Basic MacroEconomic Relationships

We start with the most simple economy (households and businesses – but no government or foreign trade). This is often referred to as the closed, (meaning no-international trade) no government model. We have to have businesses (this is the producing sector) and households, (the consumers) or there is no economy. Even with a one-person economy, the differences exist: Based on what he wants to consume, Robinson Crusoe chooses what to produce. This is the sovereign consumer sending the signal to the firm what they would be willing to buy.

The Income-Consumption and Income-Saving Relationships: The idea here is that we have two choices with how to use our incomes (usually abbreviated as “Y” in economics). We can spend it (Consumption – usually abbreviated as “C” in economics) or we can save it (Saving - usually abbreviated as “S” in economics). If we use an equation to show this – it would be

Y = C + S

The entire amount of our income has to be used in one of these two ways. Now spending in the entire economy must also equal total  incomes – otherwise where would it come from if not from people’s spending? This means that household spending (called Consumption = C) and Business Spending (called Investment = I) must add up to total income (Y) in the economy. As an equation that means:

Y = C + I

Therefore, in a closed, no government economy (no government, no international trade), S must equal I because:

Y = Y
C + S = C + I
S = I

This means that for Investment to rise, people must save more.

45° (degree) line: This seems odd at first – because we are making a graph with both axes measuring the same thing. Imagine making a graph with your height on one axis and your height on the other. If you were 6 feet tall – then measuring you on the vertical
axis would give us a level of 6 feet. Measuring you lying down would give us a distance of 6 feet. Identifying that point on the graph would give us 6’ up and 6’ over. Seems pretty ridiculous! Another person who is 5’8” (the perfect height for an economics professor), would measure 5’8” up and 5’8” over. If we graphed every person, we would get a bunch of points all with two identical measures.  Graphically, it would look like a ray coming out of the axis at a 45 degree angle.

In our case we are measuring total expenditures on one axis (called Aggregate Expenditures or “AE” - and in the closed, no  government model would equal C + I). We measure total income (Y) or production (GDP) on the other. In equilibrium, total spending in the economy will be equal to total income generated from producing those goods that people bought – which would equal the value of the production people got paid to produce (and the amount people paid to produce those items).

So what is the point? The 45 degree line represents all the possible equilibrium points – only one would be our equilibrium point (at  any given time) but any point that is in equilibrium (where AE = Y = GDP) must be on that line. You may recognize these three concepts as GDP added up as production (GDP) as Income (Y) and as Expenditures (C + Ig + G + Net exports) We are building  expenditures up piece by piece – starting with consumption (the biggest part of the economy – 68% of it)

The Consumption Schedule – We know that the more money we have – the more money we spend (all other things equal). It’s only human nature that we buy more when we have more. But we also know that even if we had nothing, we would spend some money – by either borrowing it or by dipping into our savings accounts. These two obvious relationships help us determine the shape of the  Consumption curve. Even if income is “0”, we know that spending would be more than zero (we do have to eat!). And as income rises from “0”, we expect consumption to rise too.

Like any line – we can make an equation of this line of the form (y = mx + b).

• We used to call “b” the “y intercept” or “the point where the curve crosses the vertical axis). We will call this point “autonomous  consumption” – which just means the amount of consumption we do that does not depend on how much income we have – i.e. – we would buy this much stuff even if your income was “0”. As an abbreviation – we use the letter “a” for autonomous consumption.
• What was “m” in the original equation (the slope of the curve), we will call “b” and we’ll get back to the economic meaning of this below. I know that’s confusing to take what “b” used to mean (y intercept) and now use it to mean slope – but that’s how economics does it.
• Substituting Income or “Y” for the original formula’s “x axis variable” and Consumption Expenditures or “C” for the for the “y axis variable”, we get the formula :
  • C = a + bY

A little playing with it will show you that it is still just an equation of a line.

The Saving Schedule: We’ve already noted that Saving and Consumption are linked. (Totaled together they equal income --> Y = C + S). Since that’s true, their curves must be linked. So for example, if our income (Y) is “0” and C = 40; then S must be –40. If income is 100, and C is 80, the other 20 must have been saved. I.e at very low levels of income, we spend more than we make – so we dissave  (or borrow) – so S would be negative. At some point, we might make more than we spend, so now S would be positive.

We also know that the faster the C curve rises, the slower the S curve rises – because if we spend 90% of what we make (a slope of the C curve of .9), then our savings must be rising only at 10% (a slope of the S curve of .1). How do we get this? We play with the equation and think like a household.

Y = C + S

If when Y=$100, C= $60, then S must be $40.

$100 = $60 + $40

If I get one more dollar, and spend 90% of it, C rises to $60.90, then Savings must have risen to $40.10 to equal the entire income of $101.

$101 = $60.90 + $40.10

Graphing, the C curve rose .9 as we moved $1 to the right along the Income (Y) axis.

Rise / Run = .90/$1.00 = .9

Graphing, the S curve rose .10 as we moved $1 to the right along the Income (Y) axis.

Rise / Run = .10/$1.00 = .1

In all cases, the slope of the C curve and the slope of the S curve will add up to 1.

By playing with the equation, it shows that a change in income (delta-Y) is used up as either additional consumption spending (delta-C) or as additional saving (delta-S) – or both (where the symbol "delta" means “change”). But the sum of the change in consumption and the change in saving can not be more than the change in income.

delta-Y = delta-C + delta-S

dicing both sides by delta-Y, we get:

delta-Y/delta-Y = delta-C/delta-Y + delta-S/delta-Y

since anything divided by itself is equal to 1 – that means:

1 = delta-C/delta-Y + delta-S/delta-Y

1 = b + (1-b)

and since delta-C tells us how much the C curve rises whenever Y changes by delta-Y, then delta-C/delta-Y must be rise over run – or the slope of the C curve – which is called “b”. Likewise, since delta-S is how much the S curve rises as Y changes by delta-Y, then delta-S/delta-Y must be the rise over run – or the slope of the S curve – which would be “1-b”. Here again, we see that the slopes of the two curves have to add up to  1. It also means that (adding a little common sense here) since consumption rises (or at least does not fall) as our incomes rise, the slope of C must be positive (i.e. greater than “0”). And since savings do exist, the slope of S must be positive too (since it started out  at a negative number) so it must also be greater than “0”. That means that b must not be more than “1” (since the two slopes have to add up to 1).

So: 0 < b < 1 and also 0 < 1-b < 1

Let’s look at what that does to our graph:

If it copies to your word-processing program correctly – you’ll also notice that I’ve drawn it so that S crosses the x axis at the same level of income as C crosses the 45 degree line. At that level of income (Y*), C = Y (we spent all our income and didn’t borrow or have anything left over), and therefore, S must equal “0” (we didn’t borrow, or save any money).

If we increase the slope of the C curve (started spending more of each additional dollar of income) we must simultaneously have decreased the slope of the S curve (started saving less of each additional dollar of income) . Above we show that the break-even point (where we don’t borrow or save) moved too. But even here, when C = Y, S must still be equal to “0” since Y = C + S. The break even point moves out, as we save more slowly, but the relationship between the S curve and the C curve is unbroken.

Now we give this “b” an economic meaning:

Marginal Propensity to Consume out of additional Income (MPC): This is how much more spending we will do when our incomes rise (delta-C/delta-Y), i.e. – it’s the slope of the C curve. It is our tendency (propensity) to spend more (delta-C) as our incomes rise (delta-Y). We assume that this tendency is constant for our model - i.e. the slope of C will be assumed to be constant over the range of income. Therefore, C is a straight line. If we change the MPC (from .8 to .9 for example) – we change it along the entire relationship – i.e. it’s still a straight line, just the slope changes.

Marginal Propensity to Save out of additional Income (MPS): This is how much more saving we will do when our incomes rise (delta-S/delta-Y), i.e. – it’s the slope of the S curve. It is our tendency (propensity) to save more (delta-S) as our incomes rise (delta-Y). Likewise, we assume that this tendency is also constant for our model - i.e. the slope of S will be assumed to be constant over the range of income.  Therefore, S is also a straight line. If we change the MPS (from .2 to .1 for example) – we change it along the entire relationship – i.e. it’s still a straight line, just the slope changes.

Average Propensity to Consume out of Income (APC) – like any average, we get it by dividing one number by another – in this case, Consumption by Income. It is, on average, how much of our incomes we spend.

APC = C / Y

Average Propensity to Save out of Income (APS) – like with APC, we get this by dividing Saving by Income.

APS = S / Y

Non-Income Determinants of Consumption and Saving:

• Wealth – as our wealth rises, we can spend more – therefore, we spend more at every level of income – including when we have no income. Therefore the C curve shifts up.
• Expectations – as our expectations change, we may spend more (or less, depending on what we’re expecting. Therefore, we spend more (or less) at every level of income – including when we have no income. Therefore the C curve shifts up (or down).
• Real Interest Rates– as real interest rates fall, we may borrow more – therefore, we can spend more at every level of income –  including when we have no income. Therefore the C curve shifts up.
• Household Debt– as our debt rises, we find it more difficult to spend more – therefore, we are forced to curtail spending at every  level of income. Therefore the C curve shifts down.
• Taxation– as tax rates rise, we have less left over after taxes to spend – therefore, we spend less at every level of income –  including when we have no income. Therefore the C curve shifts down.

Terminology – as income rises, we move from one point on a C curve (or on an S curve) to another but the relationship between C (or S) and income (Y) has not changed. Therefore, this is not a change in C (or a change in S) it is a change in the level of C (or S).

If, however, the relationship between Consumption and Income (Y) changes (or the relationship between Saving and Income  changes), the C curve (or S curve) shifts or changes slope (depending on how it changes). We would not only have a different level of C (or S), but also a new curve as well. That is a change in Consumption (or a change in Saving) – and it might also be a change in the level of Consumption (or Saving).

Stability – Consumption (and therefore Saving) decisions are generally made on the long term. So while the things that effect C (or S) may change drastically, they tend to have muted or subdued changes on the C or S curves. The 9/11 attack, for example, had a relatively short term effects on our spending behavior. Most events pale in comparison to that – so too might their effects on  Consumption. If you’re interested in the theory why – it is called the “Permanent Income Hypothesis."

The Interest-Rate - Investment Relationship: Like any demand curve, the Investment demand curve is downward sloping and the level of Investment falls as the price of Investment rises. But what is the Price of Investment? Since many businesses borrow to Invest, we call that cost – the interest rate. They have to pay that cost to invest. You’ll quickly think “hey wait, sometimes they use money they already have instead of borrowing” True, but that means they forgo the money that they would have earned by saving it – i.e. they lose that interest rate. So either way – the cost of investment is interest. The higher the price (the rate of interest) the less Investment happens.

Expected Rate of Return r – the expected rate of return is the internal profit we expect to have from an investment. What does that mean? It means that If I know an investment will cost me $100,000 and will give me back $120,000, I’m gaining 20% over cost of the item.

Why is it called “internal” – because it ignores the fact that some of that return is “unrealized” – because we had to borrow money (at a cost) to invest in this project.

The Real Interest Rate i – This takes into account the costs of investing. So an investment that gives an internal return of 20%, when the interest rate is 12% - only gives a net return of 8% over costs. As long as an investment gives a better rate of return than the interest rate cost of investing, a project will be profitable. So if r > i, then it’s profitable, but if r < i, then it’s not profitable.

Shifts in the Investment Demand Curve:

• Acquisitions, maintenance and Operating Costs – the more it costs for other things (like maintenance) the more internal rate of return is necessary to make that investment profitable. So the higher these costs are, the less investment there will be. The ID curve shifts back.
• Business Taxes – The higher the taxes are to businesses, the more internal rate of return is necessary to make that investment profitable. The ID curve shifts back.
• Technology Change – Technological changes create profitable opportunities – no matter what the interest rate is. So the more  technological change – the more the ID curve shifts out.
• Stock of Capital Goods on Hand – The more capital goods we already have, the less likely we are to invest in more capital. Therefore, the ID curve shifts back.
• Expectations – Again – it depends on what we expect, but if it’s a good expectation, we will be more likely to invest, and the ID curve shifts out. If it’s a bad expectation, the ID curve shifts back.

Instability of Investment: Investment varies a lot. It jumps all over the place. There are several reasons for this:

• Durability – because many investment goods are durable goods, we can postpone investment until conditions make it more profitable to invest. Because of this, whenever anything changes the profitability of an investment, the level of Investment reacts.
• Irregularity of Innovation – As inventions and innovations come to light, there are new opportunities for investment. Since these  innovations are not regular – neither is their effect on investment levels.
• Variability of Profits – So many things effect profits, that a change in present profits may change a firm’s appetite for further  investments.
• Variability of Expectations – Again, this seems fairly obvious. Since our expectation can vary widely – so can the level of investment.

The Multiplier Effect – The change in spending can echo through the economy. In other words, when I spend $100 more than before, that isn’t the only change in the economy. I can’t just say that income goes up by $100 when I do this, because after it goes up for someone – they go out and spend part of it. And then someone else’s income goes up because of that. So if everyone spends 80% of their income (MPC = .8). My injection of $100 into the economy, creates $100 of extra income for someone. They go out and spend $80 more than before, because they have $100 more than before. That’s increases a third person’s income by $80, and they go out  and spend 80% of that (.8 * $80 = $64). This goes around and around until it dies out.

The Multiplier and the Marginal Propensities: You’ll notice that if the MPC is changed, the values of each echo changes too. For example, if we change the multiplier to .9, we get:

You’ll notice that each echo is larger than in the MPC = .8 case – and if we worked it all out, there would be more rounds of echoing too.

What’s the connection between the multiplier in the marginal propensity? The connection can be summed up in a very easy formula:

so that means if b is .9, then the multiplier is 10.

How Large is the Actual Multiplier Effect? - Despite our large MPC, the multiplier isn’t that large (= to about 2), because we don’t echo all of that income back into the US economy. Why? Some gets spent on imports (which doesn’t increase our income), some is  absorbed by government through taxes, etc. These things are not in our model (yet) so we have what is called a simple multiplier. We’ll complicate it later.