Open economy Keynesian multiplier

1
Open economy Keynesian multiplier

• Real income, Y, is measured in physical
  unitstons of rice for simplicity, but really the
  sum of the physical quantity of every good
  produced, each multiplied by its price in some
  base year. Imports, which are a different good,
  are subtracted at their price in the base year.
• For simplicity, we shall ignore imports of
  intermediate inputs, such as raw materials, and
  imports for investment, government expenditure
  and re-exports. Well pretend that all imports
  are for domestic consumption.

2

• Consumers save a fraction s of their real
  income and consume the rest
• C ( 1 s) Y
• Consumption, C, covers both consumption of
  domestic goods and imported goods.
• The ratio of imports to total income is m.
  Therefore total imports are
• M mY

3

• The condition that the demand for domestic
  production is equal to the amount produced is
• Y (1 s)Y mY I G X
• The term mY is subtracted because total
  consumption, (1-s)Y, covers both consumption of
  home goods and consumption of imports. Only
• (1 s)Y mY is spent on home goods

4

• This is the national income identity
• Y C I G X M
• Well assume that X depends only on the real
  exchange rate (that is, the relative prices of
  domestic and foreign goods, SP/P) and that I and
  G are exogenous (determined outside the model).

5

• With this notation, the condition for the demand
  and supply of domestic output to be equal to each
  other is
• Y (1 s m)Y I G X(SP/P)
• We also temporarily assume that S, P and P are
  determined outside the model. This fixed exchange
  rate assumption means that I, G and X are all
  determined outside the model. The solution for Y
  is therefore

6

• Y IGX(SP/P)/s m
• 1/s m is called the multiplier, or the
  foreign trade multiplier, because an increase
  in export demand of 1 unit leads to an increase
  in output of
• 1/s m units.

7
Leakages away from demand for domestic output

• Note that any increase in domestic output, Y,
  induces some extra spending on domestic output
  itself, while the rest goes into 2 leakages.
  That is, into two things other than spending on
  domestic output. The two leakages are
• Private savings s
• Imports m

8
Intuition behind the multiplier

• One way of thinking about the multiplier is that
  the increase in income must be large enough to
  create a total leakage equal to the initial
  exogenous increase in demand.
• ?Y ?induced demand ?exogenous
  demand,
• And
• ?Leakage ?Y ?induced demand
• Therefore Y must rise by an amount big enough to
  create a leakage equal to the initial increase in
  exogenous demand
• ?Leakage ?exogenous demand

9

• The increased leakages are
• ?Private savings s?Y
• ?Imports m ?Y
• ?Total leakage s m ?Y
• Therefore output must rise by enough to ensure
  that
• s m ?Y ?X
• This is just a slightly different way of writing
  the multiplier formula.

10
Numerical example

• s 0.3, m 0.2.
• Therefore s m 0.5, so that the multiplier
  is 2.
• Suppose that exports rise by 3 and government
  spending and investment each rise by 1. Total
  increase in exogenous demand 5

11

• Output must rise by 10.
• The increased leakages are
• ?Private savings 0.3 x 10 3
• ?Imports 0.2 x 10 2
• ?Total leakage 5 ?I ?G ?X

12

• ?Income 10
• ?Private consumption (1 0.3) x 10 7
• Demand (for both domestic and foreign goods)
  rises by
• ?C ?I ?G ?X 7 1 1 3 12
• The supply of domestic and foreign goods rises by
• ?Y ?M 10 2 11.

13
Current account

• Note that in response to an increase in export
  demand, the CA rises, but by less than the
  initial increase in export demand
• ?CA ?X ?M ?X m?Y
• ?X m?X/s m
• ?X (s/s m)
• Therefore, if ?X is positive, ?CA is also
  positive, but smaller than ?X

14
Current account (continued)

• An increase in autonomous domestic demand (?I,
  ?G) will worsen the current account. Exports
  dont change, but there is an induced leakage
  into imports.

15

• In the earlier numerical example, the CA effects
  of the increases in exports, government spending
  and investment are therefore partially
  offsetting. What is the overall effect on the CA?