Students Again

Again, we are still working with a simplified AE model – i.e. there is no government or international sector yet. But for this model, right now, equilibrium would be where: total Aggregate  Expenditures (AE) = Income (Y) = GDP (production)

Right now, AE is just C + Ig

Consumption and Investment Schedules:
We already talked about what the C curve looks like – but we didn’t talk about the Ig curve (we did talk about the ID curve – but that isn’t the same thing). The Ig curve tells us what level of Investment we can expect at each level of Income (Y) or GDP. But wouldn’t the business sector also spend more on Investment when Y was up? Wouldn’t the business sector spend less on Investment when business was down? The answer in short is: not really. We have to remember that Investment takes time – so spending more on Investment today has little to do with how the economy is performing today (good or bad). It has more to do with how we think it will do in the future, and what we have to pay to invest (the i rate) and what the tax costs of  Investing today are…

When we graph the Investment Curve in “GDP or Income space” (meaning GDP or Income is on one of the axes), we have to conclude that Investment does not rise or fall as GDP rises or falls. In effect – it would look flat.

That’s not to say, that Investment doesn’t change – remember we said, that Investment is volatile. When Investment changes, the I curve shifts up and down.

So, when the level of Investment is determined in the left graph (the ID graph) by the positioning of the ID curve and the level of the interest rate (i*), that level of Investment (I*) becomes the height of the I curve in the right graph.

If the interest rate change, we get a new level of Investment in the left graph – and that either raises or lowers the I curve in the right graph.

Planned investment: The amount of Investment a firm plans on making – including by building new buildings, buying new equipment and the products they produced but did not sell (an investment in inventories). Sometimes firms want to build inventories (to protect against stock outs etc) and sometimes they want to decrease them (to decrease costs of storage etc). If investment rises or falls unexpectedly, the most likely cause is that sales were not what they figured they would be – in other words, they guessed wrong and now have either too much inventory (sales were weaker than expected) or too little inventory (sales were stronger than expected). If firms find inventories growing too much, their likely response is to cut back on production (lower the I curve). If they find inventories are dwindling, they may increase investment spending to re-invest in inventory stock.

Equilibrium GDP: AE (now just C + Ig) = Y = GDP

Adding the sectors of the economy together, we get the formula above. But graphically, we stack the C curve and the Ig curve like in the graph below.

The new curve should be parallel to the C curve (since that’s the only one with any slope) and should start at a point equal to a (autonomous consumption) and Ig (that constant amount of Investment). Where the combined curve crosses the 45 degree line (at an income level of Y*) is the point of equilibrium in our restricted (no government, no international) model. This is the point where spending (AE) just equals Production (GDP) and just equals Income (Y)

Tabular Analysis: on a table, we would be adding values of C and I to get AE. When the value of AE equals the value of Y needed to support it, we have equilibrium.

Notice:

• Y must equal C + S
• The autonomous consumption level can be seen when Y=0 (C= 60 when Y=0, so “a” = 60)
• The slope of the C curve can be found by finding delta-C/delta-Y. As Y increase by 100 with each row, C increases by 80 – so delta-C/delta-Y = 80/100 = .8. That’s the MPC or “b”.
• The level of Investment does not change as Y changes (it does not depend on the level of current GDP)
• AE always equals C + Ig
• Equilibrium is where AE = Y (at a level of 500)
• At equilibrium Ig = S, as we expected when we noticed that Y = C + S and Y = C + I, we found that S had to equal I in equilibrium.

Disequilibrium: If we were at a GDP (production) level that was less or more than Y*, we would not be in equilibrium – i.e. the market would not stay at this level of production.

If, for example, we were only producing Y’ of output, we would be losing inventory. Firms would eventually increase production to rebuild their stocks – driving the level of Y to the right towards Y*. You can see that at Y’, there are more sales (where it crosses the AE curve) then production (production is reflected in the height of the 45 degree line).

If we were producing Y’’ of output, we would be gaining inventory. Firms would eventually decrease production to reduce stocks – driving the level of Y to the left towards Y*. You can see that at Y’’, there are fewer sales (where it crosses the AE curve) then production (production is reflected in the height of the 45 degree line).

Adding International Trade:
Adding the international sector means we have to change a few things. First we have to change the multiplier. Why? Because when we inject money into the economy and we used to get those echoes – now some of those echoes leak overseas into someone else’s economy. It ceases to echo here. Now if they spend that money back in our economy – then it’s “as if” the money never left. If they don’t, we lose part of the multiplier effect.

What does the international sector look like?

Exports depend on how much other nations want to )(and are able to) buy from us. So, as US GDP (US income) rises, it has no effect on the rest of the world’s ability to buy things from us. So in the first graph, we show, Exports not rising as Y rises.

Imports are us buying foreign goods. It makes a difference how much money we have. The more money we have, the more we can buy from others (even France!). This is shown in the second graph. In the third, we put the two together to get a Net Exports curve. Net Exports is just Exports minus Imports.

It is common to use M for Imports and X for Exports, but I find those symbols get confused with M for Money Supply (a concept we cover later) and X for good “x” and the “x” axis etc. I prefer to use EX for Exports and IM for Imports. That makes Net Exports (EX-IM)

You’ll notice that Ex-IM becomes negative after IM crosses over EX. Basically, at sufficiently high levels of income, we can afford to buy more goods from the rest of the world than they can and are willing to buy from us. The further we are beyond this “Trade Balance” point, the more of a trade deficit we will have.

Net Exports and Aggregate Expenditures -
Adding the EX-IM curve to the graph we were working on decreases the slope of the AE curve (which is now AE = C + Ig + (EX-IM)). Our new “open economy” model AE curve starts out higher than the closed economy model AE curve, but later crosses it as Imports leak away some of our multiplier effect. The point where Net Exports equals zero is the same point where the old closed economy AE curve will just equal the new “open economy” AE curve.

The slope of this new AE curve takes into effect the leak to Importing behavior.

MPI stands for the Marginal Propensity to Imports out of additional Income – which means: how much of our next dollar we are going to spend on products that come from other  economies – and therefore do not re-circulate money back into our economy. The more we tend to import – the less powerful or multiplier is.

International Economic Linkages (what effects the MPI)

• Prosperity Abroad – the more prosperous they are, the more they can afford to buy goods from us – raising the Exports curve and increasing the trade balance point. Shifts EX up, Shifts EX-IM up.
• Tariffs – the more barriers there are to trade, the less international trade occurs. Removing tariffs on goods coming into a country increases imports. Removing tariffs on goods leaving our country increases exports.
• Exchange Rates – the rate at which two currencies are traded for one another can affect relative prices, making foreign goods either cheaper (raising imports) or more expensive (lowering imports).

Adding the Public Sector:
Government Purchases and Equilibrium GDP: Government purchases (and this does not include transfer payments) are determined by politics (mostly). They are not determined by the level of GDP or Income in the economy. If they were, then as GDP rose, government would buy more stuff and when GDP fell, government would buy less stuff. There is no such  relationship. In times of war, for example, government spends more money. It does not say “since we have a recession, we’ll only fight half as expensive of a war”. Government also  spends more on many programs as the economy worsens (like unemployment compensation).

In terms of graphing, we will just assume that Government spending does not depend on GDP. Like Investment, Government spending will be a flat line and will not change the slope of the AE curve.

Our new complete AE curve (AE’’) will be the same slope as AE’ was. It will be higher up by the height of G.

Now that we have done all this – we can drop the other curves that we used to build it:

Tabular Example -

You’ll notice that:

• - Y still equals C + S
• - Ig and G are both constants as GDP (or Y) changes
• - EX-IM falls as GDP rises – eventually becoming negative
• - AE = C + Ig + G + (EX-IM)
• - Equilibrium is where AE = GDP = Y – which does not appear as a nice round number – but we can find it.
• - “a” is 60, MPC or “b” is still .8
• - the MPI is delta-IM/delta-Y – which is .02
• - the multiplier is now 1 / (1 - .8 + .02) = 1/.22 =~ 4.545454545454

We can see that AE is greater than Y, up until GDP hits 700. Therefore, the equilibrium level must be a level of GDP between 600 and 700.

Taxation and Equilibrium GDP: When we introduce taxes into our model, we find that the multiplier is decreased. It depends on what type of taxation we are doing – a head tax (a.k.a. a lump-sum tax) or a tax rate (regardless of the type of rate). If we use a tax rate the multiplier becomes

This is definitely smaller than our original multiplier of 1/(1-b) as long as both t and b are positive (and they always are). For example if b is .8 and t is .5. The multiplier without taxes is:

1 / (1-b) = 1 / (1-.8) = 1 / (.2) = 5

With a tax rate of .5 (which is 50%), the multiplier becomes

1 / (1-b + bt) = 1 / (1 - .8 +.5(.8)) = 1 / ( 1 -.8 + .04) = 1 / (.24)

That would approximately be equal to 4.

No matter what numbers we plug in for b (the marginal propensity to consume) or t (the tax rate), including taxes decreases the multiplier.

Graphical Analysis: What this does is decrease the slope of the AE curve.

And that, as you can see, decreases equilibrium GDP. Therefore, taxes are a drag on the economy. They are a leak.

If taxes are lump sum – the multiplier is still:

but the amount of money that gets multiplied is reduced by bT (where “T” is the amount of taxes collected). It’s still a leak – it just gets figured in differently. Technically, “bT” is the  amount of money that doesn’t get spent because consumers didn’t have it to spend.

Injections, Leakages and Unplanned Changes in Inventories: Remember, when we talked about S = I in our simple model? Well, the model is more complicated now – and so is our equation. In effect all leakages (savings, imports and taxes) must add up to equal all of what we call injections (investment, exports and government spending). You’ll notice that each leakage has it’s own injection:

• Savings supplies the money to be borrowed and turned into investment
• Taxes supply the government with money to pay for government spending
• Imports send US currency out of the economy, exports bring it in.

When these 3 sets of counterparts are individually balanced, we have

• equilibrium in the market for loanable funds – (i.e. all the money we save, gets borrowed at an equilibrium interest rate that clears the market of loanable funds)
• equilibrium in the government budget (government has a balanced budget – i.e. G = Tax Revenue)
• equilibrium in the international market (a trade balance where EX = IM)

If one of these is not in equilibrium – then at least one of the others must be out of equilibrium as well.

S + IM + T = Ig + EX + G

Equilibrium versus Full-Employment GDP: Just because we have equilibrium – does not mean that we have full-employment. We can be at equilibrium (markets clear and there is no pressure to change) and still have massive unemployment (the Great Depression showed this).

Recessionary Gap: The amount by which equilibrium GDP falls short of Potential (or Full-Employment) GDP.

Inflationary Gap: The amount by which equilibrium GDP exceeds full employment (or Potential) GDP. This tends to cause prices to rise (too much pressure on labor to produce causes wages to rise and therefore prices as well).