Ignore supply side for now. Focus on Demand.

Objective: understand location of AD curve and how it shifts.

AE = C + I + G + X - M

C: Desired Household Expenditure

- disposable income, Y_d , is a key determinant

Def’n: Y_d is national income per period of time available to Canadian households for spending or saving.

Y_d = gross national income + transfers - taxes

Def’n: the consumption function relates C to Y_d

Tabular example:

Note: Desired consumption plus desired savings, S, equals Y_d

Graphically:

use of 45^o line: provides

reference points where

value on vertical axis

equals value on

horizontal axis.

Algebraically:

General form of straight line: C = a + b Y_d

a, b are parameters - "a" captures autonomous changes

- "b" captures induced changes in C

To get the data in the table above, a = 50 and b = .75, so consumption function for this economy is

C = 50 + .75 Y_d

Values found empirically.

The savings function can also be found:

since S = Y_d - C

then S = Y_d - 50 - .75 Y_d

= -50 + .25 Y_d

Def’n: The marginal propensity to consume (mpc) out of disposable income is the change in C per unit change in Y_d .

from table of numbers, as Y_d increases by 100, C increases by 75.

Graphically, mpc is the slope of the consumption function.

Algebraically, mpc is the value of the parameter b.

Do not confuse mpc with the average propensity to consume out of disposable income, apc, = C/Y_d

Stylized fact: 0 < mpc < 1.

Def’n: The marginal propensity to save, mps, is the proportion of each new dollar of disposable income that is saved.

Since mpc + mps = 1, mps = 1 - mpc.

A minor complication ...

Step 1: how does Y relate to Y_d ? Suppose Y_d = .8 Y (i.e., gov’ts take 20% of gross income in form of taxes.

generally, Y_d = (1 - t )Y where t is tax rate in economy.

Step 2: Since C = a + b Y_d and Y_d = (1 - t )Y

then C = a + b (1 -t )Y

using our parameters, b = .75, t = .2

C = 50 + .6 Y

out of each dollar of new income, governments take $0.20 and Cdn. households spend .75 of the remaining $0.80, or $0.60.

The consumption function shifts up or down as other determinants change (change in the value of the parameter a).

I - Desired Investment Expenditure

- recall, real expenditure on capital goods, inc. new housing

will depend on: - interest rates (cost of financing the investment)

- anticipated changes in demand for product

but no good reason to expect that I is strongly dependent on the level of national income.

- therefore, model I as independent

of level of Y. I = I

ignore G, X, M for now.

Suppose the economy is as follows:

household sector: C = 50 + 0.6 Y

investment sector: I = 70 (billion $)

Tabular data:

Suppose actual level of national income is 200. This level of national income generates a desired expenditure of 240. If firms responded to demand, we expect upward pressure on production.

Similarly, at Y = 500, AE equals only 420 : we expect downward pressure on production.

At Y = 300, AE = 300. Actual production is consistent with planned expenditures. Leads to ...

Def’n: Equilibrium Expenditure: the level of AE equals Y. The level of national income which, if produced, would generate a demand exactly equal to itself.

Graphical determination of equilibrium Y.

Algebraic determination of equilibrium Y.

AE = C + I - describes structure of economy

C = 50 + .6Y - describes C

I = 70 - describes I

Find Y so that, Y = AE equilibrium condition

or Y = 50 + .6Y + 70

Y = 120 + .6Y

Y - .6Y = 120

.4Y = 120

Y = 300

Using general parameters:

AE = C + I

= a + bY + I

solve Y = AE

Y = a + bY + I

(1 - b)Y = a + I

or Y = (a + I )/(1 - b)

Suppose interest rates fall and I increases from 70 to 110 billion $

Now, equilibrium occurs at Y = 400. So, a 40 unit increase in I causes equlibrium AE to rise by 100 - a multiple of 2.5 .

The simple investment multiplier is the change in equilibrium Y per unit change in I. In this example, = 2.5

Graphically,

Algebraically,

The logic of the multiplier: increased demand causes increased production causes increased income causes increased demand causes .....

KNOW why multiplier depends on the value of mpc.

Model more complex/realistic, basic concepts remain.

Gov’t sector: G assumed independent of Y, G = G

T (net taxes) assumed a constant fraction of Y, tY

- taxes imply Y_d less than gross income, Y_d = (1-t)Y

Rest of world: X assumed independent of Y, X = X

The graphical model:

The Algebraic model:

AE = C + I + G + X - M

C = a + b Y_d = a + b(1-t)Y

I = I

G = G

X = X

M = mY

To find equilibrium, solve,

Y = AE

or,

Y = a + b(1-t)Y + I + G + X - mY

or,

Y - b(1-t)Y + my = a + I + G + X

or,

Y[1 - b(1-t) + m] = a + I + G + X

or,

Y =

MOVING FROM AE TO AD

Every AE equilibrium is a point on an Aggregate Demand curve.

Case 1: AE shifts for reason other than a P change.

Result: AD shifts by a vertical distance equal to change in autonomous desired AE times the multiplier.

Case 2: AE shifts because P changes. Recall, P changing affects C (through wealth effect) and X , M (through substitution effect).