BlCh3 1

The Goods Market• Some definitions (or identities):

– Value of final production – Total output total output

• If aggregate sales is the same as aggregate purchases, we can break down Y into the

for it.

• i.e. we can focus on the

for output Y.

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Composition of aggregate demand Z

• C • I

– Fixed• Residential (consumers)• Non residential (firms)

– Inventories

• G• NX

– X– Less IM

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• Consumption– Consumer – Some might be some sort of consumers investment

like

• Investment (not financial)– Firms– Consumers

• Government (on goods and services only)– Excludes (e.g. medicare, S.S.)– and – (total would be called government )

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• Exports are (demand for Y)

so they should be included in Y as they are demand for domestic output.

• Imports are (goods produced abroad) - they should not be included in Y as they are not demand for domestic output. However as they are already included in consumption and other purchases, they

• Net Exports =

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• Inventories corresponds to goods

• To get an accurate account of production during the year, we must

• inventories at the beginning of the year (they were produced in the previous year)

• inventories at the end of the year (produced this year but not sold)

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Determination of aggregate demand Z• By definition (identity):

Z in an economy Z in a economy• Assumptions of the model:

– prices (short run Keynesian model)– (everything is in real term)– economy

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Short run - medium run - long run

• Short run - period too short to allow prices to adjust - fixed prices - unemployment possible

• Medium run - economy is always at full employment (labor market must adjust) - prices adjust to bring economy back to full employment - capital stock is fixed

• Long run - growth theory - capital stock increases through investment in the economy

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Determinants of consumption C

• Let’s define YD - - as

YD

• Consumption is determined by disposable income: C as YD

• so consumption is a function of YD

C =

this is a relation which can be specified with the following linear form:

C = c1 is the

BlCh3 9

Consumption function

C

YD=Y-T

BlCh3 10

Endogenous versus exogenous variables

• Definition– Endogenous variables are determined

– Exogenous variables are determined of the model, i.e. they are

• Investment I is considered as an variable in this chapter• Government spending G and taxes T are variables - they are policy instruments for the

government.

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Model

• C =

• I = (exogenous - given)

• G = (exogenous - policy variable)

• Z by definition

• Y = (equilibrium condition)

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Algebraic SolutionSince in equilibrium,

by replacing we get:

Y =

=

Ye =

is the multiplier m

and is autonomous spending Z0

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Graphical solution

Z

Y

Ye

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The multiplier• Assume a specific consumption function

C = i.e. MPC =

The multiplier m = 1/(1-c1) =

Since Ye = m (c0 + I + G - c1T)

If G increases by ∆G, Y will increase by

∆Y =

In the example above an increase in G equal to 100 will result in an increase in Y of

BlCh3 15

Effect of an increase in G

Z

Y

Z0

Z = Z0+c1Y

Y=Z

Ye

∆G 1

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Explanation• Starting at 1, the economy is in equilibrium.• An increase in G equal to ∆G immediately translates into an

equal increase in aggregate demand : 1 to 2• In 2 the economy is not in equilibrium as Z > Y so firms must

increase production by ∆G to meet the additional demand: from 2 to 3

• In 3 the economy is still not in equilibrium (below ZZ’)• As production increases by ∆G , income increases equally so

consumption demand will increase by c1 ∆G: this is an additional increase in aggregate demand : 3 to 4

• Then production must increase again by c1 ∆G this time to meet this new increase in aggregate demand and so on…

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Rational

• Production depends on

as Y = in equilibrium

• Demand depends on

as Z =

and C =

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• When there is an exogenous increase in demand, production will increase equally, and this increase in production (i.e. in income) results in an additional increase in demand.

• However the additional increase in demand is smaller than the original increase because the marginal propensity to consume is less than 1 (some of the increase in income is saved): this process will not result in an infinite increase in output as the additional increases in demand get smaller and smaller and tend towards zero.

BlCh3 19

Alternative calculation of the multiplier

Period

1 2 3 4Total increase

(many periods)

∆G ∆G ∆G

∆Y ∆G c1 ∆G c1

2 ∆G(1+c1+c1

2+ …) ∆G

∆C c1 ∆G c12 ∆G c1

3 ∆G (c1+c12+c1

3+ …) ∆G

∆Z ∆G c1 ∆G c12 ∆G c1

3 ∆G (1+c1+c12+c1

3+ …) ∆G€

= 1

1- c1

ΔG

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Alternative approach: Investment = saving

• Approach used by in the “General Theory of Employment, Interest and Money” 1936

• By definition, private saving is what

Sp

Hence Sp

or Y

The equilibrium condition of the model above was:

Y =

By replacing, it becomes I =

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Interpretation

• In a one person economy, investment equals savings because the decision to save and to invest is made by the same person.

e.g. Robinson Crusoe’s island

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Role of government:

• In the above equation, the government

1. takes a share of income in the form of tax

2. spends it in the economy in the form of G

so T - G corresponds to the amount of tax receipts that the government did not spend, i.e. that the government saved.

• In sum, T - G (the budget surplus) can be interpreted as the

BlCh3 23

Solution of the model using the alternative equilibrium condition

• Let’s derive the saving function from the consumption function (c1 is the MPC)

C = and Sp

SP = YD =

Sp = with MPS =

– Note that MPC + MPS = 1 as mentioned earlier

• We can now use the saving function and the new equilibrium condition to find equilibrium Y (Ye)

BlCh3 24

I = Sp + (T - G) (equilibrium condition)

= - c0 + (1 - c1)(Y - T) + T - G

= - c0 + (1 - c1)Y - (1 - c1)T + T - G

= - c0 + (1 - c1)Y - T + c1T + T - G

(1 - c1)Y = c0 + I + G - c1TFinally

as before.

€

Ye =1

1- c1

(c0 + I_

+ G - c1T)

BlCh3 25

Problem # 2 P. 62

C = 160 + 0.6 YD

I = 150

G = 150

T = 100

a. In equilibrium Y =

i.e. Y - 0.6Y =

Y =

Y =

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b. YD = Y - T = c. C = Problem # 3a. Z = C + I + G = so Y = Z = (equilibrium condition)b. If G = 110 ∆G = as the multiplier m = 2.5 and ∆Y = m ∆G ∆Y = and the new equilibrium Y is

consumption drops by c1* ∆Y or and Z = C’ + I + G’ =

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c. Private savings Sp = Y - T - C

=

Government savings Sg = T - G

=

Equilibrium condition: I = Sp + Sg

I =150

Sp + Sg =