chapter 11 info

Chapter 30 Aggregate Expenditure - Keynesian Model/SR Macro Model

A.  The Consumption Function and SR Macro Model

Recall: Classical Economists – this was the group of economists and economic ideas that predominated from Adam Smith the Great Depression in the US.

They believed in:
- Lassiez Faire (or hands off approach)
-markets clear
-Saye’s Law – If you produce it…it will be purchased.  So supply creates its own demand.
- All income is eventually spent

The classical model/school dealt with LR growth and its components.  It painted a very rosy picture of how the economy should work.  If we had our 3 assumptions of what should occur in the LR occur then the economy should work out fine.

In the classical model unemployment was temporary and the result would be a short lived.

-so due to the outcome of the Great Depression we realized that although markets will self-correct in the LR, in the SR there can be huge swings in output that affect both GDP and unemployment.  So what should a nation do if their economy is in a trough, recession, or slump?

This was answered by an economist named John Maynard Keynes in the 1930’s who noted that fluctuations coincided with changes in spending and if we wanted to affect overall output we could, as a government, change:

(a) Taxes
(b) Government Spending
(c) Alter interest rates

Each of these items could spur on private spending and help bring out of a recession.  With that the SR or Keynesian Model was formed.

1. SR Model Assumptions and Notes

a. The SR Model focuses on the role of spending in explaining fluctuations

b. We assume that spending affects output (which it does not do in the LR model due to
crowding out).

c. We look at spending or Aggregate Expenditure – AE - in the following sectors:
i. Consumption – done by HH
ii. Investment (Planned) – done by business firms
iii. Government – done by Gov’t on G/S → so don’t include transfers
iv. NX – net spending on US G/S by citizens of other nations

2. Consumption and the Consumption Function

a. Disposable Income – YD = Y – T; It is how much money you actually have to spend as a consumer.  So we have to subtract taxes from your income.  If we break up disposable income into two components we find that it is part Consumption (C) and what is not spent, or saving (S).  We may also write:

YD = C + S    **A logical equivalent is S = YD - C

b. Determinants of Consumption Spending:
i. Interest Rates – r – (inverse relationship)
ii. Wealth (positive relationship)
iii. Expectations
iv. Price Level (inverse relationship)
v. Disposable Income → this is the most important, so when we look at the consumption function we look at how C changes with YD

So C & YD are movers while r, W, and expectations are shifters.

c. Consumption Function – relationship between C and YD
mathematically: C = a + b* YD
graphically:












d. Important Concepts in Consumption Function
(i) The consumption function shows the ideas of the marginal propensity to consume, or MPC in its slope. As disposable income changes we get a change in consumption.  This is the concept of the marginal propensity to consume. It tells us how much C changes with Yd (or as we labeled it DI).  We should note that it must be between [0, 1].  If you get $1 you can’t spend more than $1.  So the MPC tells how much of each new dollar that you actually spend.
-note: what is not spent is saved. So we may note that 1 = MPC + MPS, where MPS is the marginal propensity to save.
(ii) Autonomous consumption, a, is the consumption that is unaffected by disposable income.  It is the intercept on the consumption axis.  Autonomous consumption is what you would spend even if you had no income.  It can be thought of the amount of spending you need to do to just maintain a poverty level standard of living.

(iii) Marginal Propensity to Save- MPS – this is the change in saving over the change in disposable income.  As mentioned before we can find MPS by:  1 - MPC = MPS

(iv) Dissaving – when the amount that you purchase exceeds your disposable income.

Graph 1:









-If MPC changed we would get a change in the slope of the line b/c MPC is the slope of the Consumption Function.  It could be a negative or positive change. If the MPC increases the slope increases.  If the MPC decreases the slope decreases.  In Graph 2 below we can see an increase in the MPC.
-If we have a change in autonomous consumption we get a change in the intercept. Once again, a positive change would shift the intercept upwards and a negative change would shift it downwards.  We can see below in Graph 3 that autonomous consumption increased from a1 to a2.
Graph 2:













Graph 3:












3. A Closer look at I, G, & NX
a. Investment – Consists of business spending on plant equipment, purchase of new homes by HH, and accumulation of unsold inventories.  We will take a closer look at how investment is affected and how its demand changes due to its large effect on overall spending.

b. We treat IP, G, & NX as given.  So although we could also analyze each in similar fashion as consumption, we will assume that all are given levels in the economy.  Since C is nearly 2/3 of total spending in the economy this is another reason we will focus less on these 3 sectors.  See marginal propensity to import below.

4. Investment and the Investment Demand Curve

a. Investment Demand Curve – this shows the demand for investments at all possible rates of interest.  Firms generally consider how much the investment’s expected return when determining whether or not to invest in new equipment, capital, land, etc.

b. Properties of Investment:
-It is highly dependent upon expected profits, so it tends to be very volatile and can be influenced by:
i) expectations (i.e. higher or lower profit)
ii) tax rates –includes both after sale taxes as well as subsidies and tax credits
iii) capacity – is there a lot of capacity or not.
iv) technology

c. Autonomous Investment Spending vs. Investment Demand

-if we note that some forms of investment are long run and short run we may note that there are two types of I.  In the SR since all the variables above can be seen as fixed we get an autonomous amount of investment.  This is investment that does not depend on real interest rates, which is called autonomous investment.  Then there is investment that does depend on the previous variables.

5.  Aggregate Planned Expenditure (i.e. total spending) –AE – this is the sum of all spending from all 4 sectors on final goods and services in the US.
a. mathematically: AE = C + I + G + NX
also, ΔAE = MPC * ΔY

b. AE-Line: This shows us the total spending that takes place in an economy.  When we look at this graphically we make use of a 45o line.  This is just a reference line.  It perfectly bisects the X & Y space, so if we look at AE and GDP is shows us where they are equal.  So when the AE-line crossed the 45o line it is at SR equilibrium b/c it shows us where total spending equals total output.  This means that all the items that are being produced are sold.  Recall that this is our definition of equilibrium in the economy.
Note:
-autonomous expenditure – the sum of all spending components that does not change with GDP
-induced expenditure – the sum of all spending components that change when real GDP changes.

Graphically:














So change in inventories = GDP – AE.  If it is (+) then inventories are increasing.  If it is a (-) value then inventories are decreasing.
If the economy were at a point above the equilibrium level of spending and GDP, then we would have a point where spending was insufficient for that level of GDP. This would cause inventories to go up b/c goods that were being produced would not be bought.  This would cause a decrease in production and bring us back to a point where GDP and spending are at equilibrium.
c. Spending Multiplier - If the spending in the economy changed then overall output in the economy changes by a greater factor than 1:1.  We can see this in the following summation.  If we were given there was an MPC of .6 would get a change in GDP of:
$1 + $0.60 + $0.36 + $0.196 + ….  The reason that this occurs is that if you change spending by $1 this becomes someone’s income.  So they will spend 60% of it based on the MPC.  When they spend 60 cents this becomes someone else’s income.  They then spend 60% of this.  This continues on.  This overall sum is captured in the following equation:
i. Spending Multiplier =
ii. Δ GDP = Δ spending * exp multiplier = (1/ (1-.6)) = 2.5
What this 2.5 means is that for every $1 spent it creates $2.50 of GDP

Example:  Suppose that we have Government increase spending by 100 Million, what would the change in GDP be if MPC = 0.8?

If we use our previous formula we get: Δ GDP = Δ spending * exp multiplier
 =100 Million * (1/ (1-0.8)) = 100 Million * 5 = 500 Million.

If it were the case that Government decreased spending by this same amount the value would be (-)

iii. Marginal Propensity to Import – the fraction of real GDP increase spent on imports.

Mathematically: MP to Import  =

6.  Inflationary and Recessionary Gaps

a. Recessionary Gap- This is when the current level of AE is below what is required to be at FE.  Graphically it can be seen below.












To get to FE we need to increase AE.  In this instance we would need to increase AE enough to where the equilibrium would then be at GDPFE.

Example:  Given a recessionary GAP of 500 Billion dollars with a MPC of 0.75, calculate the increase in spending needed to achieve FE-GDP.

Δ GDP = Δ spending * exp multiplier → 500 Billion = Δ spending * (1/ (1-0.75)) →
500 Billion = Δ spending * 4 → 500 B / 4 = Δ spending or we need about an increase of 125 Billion dollars to get to FE-GDP.

Note: To get the same result with taxes you use the following formula:
Δ Taxes = Δ spending required /MPC

Example: So to get the same result as above but, doing it by taxes we would need a tax cut of:
Δ Taxes = Δ spending required /MPC = 125 B / 0.75 = 168.9 Billion dollar tax cut to get an increase in GDP overall of 500 Billion dollars.

b. Inflationary Gap – this is the amount that AE is higher than the amount needed for FE-GDP.  Graphically it can be seen below.














Note: in order to find out how much to reduce spending you use the same process as before, but now instead of increasing spending you decrease it.  Likewise, in order to decrease the inflationary gap you increase taxes instead of reducing them.

7. Employment and GDP in the SR Model
-We now may ask ourselves…if we have found what equilibrium GDP is in the economy is it an efficient level?  For this to be the case it must be a FE value. So to check this we will introduce an APF and compare our value of FE.

Note: To make a comparison you must be given what FE is.   This will always be given to you in order for you to compare.  It provides a reference point in which you can then go and determine if the economy is operating at potential or not.









Graphically:




















Note: that the APF is inverted here.  We do this so we can use the same method that we used before in just dropping down from the previous graph.  Since we have GDP on the horizontal axis we must invert the APF to have GDP line up.

We can see that if FE is above LE then we are not at LR equilibrium.  But recall that FE was given (or imposed) so it might just as well have been below LE or equal to LE.  If it were equal to LE, then our SR values and LR values would be the same.  If we go back to our typical graph of GDP when A.GDP and P. GDP are the same that is when LE
equals FE.  The case above is that FE > LE, so we are less than full-employment so this is like a recession or trough shown below.












Note: if we had potential and actual GDP equal to one another we are at FE, so FE would also be our SR equilibrium.  An example is like point A above.  We now see that we can show fluctuations in GDP.  They are now caused by changes in spending.  In this case we can now show that our current yr GDP (or actual GDP) is not guaranteed to be at our potential value, and we are therefore not at FE levels.