# (S - I) = (G - T) + (X - M)

Hello everyone ! I would like to solicit your help on macroeconomics for AS/AD model… First of all, i read this part on schweser many times, curiculum, investopedia, wiki etc… 3 days that im stucked with this :

The equation :

(S - I) = (G - T) + (X - M)

as an example :

100 = 100 + 0

(or 100 = 0 + 100)

my explanation :

100 of surplus from economy that goes on markets (after I is deducted) gives us = 100 borrowed by governement on markets for a G too high / T too low.

(or 100 of surplus gives us a positive trade balance of 100, meaning 100 of goods exported or money lent to foreigners)

or of course a mix a both

Problem :

If now income increases, S increases (but we consider I remains constant)

so if (S-I) increases, as a consequence = (G –T) decreases because T is higher… but i dont understand why the surplus of trade balance decreases too : if the both part decreases when (S – I) increases the equation cannot be equal :

“Other things equal, higher aggregate income causes the fiscal deficit (G - T) to decrease. or a fiscal surplus to increase, because taxes increase with income. Higher aggregate income in the domestic market also causes the trade surplus (X - M) to decrease, or a trade dcficit to increase, because imports increase with income. Thus. we can represent the sum (G - T) + (X - M) as a decreasing function of aggregate income.” A thousands thanks by advance to whom will be able to help me. Coritani.

What you’re ignoring is that the value (S – I) is also influenced by interest rates: the higher the level of interest rates, the greater the value of (S – I), all else being equal. Thus, there are many (S – I) vs. Y (aggregate income) curves: one for each level of interest rates.

I wrote a series of articles on the IS and LM curves that may be useful; they start here: http://financialexamhelp123.com/islm-deriving-aggregate-demand-synopsis/.

Thank you for the website, i put it in favorites ! So i read you and this sentence is my problem : « When real aggregate income increases, taxes (T) increase as well. Additionally, imports (M) increase with increasing real aggregate income »

If real aggregate income increases ( C + S + T ), _ for C and T constant _, then S increases and so there is more money in the financial markets. Exports should increase = we dont need more M = we already are saving the money in surplus (S) we dont need to use !

coritani

I see your problem: you’re assuming that as aggregate income increases, C and T are constant.

They’re not: they both increase.

And an increase in C leads to an increase in M.

The rest, of course, is legendary.

I understand that Aggregate income = C + S + T and that the three components may increase. I was considering T & C constant in order to show effect of an increase in S on (X - M) there is something i dont understand about the equation (S - I) = (G - T) + (X - M) In your website, for interest rate assuming to be constant (S - I) increase as (G - T) + (X - M) decreases : so the equation is not equilibrate anymore !! (S - I) =/ (G -T) + (X - M) but it must be equal at any time… The change in (S - I) should be equal to the change in (G -T) + (X - M)

The point is that if interest rates change, something else must change as well: real aggregate income. (The mechanism is that interest rates change, causing price level to change, causing real aggregate income to change.)

A=B+C

The question being asked by OP is: If B and C go down in value, how can A now be bigger?

I understand the question that OP is asking.

My response is that C doesn’t necessarily go down in value.

However, if you’re more qualified than I to answer OP’s questions, by all means: jump in and answer them.

First things first, OP mentioned “If now income increases, S increases (but we consider I remains constant)”. This is not necessarily true. Following the equation where Y = C + S + T (in equilibrium), increases in Y may not necessarily result in S increasing in the first place (it is theoretically possible for C and / or T to increase instead – in fact, usually, consumption levels increases when aggregate income increases due to a wealth effect).

Setting that aside, assuming that there is an arbitrary increase in S. In that case, all the (S - I) + (T - G) = (X - M) is saying is: -

Y =

C + S + T = C + I + G + X – M

If only S increases on the left hand side of the equation (other components remaining unchanged), the resulting increase in the saving must go somewhere in equilibrium. Given that we have established that it C and T are constant, it implies that the increased savings must result in the increase in one of the components on the right hand side of the equation (except C). This usually means that an arbitrary increase in savings would flow to private investments, government expenditure (where the public sector makes a borrowing from the private sector) or the foreign sector.

The effect on the foreign sector* can be a little tricky though but as S2000 mentions, in practice, increases in savings do not occur in a vacuum – savings would increase only if there is a corresponding increase in other elements. Even if there was an arbitrary increase in savings, the funds must go somewhere in the equation (again, assuming equilibrium). Depending on the cause of increased saving, the answer to your question can be quite different.

This is not accurate. Increase in savings do not necessarily result in increase in exports. In fact, if income increases (in your example), imports are generally expected to increase as consumption and imports are generally treated as an increasing function to income.

Thank you very much i think i understand that the equation is just algebra and has no “predictive value” as i tried to make very precise assumptions for a change in some elements. Every thing must be balanced, wherever it is in the economy. It is like the put call parity actually : the equation dont tell us how the prices will fluctuate but only that both side must be balanced for no arbitrage opportunity That was the first part of my problem :-), the underlying second part is this part of the CFA curriculum : With (S - I) = (G - T ) + (X - M), we can draw the (S- I) and the (G - T ) + (X - M) curves Independently, i understand everything in the explanation (the effect of interest rate on I, on S…, the effect of an increase in income on S, on I etc… it is clear ) BUT we know now that in a country, ALWAYS (S - I) = (G - T ) + (X - M) right ? So why CFA curriculum says that, for in increase in income : - if (S - I) > (G - T ) + (X - M) then it is an “excess saving or excess expenditure” - if (S - I) < (G - T ) + (X - M) then it is that “planned expenditure exceeds output”… Does the money evaporate of the economic cycle ??? Moreover, i still do not understand how these two curves can be “equal at any time” as they move in opposite direction with a movement of income s-/ Thank you by advance, Coritani

I won’t say that the Mundell-Fleming model no predictive value – in theory, in the long run, there is a tendency for the economy to equilibrate though unlike the put-call parity, the Mundell-Fleming model is a little more philosophical and abstract. The put-call parity theoretically has some form of predictive value. If the put call parity does not hold, prices will tend to change to that predicted by the model because of arbitrage. The reason why I said “theoretically” is simply because in the real world, computerised trading algorithms would usually eliminate any violations of the put-call parity before you can whip out your BA-II+.

Actually, it is not true that “in a country, ALWAYS (S - I) = (G - T ) + (X - M)”. This scenario only happens when in equilibrium (for the real economy, at least – there are other forms of equilibrium. The short version of the story is that the economy is not always in equilibrium (in fact, as you will learn later, the economy may actually take some time. In fact, whether the economy equilibrates is a subject of a whole different debate in the academia. You really don’t want to get into that). I do not actually have the L1 books (or the syllabus) with me now so I don’t really get the context of the portion you quoted (did you inadvertently misquote the syllabus there? Can you type the exact text from the syllabus). However, say in the “planned expenditure exceeds output”. In that case, the general idea is that higher planned expenditure will force producers to liquidate their inventories and subsequently increase investments to increase output. This will result in increased output, bringing it closer to actual aggregate expenditure (eventually). All the syllabus is trying to say is: - 1. The real economy will tend to equilibrate based on the (S - I) = (G - T ) + (X - M) 2. Sometimes, the economy does not equilibrate. 3. When there is a disequilibrium, you will arrive at scenarios such as “excess saving”, “excess expenditure”, etc. 4. Each of the different scenarios stated above would prompt different changes to occur to approach equilibrium (I gave an example of what would happen if planned expenditure exceeds output).

If you are stuck at understanding the IS curve, I wouldn’t bring the money market into your question if I were you (this involves another curve). The short answer is “not really”. The longer answer is “yes, but not in the way you are thinking though the full explanation will probably confuse you further since you are asking the wrong question”

Which two curves? Do you mean the one that plots (S - I) against Y and the other one that plots (G - T) + (X - M) against Y? If yes, that is precisely the point. Think of the IS as a locus where the goods market is in equilibrium. The fact that they goes in opposite direction is meant to explain why the IS curve is downward sloping. If you must know, there are other approaches to the IS-LM curve but: - 1. They are not really CFA sanctioned (or rather, I know them from my bachelor’s course rather than CFA) 2. Analyst Forum won’t allow me to attach any images without hosting them remotely… and that is a pain 3. I think it will confuse you more than it will enlighten you 4. I found an elegant proof to all your questions but the margins of this forum is a little too small for me to post it on.

I think the answer here is a lot simpler than we might think. Indeed, as Y increases, (G - T) and (X - M) fall for obvious reasons. In order to keep the equation in check, (S- I) has to fall as well, and the only possibility for it to fall is by a decreased interest rate (S decreases and I increases), hence the downward sloping IS curve. If it is not clear still, just remember that IS: Y = C (Y-T) + I (i) + XN (ER,Y) ; and knowing that I is negatively correlated with (i), the relationship between Y and I must be negative. Basically, if interest rates go down, investment goes up, and to reach equilibrium in the goods market, Y goes up as well.