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### ECON 100 Tutorial: Week 15

www.lancaster.ac.uk/postgrad/murphys4/

s.murphy5@lancaster.ac.uk

office: LUMS C85

Keynesian Cross Diagram

Last week we calculated GDP using the expenditure method where

GDP = Aggregate Expenditure (AE) = C + I + G + NX.

By definition, GDP is total output, i.e. GDP = Y.

So we call “Y= C + I + G” the product market equilibrium because we are setting total production equal to aggregate expenditure.

The Keynesian cross diagram graphs total output and aggregate expenditure as two separate lines.

The 45° line is where GDP = Y

Or GDP = total Output,

Some texts call this the Aggregate Supply curve.

AE

GDP = AE = C+I+G = f(Y)

GDP = Aggregate Expenditure

(note: sometimes we say Aggregate Demand, AD)

Where the two lines cross, Y*, is the equilibrium level of income in the economy.

Y*

The first half of Chapter 33 in Mankiw & Taylor corresponds with this tutorial material.

Why is the Keynesian Cross Diagram relevant?

Keynes published work in 1936, that tried to explain short-run economic fluctuations in general and the Great Depression in particular. His primary message is that recessions and depressions can occur because of inadequate aggregate demand for goods and services. So, he advocated policies that increased aggregate demand, in particular government spending on public works.

The Keynesian Cross Diagram and the Keynesian Multiplier build on classical economics theory to illustrate his theory.

Read through Chapter 33 of the Mankiw and Taylor textbook for more info.

Question 1 (a)

The economy is described as follows:

Y = C + I + G G = 150

C = 60 + 0.6(Y – T) T = 100

I = 250

Derive the equilibrium level of income for the economy.

For problems like this, the first step is usually to plug values into the equilibrium equation:

Y = C + I + G

Y = 60 + 0.6(Y-T) + 250 + 150

Y = 60 + 0.6(Y – 100) + 250 + 150

Y = 460 + 0.6Y – 60

Y= 400 + 0.6Y This is the equation for the AD line that we graph in (b).

0.4Y = 400

Y = 1000 This is the equilibrium value of Y (or Y*)

where the two lines will cross.

(note: the coefficient on Y in the AD equation is the MPC)

Question 1(b)

Illustrate the equilibrium on an appropriate diagram.

This graph is called the Keynesian Cross (Fig. 33.1 Mankiw)

The 45⁰ line connects all points where consumption spending is equal to national income.

The economy is in equilibrium where the C+I+G (GDP=AE) line cuts the 45⁰ (GDP=Y) line.

Aggregate

Expenditure

Y = 0.56Y + 450

1(c) Find the equilibrium value of Y if G = 200

Y = C + I + G

Y =60 + 0.6(Y – T) + 250 + 200

Y = 60 + 0.6(Y – 100) + 250 + 200

Y = 510 + 0.6Y – 60

Y = 0.6Y + 450 This is the AD line that we will graph.

Y – 0.60Y = 450

0.40Y = 450

Y = 1,125 This is Y*

Y = C + I + G G = 150

C = 60 + 0.6(Y – T) G = 200

I = 250 T = 100

Question 1(d)

What is the value of the multiplier in the economy?

We increased G from 150 to 200 and as a result, Y went from 1,000 to 1,125.

First, how do we find the multiplier?

Multiplier = ∆Y / ∆G

=(1125 – 1000)/(200 – 150)

= 125/50 = 2.5.

Also, as a check,

Multiplier = 1/(1 – MPC)

= 1 /(1 – 0.6)

= 1/0.4

= 2.5.

A side note:

MPC: marginal propensity to consume.

The fraction of extra income that a household consumes rather than saves. i.e. if MPC = .6,

then for every £1 earned, £0.60 is spent.

How do we find MPC?

It is the coefficient on Y in the equation of the Aggregate Demand line.

Question 1(e)

Y = C + I + G G = T

C = 60 + 0.6(Y – T) T = 100

I = 250

What would be the effect on equilibrium income if the government reversed policy and introduced an “austerity” budget in which it reduced G to equal T?

Again, the first step is to plug values into the equilibrium equation:

Y = C + I + G

Y = 60 + 0.6(Y-T) + 250 + 100

Y = 60 + 0.6(Y – 100) + 250 + 100

Y = 410 + 0.6Y – 60

Y = 0.6Y + 350

0.4Y = 350

Y = 875

The new equilibrium income would be 875.

Question 1(e)

What would be the effect on equilibrium income if the government reversed policy and introduced an “austerity” budget in which it reduced G to equal T?

A second, alternate, way to find Y is to use the multiplier.

Income falls from original income by the drop in G times the multiplier.

Initial G was 150 and Y was 1000

Final G was 100, a fall of 50 from the initial G.

So income falls by 50*2.5 = 125

So final Y = 1000 – 125 = 875

Question 1(f)

What are the limitations of the analysis using this model?

The model ignores a number of features of the economy. These include prices, which are implicitly assumed fixed in the model. This is an obvious weakness, despite Friedman’s view that the realism of assumptions should not matter. Friedman himself, of course, thought this assumption was too much.

Interest rates are not included in the model, an assumption that will be addressed in later lectures. Also, government spending has to be financed. This is not allowed for in either a) or c) where the government is running a deficit.

The long-term implications of such a (deficit) policy are not considered. Nor does the model include a supply-side. Everything goes through demand and capacity constraints are ignored.

Some of these limitations are addressed in developing the model beyond this simple representation.

Question 2: Deflationary Gap

If there is a deflationary gap, then that means that there is spare capacity in the economy that unemployment will rise. (here: Y1 < Yf )

The deflationary gap is the difference between full employment output and the expenditure required to raise the equilibrium employment output to the point that it equals full employment output.To remove or get rid of the deflationary gap, we then have to raise government spending in order to raise the equilibrium employment output.

So what we want to do here is find the multiplier. To remove the deflationary gap, the government should increase government spending by the deflationary gap amount divided by the multiplier.

For more on deflationary gap and inflationary gap:

Figure 33.1 and pgs. 707 and 708 in Mankiw & Taylor 2nd Ed.

Question 2 ctd.

MPS = 0.1

MPM = 0.15

MPT = 0.1

The deflationary gap in an economy is calculated to be $700 billion.

The marginal propensity to save is 0.1

The marginal propensity to import is 0.15

The marginal rate of taxation is 0.1.

By how much would the government need change its spending on goods and services to eliminate the deflationary gap?

First, let’s find MPC:

MPC = 1-(marginal propensity to save +

marginal propensity to import + marginal rate of taxation)

MPC = 1-(MPS + MPM + MPT)

MPC = 1 – (0.1 + 0.15 + 0.1)

MPC = 1 - 0.35

We can plug MPC into our equation for the value of the multiplier:

multiplier = 1/(1-MPC)

1/(1- (1- 0.35) = 1/0.35 = 2.857

So, the rise in G required is

700/Multiplier =

700/2.857 = $245 billion.

Question 2 ctd.

The deflationary gap in an economy is calculated to be $700 billion.

The marginal propensity to save is 0.1 MPS = 0.1

The marginal propensity to import is 0.15 MPM = 0.15

The marginal rate of taxation is 0.1. MPT = 0.1

By how much would the government need change its spending on goods and services to eliminate the deflationary gap?

Alternatively, pgs. 711 – 713 of Mankiw talks about the Marginal Propensity to Withdraw, MPW.

MPW = MPS + MPT + MPM

The multiplier is = 1/MPW

So, we can ignore all of the 1- ‘s in the previous slide and just use MPW:

MPW = MPS + MPT + MPM

MPW = 0.1 + 0.1 + 0.15

MPW = 0.35

Multiplier = 1/MPW

Multiplier = 1/0.35

Multiplier = 2.857

So, to remove the deflationary gap, the government should increase government spending by the deflationary gap divided by the multiplier:

Spending increase = 700/ 2.857

Spending increase = $245 billion.

Question 3

The marginal propensity to consume in an economy is equal to 0.8. It also equals the average propensity to consume. In addition, I = 300; X = 100; M = 150 and G = 100. What is the equilibrium level of national income in the economy?

Let’s start with Y = C + I + G + X - M

We have I, G, X and M, so we can plug those in.

To find C, the hint here is that we are told about the Average propensity to consume. It equals MPC. So, C = average propensity to consume * Y, so C = MPC *Y = 0.8Y.

So we can plug in to Y = C + I + G + X - M

Y = 0.8Y + 300 + 100 + 100 – 150

Y = 0.8Y + 350

0.2Y = 350

Y = 1,750

Question 3

If the full-employment level of national income is 2,000, what would the government need to do to its spending to achieve this level of national income?

We found Y* = 1,750, and want to increase it to 2,000.

To do so, we need Government spending to increase by the deflationary gap ÷ the multiplier.

The deflationary gap is the difference between equilibrium income and the full-employment level of income, 250.

The multiplier is 1 /(1 – MPC). MPC = 0.8 (from prev. slide)

So, Multiplier = 1/0.2 = 5

So to raise income to 2,000 requires an increase of 250. Thus G needs to increase by:

deflationary gap ÷ the multiplier

= 250 ÷ 5 = 50.

Question 4

Consider the following model

Y = C + I + G

C = 50 + 0.8(Y-T)

T = 0.2Y

I = 100

G = 120

where Y, C, I, G and T respectively denote income, consumption, planned investment, government spending, and tax revenues.

The equilibrium level of income is:

- 700
- 750
- 800
- 850

Question 4

Consider the following model

Y = C + I + G

C = 50 + 0.8(Y-T)

T = 0.2Y

I = 100

G = 120

where Y, C, I, G and T respectively denote income, consumption, planned investment, government spending, and tax revenues.

Y = C + I + G

Y = 50 + 0.8(Y-0.2Y) + 100 + 120

Y = 270 + 0.8Y-0.16Y

Y = 270 + 0.64Y

0.36Y = 270

Y = 270/0.36

Y = 750

This is the equation for the AD line, and from here, the coefficient on Y gives us our MPC = 0.64

Question 5

Y = C + I + G

C = 50 + 0.8(Y-T)

T = 0.2Y

I = 100

G = 120

G = 125

Consider the model in question (4) above, but suppose that G rises to 125.

The new equilibrium level of income is:

- 714
- 728
- 764
- 880

Question 5

Y = C + I + G

C = 50 + 0.8(Y-T)

T = 0.2Y

I = 100

G = 120

G = 125

Y = 50 + 0.8(Y-0.2Y) + 100 + 125

Y = 275 + 0.8Y-0.16Y

Y = 275 + 0.64Y

0.36Y = 275

Y = 275/0.36

Y = 764

Question 6

Q(4) Q(5)

Y = C + I + G G = 125

C = 50 + 0.8(Y-T) Y* = 764

T = 0.2Y

I = 100

G = 120

Y* = 750

Using the results obtained in questions (4) and (5) above, the multiplier is:

- 1.5
- 2.3
- 2.6
- 2.8

Question 6

Y = C + I + G Q(4) Q(5)

C = 50 + 0.8(Y-T) G = 120 G = 125

T = 0.2Y Y* = 750 Y* = 764

I = 100

Multiplier = Change in Y/Change in G

= (764 – 750)/(125 – 120)

= 14/5

= 2.8.

Alternatively:

Multiplier = 1/(1-MPC) = 1/(1 – 0.64) = 1/0.36 = 2.78

So an increase in G of 5 increases Y by 5*2.78 = 14

Question 7

A change in an injection causes a change in income over time in an economy as follows: +100 + 70 + 49 + 34.3 + …

What is the value of the multiplier?

- 0.3
- 1.43
- 3
- 3.33

Question 7

A change in an injection causes a change in income over time in an economy as follows: +100 + 70 + 49 + 34.3 + …

What is the value of the multiplier?

Hmm, So the pattern is:

100 + 0.7*100 + 0.7*0.7*100 + 0.7*0.7*0.7*100 + … =

100 + 0.7*100 + 0.72 *100 + 0.73 *100 + … =

(An example of what is happening here is: I get £100 buy something from you for £70, You take the £70 I paid you, spend 0.7 of it on something your neighbor is selling, they take the £49 you paid them, and spend 0.7 of that on something, etc. )

So, 0.7 is the MPC.

So our equation says the multiplier is:

1/1-MPC = 1/(1-0.7) = 1/.3 = 10/3 = 3.33

Next Week

Check Moodle for a worksheet and work through it before coming to tutorial.

Read through Chapter 33 in Mankiw & Taylor.

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