Simple keynesian model in an open economy

1. Simple Keynesian Model
in an Open Economy
Dr. Subir Maitra, Guest Faculty,
University of Calcutta
subirmaitra.wixsite.com/moocs

2. Open Economy
An economy that interacts with the rest of the world
through international trade.
Openness of an economy: Three types
1. Goods Market Openness: When goods and services are allowed to
be exported and imported.
2. Capital Market Openness: When capital and financial resources are
allowed to move in and move out of the
country.
3. Factor Market Openness: When labour is allowed to come in and
go out of a country.

3. The Model:
Consumption function: C = C0 + c YD (C0 >0, 0<c<1)
Disposable income: YD ≡ Y + TR – T
Behavioural Equations:
Transfer payments: TR = TR0 (TR0>0)
Taxes: T = T0 (T0 > 0)
Investment function: I = I0 (I0 > 0)
Government expenditure: G = G0 (G0 > 0)
Exports: X = X0 (X0 > 0)
Imports: M = m Y (0 < m <1)
Equilibrium Condition:
Y = C + I + G + X - M

4. By substituting all behavioural equations into the
equilibrium condition, we get:
Y = C0 + c.( Y + TR0 –T0) + I0 + G0 + X0 – mY
By rearranging, we get:
Y - c. Y + m. Y = C0 + c.TR0 – c. T0 + I0 + G0 + X0
Equilibrium income in SKM in an open economy:
YE =
C0 + c.TR0 – c. T0 + I0 + G0 + X0
(1− c + m)

5. Multiplier in Open Economy SKM:
To derive multiplier in respect of any exogenous parameter such as G
or I or X, take partial derivative of Y w.r.t. that specific parameter.
Investment multiplier:
𝜕𝑌
𝜕𝐼
=
1
(1− c + m)
Government expenditure multiplier:
𝜕𝑌
𝜕𝐺
=
1
(1− c + m)
Export multiplier:
𝜕𝑌
𝜕𝑋
=
1
(1− c + m)
Lumpsum Tax multiplier:
𝜕𝑌
𝜕𝑇
=
−𝑐
(1− c + m)
Transfer payment multiplier:
𝜕𝑌
𝜕𝑇𝑅
=
𝑐
(1− c + m)

6. Balanced Budget Multiplier in Open Economy SKM:
To derive Balance Budget Multiplier, we take total derivative on both sides of the
following equation derived earlier:
Y = C0 + c.( Y + TR0 –T0) + I0 + G0 + X0 – mY
After taking total derivative, we get:
dY = dC + c.( dY + dTR –dT) + dI + dG + dX – mdY
To derive BBM, we assume
dC = dTR = dI = dX = 0
and dG = dT
By substituting these in the above equation we get:
dY = c.dY – c.dT + dG – mdY
=> dY -- c.dY + mdY = – c.dG + dG
=> dY (1 – c + m) = (1 – c) dG
=>
𝑑𝑌
𝑑𝐺
=
(1 – c)
(1 – c + m)
≠ 1
Thus, BBM in Open Economy SKM ≠ 1