The Keynesian cross model. The cumulative flow curve has a positive slope. The red dot shows full employment of resources in the economy
Consumer spending(designation WITH) - household expenditures on goods and services. Consumer spending is made up of two parts:
Investments(designation I) - firms purchase capital with the aim of increasing the production of goods and, therefore, maximizing profits.
Government procurement of goods and services(designation G) - state investments, salaries of civil servants, etc.
Net exports(designation Xn or NX) is the difference between export and import. The ratio of exports and imports shows the state of the trade balance. If exports exceed imports, then the country has a trade surplus; if imports exceed exports, then there is a trade deficit, respectively.
Net exports can also be either autonomous or dependent, this time, on the marginal rate of imports ( mpm) and the level of aggregate output. The marginal propensity to import explains how much, on average, a country's imports increase for each additional unit of total income (or real GDP).
The ratio of government purchases and net taxes shows the state of the state budget. If government purchases exceed net taxes, then the country has a government budget deficit, respectively, a budget surplus means that net taxes exceed the size of government purchases.
Equilibrium output(designation Y) - equal to the total flow rate ( A.E.).
The Keynesian cross is represented on the graph as a combination of two curves:
since in macroeconomic theory it is believed that real aggregate expenditure is always equal to aggregate output.
Only the planned cumulative flow curve can change. It can either move parallel or change its angle of inclination. A parallel shift of the curve can be observed in the event of changes in any autonomous total flow parameters. The angle of inclination, accordingly, changes if either the maximum consumption rate or the maximum import rate changes, or both of these parameters change simultaneously.
The Keynesian cross is one of the most famous ways to model aggregate demand. Using this model, it is possible to determine such parameters as the equilibrium output volume, the general price level in the economy, just as in the AD-AS model. Since the intersection of the planned curve and the actual total flow curve shows full employment of resources in economics, the “Keynesian cross” can also be used to analyze the phases of economic cycles. If actual total consumption exceeds the planned one (that is, the level of output is greater than the level of full employment of resources), this means that firms were unable to sell as much as planned, which entails a decrease in output, an increase in the level of cyclical
Keynesian cross model
The Keynesian cross is the simplest interpretation of the Keynesian theory of national income.
To build this model, we consider the factors that determine the amount of planned expenses (planned aggregate demand).
Planned spending is the amount that households, firms and government intend spend on goods and services. Planned or desired expenses do not always coincide with actual ones.
Actual costs differ from planned ones if firms are forced to unplanned investments in inventories those. when they increase or decrease their inventory in response to unexpectedly high or unexpectedly low sales.
In a closed economy (where net exports are zero), planned expenditure E is the sum of consumption C, planned investment I and government expenditure G:
Let us replace equation C in this with the expression of the consumption function:
C(Y-T)= C*+MPC(Y-T), where:
(Y-T)-disposable income,
Y-total income (real GDP), T-taxes, MPC-marginal propensity to consume, Ĉ-autonomous consumption. In addition, it is assumed that the level of planned investment is fixed and does not depend on income Y (I=I*), and the level of government spending and taxes remain unchanged (G=G*, T=T*). Taking into account all these assumptions, planned expenditures (planned aggregate demand) can be represented as:
E=C*+MPC(Y-T*)+I*+C*
From this equation it follows that planned expenses are a function of total income Y.
In Fig. 20, planned expenses are depicted graphically as a function of income. This line has a positive slope because a higher level of income leads to a higher level of consumption and thus a higher level of planned expenditure. The slope of the line represents MPC, which shows how much planned expenses will increase if total income increases by 1 ruble.
Rice. 20 Function of planned expenses
The economy is in equilibrium when actual spending equals planned spending. Since the costs of purchasing manufactured products are always equal to the income of economic entities (the main identity of the system of national accounts). Y is equal not only to total income, but also to actual expenditure on goods and services. Therefore, the equilibrium condition is written as follows:
A line drawn at an angle of 45º in Fig. 21 marks all points where this condition is met. If we combine this line with a graph of the planned spending function, the diagram becomes a Keynesian cross.
Fig 21 Keynesian cross
Equilibrium is achieved at point A, where the graph of the planned expenditure function intersects a line with a slope of 45º (bisector).
It should be noted that according to Keynes, equilibrium income (Y A) may not coincide with potential income (Y*), i.e. with the full-time income level. Keynes substantiated the thesis that equilibrium is possible under conditions of underemployment.
Inventories play an important role in the process of moving towards an equilibrium state. If firms produce more goods than consumers want to buy, they increase inventories. If, for example, GDP is at a level exceeding the equilibrium level (Y1 in Fig. 22), then the planned expenditures E 1 are less than Y 1. Firms manage to sell less than they produce, so inventories increase: this accumulation of inventories represents unplanned investment. Rising inventories are forcing firms to lay off workers and cut production. GDP will decline until it reaches the equilibrium level Y A.
Conversely, if firms produced less than consumers want to buy, firms sell off some of their inventory. If GDP is at a level below the equilibrium level (Y 2 in Fig. 22), planned expenditures E 2 are greater than Y 2. Now firms sell more than they produce. Inventories decrease, so firms hire more workers and increase production, thereby causing GDP to increase. This process continues until the level of income equals the planned expenses.
The Keynesian model of macroeconomic equilibrium was set out by J.M. Keynes in his work “The General Theory of Employment, Interest and Money.”
Equilibrium model “national income – aggregate expenditures” or “Keynes cross”:
– used in analyzing the impact of macroeconomic conditions on national flows of income and expenses;
– clearly shows what impact a change in each component of total expenditure can have on national income.
Aggregate demand in the Keynesian model depends on such important categories as the consumption function and the saving function. Both consumption and saving are functions of income. For better understanding, the following quantities are used:
– marginal propensity to consume (MPC) calculated using the formula: , (1)
– marginal propensity to save (MPS): ,
Example. If the additional income of a household is 100 rubles, of which 75 rubles. is used for consumption, and the remaining 25 rubles. – for additional savings, then MPC will be 75/100 = 0.75, and b3S – 25/100 = 0.25.
The marginal propensity to consume is between zero and one: 0< МРС < 1. Их сумма всегда равна единице.
Average propensity to consume (APC) calculated by the formula: 
Average propensity to save (APS)
Let's build a simplified model, assuming that all total expenses (AE) are represented only by consumption expenses.
Planned or desired consumption expenditures (C), which represent all total expenditures, are plotted on the y-axis. The amount of output, income Y is plotted on the x-axis. If total expenses exactly corresponded to total income, then this would be reflected by any point lying on a straight line drawn at an angle of 45º, expressed by the equation C = Y. But in reality, such a coincidence does not occur, the MPC is less than 1, and only part of the income is spent on consumption . The slope of curve C at all its points is determined by the marginal propensity to consume. Therefore, the graph of the consumption function should deviate downward from the 45º line. Hence the consumption function:
Consumption function without taking into account autonomous consumption
Consumption exists even at zero income.
Autonomous consumption- consumption independent of the level of current income.
Graphically, autonomous consumption is a line running parallel to the x-axis.
Autonomous consumption
Factors determining autonomous consumption:
– expectations.
– wealth Example. A fall or sharp rise in the performance of stock exchanges will affect the behavior of those who store their wealth in the form of securities.
– credit.
Let's assume that autonomous consumption will be 100 billion rubles. Taking this into account, the formula for determining the consumption function takes the form:
Graphically, this means that the consumer spending curve is constructed as a vertical summation of the curves. The consumption graph does not start from the origin of the coordinate axes, but from the point lying on the ordinate axis corresponding to the level of autonomous consumption.
Consumption function taking into account autonomous consumption.
To build a model in its simplest form, it is necessary to solve a system of two equations:
Y = C (graphically represented by the 45º line
(consumption function graph)
Example. If MPC = 0.75, and autonomous consumption is 100 billion rubles, then we get: C = 100 + 0.75 Y. Since Y = C, then, substituting the symbol Y instead of C, we can write: Y = 100 + 0 .75Y. Consequently, the equilibrium level of income will be 400 billion rubles. The intersection of the 45º line and the consumption schedule at point E means the level of zero savings. To the left of this point you can see a shaded area reflecting negative saving (i.e. “living on debt”), and to the right – positive saving.
Equilibrium is observed at point E, since only here income and expenses are equal. With an income level equal to, for example, 700 billion rubles, the amount of consumption C will be: 100 + (0.75 x 700) = 625 billion rubles. The vertical distance between the 45º line and the consumption schedule, indicated by the letter S, is the value of savings equal to 75 billion. rub. (700 – 625).
"Keynesian cross": the simplest model
The saving function is defined
The most important component of planned total expenditures is investment, I. The level of investment has a significant impact on the volume of national income of society.
Investments (capital investments) throughout the country affect economic growth. The source of investment is savings. Savings are disposable income minus personal consumption expenses: (Y – T) – C. The problem is that savings are carried out by some economic agents, while investments can be made by completely different groups of economic entities.
Factors influencing investment:
1. Expected rate of return
2. Interest rate level
3. Changes in technology and innovation
4. Taxation level
5. Rate of inflationary depreciation of money
Investments whose value does not depend on current income are autonomous investments.
With the revival of business activity and employment growth, the desire of various groups of entrepreneurs to invest will increase. These investments are usually called derivatives, or induced, they depend on the dynamics of national income. The higher the level of income in a society, the more investment is made, and vice versa.
Investment is a function of the interest rate: I = I (r)
This function is decreasing: the higher the interest rate, the lower the level of investment. The balance between investment and savings is determined by a flexible interest rate.
According to Keynes, saving is a function of income, not interest rate: S = S(Y).
In a closed economy without government spending, the most important macroeconomic identity is: Y = C + I
On the one hand, national income when used is equal to the sum of consumption expenditures (C) and investment (I).
On the other hand, the generated national income can be represented as:
Y = C + S, where S is a function of current income.
The Keynesian cross model is interpreted based on the injection approach.
Keynesian cross model
The third component of expenditure is government expenditure (G). Let us assume that their value is 200 billion rubles.
The fourth component of autonomous aggregate expenditure is net exports (Xn). It also does not depend directly on current income. Let's assume that net exports amount to 50 billion rubles.
The ordinate axis shows the value of all components of autonomous costs:
C a = 100 billion rubles, I = 150 billion rubles, G = 200 billion rubles, Xn = 50 billion rubles. In total, the value of autonomous expenses is designated A and is equal to 500 billion rubles. The highest line (C a + I + G + Xn) reflects all components of autonomous costs. At any equilibrium point located on the 45º line, total expenses AE are equal to income Y and can be represented by the formula: .
Macroeconomic equilibrium is shown by points E 1, E 2, E 3, E 4, reflecting a higher level of income as the autonomous components of total expenditures increase. Line F shows the level of full employment at which income is equal to 2000 billion rubles.
The graph of consumer spending that we constructed earlier rises by an amount equal to the sum of all components of autonomous spending.
Macroeconomic equilibrium at full employment can be achieved graphically by shifting the total expenditure curve upward.
At point E 4, the equilibrium level of income at full employment is 2000 billion rubles. The equilibrium value of Y E is determined by the formula:
A is the amount of any autonomous expenses.
An upward shift in the aggregate expenditure schedule is caused by an increase in any of the components of autonomous aggregate expenditure. This is explained by changes in the determinants of autonomous consumption expenditure, investment, government expenditure and net exports.
Cartoonist
"Multiplier" means "multiplier". The essence of the multiplier effect is as follows: with an increase in any of the components of autonomous expenses, the national income of society increases, and by an amount greater than the initial increase in expenses.
Value M 
- autonomous expenditure multiplier.
The multiplier formula can also be expressed in terms of the marginal propensity to save: M
The higher the propensity to consume and, accordingly, the lower the propensity to save, the greater the Mk and the greater the increase in national income will accompany the initial increase in investment. Thus, the multiplier can be defined as the ratio of the change in income to the change in any of the components of autonomous expenses M
The multiplier effect acts not only in the direction of increasing the level of income or output. A reduction in any of the components of autonomous spending will cause a multiple reduction in income and employment. Then, in our case, the schedule of aggregate expenditures will shift downward, and the macroeconomic equilibrium will be established at an increasingly lower level of income.
To avoid significant losses from a decline in production, an active government policy is needed to regulate aggregate demand. Therefore, Keynes' theory is called the theory of aggregate demand.
Actual investments include both planned and unplanned investments. The latter represent unforeseen changes in investment in inventory. They reconcile the actual amounts of savings and investment and establish macroeconomic equilibrium.
Planned spending is the amount that households, firms, governments, and the outside world plan to spend on goods and services.
Actual costs differ from planned ones when firms are forced to make unplanned investments in inventories in the face of unexpected changes in sales levels.
Fig. 11. Keynes Cross
Function of planned expenses:
E = C + I + G + NX.
The line of planned expenses will intersect the line where real and planned expenses are equal to each other (line Y=E) at point A. This graph is called the Keynes cross. On the Y=E line, equality of planned and actual investments and savings is always maintained. At point A this equality is achieved, i.e. macroeconomic equilibrium is established.
If the actual volume of production (Y1) is greater than the equilibrium level (Y0), then buyers purchase less goods than firms produce (AD< AS). Возрастают ТМЗ, что вынуждает фирмы снижать производство и занятость. В итоге снижается ВНП. Постепенно снижается до, доход и планируемые расходы становятся равными (AD = AS).
If the actual output Y2 is less than the equilibrium Y0, then firms produce less than buyers are willing to purchase (AD > AS). Increased demand is met by reducing inventories of materials, which creates incentives to increase employment and output. As a result, GNP increases to Y0 (AD = AS).
Keynesian cross (Keynesian cross) is a macroeconomic model in economic theory that shows the positive relationship between aggregate spending and the general price level in a country.
The theory of aggregate demand is often called Keynesian economic theory. The Keynesian model is based on the identity of total expenses and total income (Say's model): V = E, where V is income, output; E - expenses.
There are real and planned expenses. Planned expenses represent the amount of expenditure that all economic agents plan to spend on goods and services. Real costs occur when firms are forced to make unplanned investments in inventory in the face of an unexpected change in sales levels.
If the economy is closed, then planned expenditures can be defined as the sum of consumption, planned investments and government expenditures:
E = C + I + G.
We express the consumption function by the identity: C = C (V - T), the investment function - I = I' (investments are fixed), the amount of government spending and the amount of taxes are stable, that is, G = G' and T = T', in this case in closed economy:
E = C (V - T) + I’ + G’.
This equality means that the amount of planned expenditures is a function of income, planned investments and planned government purchases.
Keynesian cross
On the graph, point A is the point of equality of actual and planned expenses. In this case, the output volume is equal to the potential one. This model is called "Keynesian cross". If aggregate demand (AD) increases to level E 1 and the growth of aggregate supply begins to outpace the growth of aggregate demand (AS > AD), that is, firms increase their output to a greater extent than aggregate demand grows, then an unplanned accumulation of inventories occurs. If aggregate demand falls to E 2 and firms reduce supply to V 2, there will be an excess of aggregate demand over aggregate supply: (AD > AS), it will be satisfied by reducing inventories. Reducing inventories will stimulate production growth and the economy will begin to shift towards natural output.
The equilibrium output V o may fluctuate depending on changes in the value of any component of total expenditure. An increase in any of the components shifts the planned expenditure curve upward, which affects the growth of the equilibrium level of output. A decline in any component of aggregate demand entails a decline in the level of employment and equilibrium output.
If the actual output volume is less than the potential output (V o< V"), то это говорит о том, что совокупный спрос неэффективен, т.е. совокупные расходы в экономике недостаточны для того, чтобы обеспечить полную занятость ресурсов. Эффект недостаточности совокупного спроса депрессивно влияет на экономику - возникает recessionary gap(although AD = AS). In order to overcome this recessionary gap, as well as ensure full employment, it is necessary to ensure an increase in aggregate demand to a level that ensures that the actual volume of output is equal to the potential: V o = V."
If the actual volume of output is greater than the potential (V o > V"), then this indicates that aggregate expenditures in the country are excessive. Due to excess aggregate demand, inflation boom: the price level consequently increases. Firms are not able to expand production in proportion to increasing aggregate demand, because all available resources are already occupied in production - an inflationary gap arises. The inflation gap is overcome by restraining aggregate demand.
The Keynes cross can only be used for the purposes of macroeconomic analysis in the short term, because implies fixed prices and cannot be used to analyze the consequences of macroeconomic policy in the long term, which are associated with an increase or decrease in the level of inflation.
The Keynesian cross shows only how the equilibrium output level is established at a given level of planned investment, government spending and taxes.
The paradox of thrift is a paradoxical phenomenon, the essence of which is a reduction in savings due to an increase in the desire to save (that is, an increase in frugality). The reasons for this phenomenon are that frugality causes a decrease in consumption and, consequently, leads to a reduction in the volume of product sales. As a result, companies are slowing down the investment process and hiring less and less labor. Revenues are falling. Ultimately, despite the possible increase in the share of income that is allocated to savings, income itself is reduced so that the total volume of savings also decreases.
Figure 1. The paradox of frugality
An upward shift in the graph of the saving function from S to S 1 with a constant level of autonomous investment I will lead to the fact that, due to the multiplier effect, the economy will operate at a lower output level. So, if previously the equilibrium between savings and investments was established at point E with an income value of Y 0, now the equilibrium will be established at point E I with a value of Y I. Thus, the paradox of thrift means that more savings leads to less income.
