know to pass an Economics Exam/Interview 3: Income and Spending

 (Reference:  Dornbusch, Fischer and Startz, Chapter 9)

1. Output is at its equilibrium level when the aggregate demand for goods is equal to the level of output.
2. Aggregate demand consists of planned spending by households on consumption, by firms on investment goods, and by government on its purchases of goods and services and also includes net exports.
3. When output is at its equilibrium level, there are no unintended changes in inventories and all economic units are making precisely the purchases they had planned to. An adjustment process for the level of output based on the accumulation or rundown of inventories leads the economy to the equilibrium level of output. Know, that AD is equal to planned aggregate spending, on the 45 degree line Aggregate Spending=Output. When the AD curve intersects the 45 degree line planned aggregate spending equals output and Saving equals planned investment.
4. The level of aggregate demand is itself affected by the level of output (equal to the level of income) because consumption demand depends on the level of income.
5. The consumption function relates consumption spending to income. Consumption rises with income. Income that is not consumed is saved, so the savings function can be derived from the consumption function.
6. The multiplier iss the amount by which a $1 change in autonomous spending changes the equilibrium level of output. The greater the propensity to consume, the higher the multiplier.
7. Government purchases and government transfer payments act like increases in autonomous spending in their effects on the equilibrium level of income. A proportional income tax has the same effect on the equilibrium level of income as a reduction in the propensity to consume. A proportional income tax thus reduces the multiplier.
8. The budget surplus is the excess of government receipts over expenditures. When the government is spending more than it receives, the budget is in deficit.The size of the budget surplus or (deficit) is affected by the government’s fiscl policy variables-government purchases, transfer payments, tax rates.
9. The actual budget surplus is also affected by changes in tax collection and transfers resulting from movements in level of income that occur because of changes in private autonomous spending. The full employment budget surplus is used as a measure of the active use of fiscal policy. The full employment surplus measures the budget surplus that would exist if output were at its potential(full-employment) level.