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## Aggregate demand## The consumption function
Remember that in the classical model, consumption depends on the real interest rate. In the cross model it depends on GDP. Note that it is not possible to include on C Y.## Consumption and GDPAt first, it might seem obvious that consumption will depend on Y. If GDP is doubled in real terms over a number of years, private consumption, government consumption and investment will also each roughly be doubled. If you draw a graph of GDP and consumption over time you see that consumption does grow by about the same rate as GDP. However, from this reasoning, we depends on the C because Y from our variables growth has been removed and Y. We need to think of C as a variable that varies over time around some average. Sometimes it is above the average and sometimes it is below the average but there is now upward trend. The same is true for C.Y The crucial question then is whether consumption is above its average in periods when GDP is above its average and vise versa (technically, if the detrended variables are correlated over time). Keynes would have said yes, while classics would have said no. Keynes’ motivation: In good times, when The classical motivation: Consumers want to smooth their consumption over time. In good times, consumers know that this is a temporary state. Instead of increasing consumption, they
## The rest of the world in the cross model
In the classical model, imports does not depend on Y. The discussion whether imports depends on increases, consumption will increase by more than imports. This makes sense since C is usually larger than Y. For example, suppose that Y is 1000 while C is 100 and that Im increases by 10%. If Y and C increase by 5% each, Im will increase by 50 while C will increases by only 5.Im Net exports - X will depend negatively on the Im and rest of the world savings Y = SR -Im depends positively on X in the cross model. If we want to be explicit about these dependences we write:Y ## The government in the cross model
In this model, when national income increases, the amount individuals pay in income taxes will increase. This is because income tax is specified as a percentage of total income. Other taxes may also increase when will increase when NT increases.Y Even though may change even if NT does not change. This means that Y is part exogenous (as it may be controlled by the government) and part endogenous (as it will automatically change when NT changes). Therefore, we write Y but we must remember the exogenous nature of net taxes. Government savings, which is also part endogenous and part exogenous, depends positively on NT(Y) and we write:Y ## Savings
Household savings depends on = SH - Y - C and NT and C both depend on Y. How it depends on NT cannot be conclusively be determined from this relationship as Y and C both depends positively on NT We always assume that this dependence is positive and the following example illustrates why this assumption makes sense.Y. Suppose that is a constant between 0 and 1.tis the proportion of income that we pay in taxes. Next, suppose that C = c- 1where Yd is a constant between 0 and 1. c is proportion of disposable income that we use for consumption. If income c increases by 1, NT increase by t, disposable income increases by 1 - Y and C increases by c(1 - t). Thus, t increases by 1 - c(1 - t) - t = (1 - c)(1 - t) > 0.SH Since S = + SG and all parts on the right hand side depends positively on Y, total saving S will depend on positive SR and we write Y for total savings (net total supply of savings).S(Y) ## Aggregate demand in the cross modelSince C and Im depends positively on and I are exogenous, aggregate demand X will depend positively on YD Y:When Y increases, increases but since Im increases more than Im, aggregate demand will increase when C increases.Y You may react to the the notation as the national income (GDP = national income) then Y simply tells us that aggregate demand depends on income. Aggregate demand is the total quantity of finished goods and services that all sectors (consumers, firms, government and the rest of the world) together wish to buy under different conditions. The notation YD(Y) tells us that the only endogenous variable that affects aggregate demand is national income. The higher the income, the more we wish to buy. YD(Y) and YD, C, Im, S, SH, SG, SR all depend on NT while Y and I, G are exogenous. We can illustrate this using the following diagrams.X
Each diagram has real GDP on the x-axis. • The first diagram shows exports = 1.3 and X = 0.56 + 0.2 Y.Im • The second diagram shows private consumption (C), investment (I ), government spending
and aggregate demand (NX) = (YD + C + I + G Here, NX). = 0.22 + 0.4C Y,
= 0.7.G • The third diagram shows private savings (SH), public savings (SG), the rest of the world savings (SR) and the total savings (S = + SR). They are created from SG = 0.26/.NT This diagram summarizes all variables in the cross model and how they depend on Y. Actually, these dependences will be the same in all of the Keynesian models. |

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