BlCh3 1

The Goods Market• Some definitions (or identities):

– Value of final production national income Y– Total output sold total output purchased

• If aggregate sales is the same as aggregate purchases, we can break down Y into the various kinds of demand for output.

• i.e. we can focus on the composition of aggregate demand for output Y.

BlCh3 2

Composition of aggregate demand Z

• Consumption C• Investment I

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

– Inventories

• Government spending G• Net exports NX

– Exports X– Less Imports IM

BlCh3 3

• Consumption– Goods and services purchased by consumers– Some might be some sort of investment like durables

• Investment (not financial)– Firms invest in new plants and equipments– Consumers invest in new houses

• Government spending (on goods and services only)– Excludes transfers (e.g. medicare, S.S.)– and interest payments on gov’t debt– (total would be called government expenditures)

BlCh3 4

• Exports are foreign demand for domestic goods and services (demand for Y) so they should be included as demand for domestic output.

• Imports are domestic demand for foreign goods (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 must be subtracted.

• Net Exports = Exports - Imports

BlCh3 5

• Inventories corresponds to goods that were produced during a certain year I.e. during a specific accounting period but were not sold during the same accounting period.– To get an accurate account of production

during the year, we must• Subtract inventories at the beginning of the

year (they were produced in the previous year)

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

BlCh3 6

Determination of aggregate demand Z

• By definition (identity):Z C + I + G + X - IM in an open economy

Z C + I + G in a closed economy

• Let’s assume– Fixed prices (short run Keynesian model)– One good (everything is in real term)– Closed economy

BlCh3 7

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

BlCh3 8

Determinants of consumption C• Let’s define YD - disposable income - as

YD Y - Tax + Transfer or Y - T (T is net tax)

• Consumption is determined by disposable income: C increases as YD increases

• so consumption is a positive function of YD

C = C(YD) = C(Y-T)

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

C = co + c1 YD c1 is the MPC

BlCh3 9

Consumption function

C

YD=Y-T

co

C = C(YD)

Slope = c 1

BlCh3 10

Endogenous versus exogenous variables

• Definition– Endogenous variables are determined within the

model e.g. C , Y and YD

– Exogenous variables are determined outside of the model, i.e. they are independent of any other variable in the model

• Investment I is considered as an exogenous variable in this chapter

• Government spending G and taxes T are also exogenous variables - they are policy instruments for the government.

BlCh3 11

Model

• C = c0 + c1 (Y-T)

• I = I (exogenous - given)

• G = G (exogenous - policy variable)

• Z C + I + G by definition

• Y = Z (equilibrium condition)

BlCh3 12

Algebraic Solution• Since in equilibrium, supply of goods (Y) should

be equal to aggregate demand (Z), by replacing we get:

• Y = c0 + c1 (Y-T) + I + G

= c0 + c1Y -c1T + I + G

€

Ye = 1

1- c1

(c0 + I-

+ G − c1T)

1/(1-c1) is the multiplier m

and (c0 + I + G - c1T) is autonomous spending Z0

€

Ye =1

1- c1

(c0 + I_

+ G - c1T)

BlCh3 13

Graphical solution

Z

Y

Z0

Z = Z0+c1Y

Slope = c 1

Y=Z

Ye

Slope =

1

BlCh3 14

The multiplier• Assume a specific consumption function

C = 500 + .8(Y-T) i.e. MPC = .8

The multiplier m = 1/(1-c1) = 5

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

If G increases by ∆G, Y will increase by

∆Y = m ∆G

In the example above an increase in G equal to 100 will result in an increase in Y of 500

BlCh3 15

Effect of an increase in G

Z

Y

Z0

Z = Z0+c1Y

Y=Z

Ye Y’e

∆G

∆Y

Z’ = Z0+ ∆G +c1Y

1

23

4

BlCh3 16

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…

BlCh3 17

Rational

• Production (income) depends on demand

as Y = Z in equilibrium

• Demand depends on income

as Z = C + I + G

and C = C(Y)

BlCh3 18

• 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 4 Total increase

(many periods)

∆G ∆G ∆G

∆Y ∆G c1 ∆G c1

2 ∆G (1+c1+c12+ …) ∆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

BlCh3 20

Alternative approach: Investment = saving• Approach used by Keynes in the “General Theory

of Employment, Interest and Money” 1936• By definition, private saving is what is not

consumed out of disposable income:

Sp YD - C

hence Sp Y - T - C

or Y C + Sp + T• The equilibrium condition of the model above was:

Y = C + I + G

By replacing, it becomes I = Sp + T - G

BlCh3 21

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

BlCh3 22

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 government saving Sg.

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 = c0 + c1YD and Sp YD - C

• SP = YD - c0 - c1YD = - c0 + (1 - c1)YD

• Sp = - c0 + (1 - c1)(Y - T) with MPS = (1 - c1)

– 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 = 160 + 0.6 (Y-T) + 150 + 150

i.e. Y - 0.6Y = 160 - (0.6*T) + 150 + 150

Y = [1/(1-0.6)] (160 - 60 + 150 + 150)

Y = 2.5 * 400 = 1000

BlCh3 26

b. YD = Y - T = 1000 - 100 = 900c. C = 160 + 0.6*900 = 700Problem # 3a. Z = C + I + G = 700 + 150 + 150 = 1000 so Y = Z = 1000 (equilibrium condition)b. If G = 110 ∆G = - 40 as the multiplier m = 2.5 and ∆Y = m ∆G ∆Y = - 100 and the new equilibrium Y is 900

consumption drops by c1* ∆Y or - 60 to 640And Z = C’ + I + G’ = 640 + 150 + 110 = 900

BlCh3 27

c. Private savings Sp = Y - T - C

= 900 - 100 - 640 = 160

Government savings Sg = T - G

= 100 - 110 = -10

Equilibrium condition: I = Sp + Sg

150 = 160 - 10 = 150