The impossible quartet in a demand led growth-supermultiplier model for a small open economy

OREIRO, JOSÉ LUIS; SANTOS, JULIO FERNANDO COSTA

doi:10.1590/0101-31572023-3448

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Brazilian Journal of Political Economy

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Articles • Brazil. J. Polit. Econ. 43 (3) • Jul-Sep 2023 • https://doi.org/10.1590/0101-31572023-3448 copy

The impossible quartet in a demand led growth-supermultiplier model for a small open economy^* * Paper prepared to be delivered at IV Workshop on New Developmentalism to be held at the Center for Studies on New Developmentalism of the São Paulo School of Business Administration, São Paulo, Brazil in the period of 25 to 26 of July, 2019.

O quarteto impossível em um modelo supermultiplicador de crescimento liderado pela demanda para uma pequena economia aberta

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The aim of this paper is to investigate the long run sustainability of a growth path led by multiple non-creating capacity autonomous expenditures in a demand led-supermultiplier model for a small open economy. Using two different models the results show that it is impossible to have in the same model long-term economic growth driven by the non-capacity creating component of domestic demand, exogenous income distribution, long-run balance between productive capacity and aggregate demand and balance of payments equilibrium. Economic viability of the balanced-growth path demands growth to be led by exports, at least for small open economies.

KEYWORDS:
Post-Keynesian economics; growth and distribution; Sraffian supermutiplier; simulation models

Steady state Equilibrium (fixed point)	Scenario 1: g _x >g _g	Scenario 2: g _g >g _x
h*	$= (g_{x} + δ) \cdot \frac{v}{u_{n}}$	$= (g_{g} + δ) \cdot \frac{v}{u_{n}}$
u*	u=u* _n	=u _n
α ^*	=0	=1

Scenarios	b ^*	r ^*
g_g >g _x	$= \frac{v \cdot (g_{g} + δ) + u_{n} \cdot [τ \cdot (1 - π) - s - m]}{u_{n} \cdot (i - g_{g})}$	=−m/g _g
g_x >g _g	$= \frac{τ \cdot (1 - π)}{i - g_{x}}$	$= \frac{s \cdot u_{n} - v \cdot (g_{x} + δ)}{u_{n} - g_{x}}$

Jacobian Element	Analytic Form	Signal
$J_{11} = {\frac{\partial \dot{u}}{\partial u}}_{(u , α , h , b , r *)}$	$- (g_{x} + δ) \cdot (1 - \frac{μ}{s + m - g_{x} - δ})$	>0 or <0
$J_{12} = {\frac{\partial \dot{u}}{\partial h}}_{(u , α , h , b , r *)}$	$- u_{n}^{2}$	<0
$J_{21} = {\frac{\partial \dot{h}}{\partial u}}_{(u , α , h , b , r *)}$	$μ \cdot (g_{x} + δ)$	>0
$J_{31} = {\frac{\partial \dot{b}}{\partial u}}_{(u , α , h , b , r *)}$	$- \frac{(g_{x} + δ) \cdot μ \cdot τ \cdot (1 - π)}{(i - g_{x}) \cdot (s + m - g_{x} - δ)}$	>0 or <0
$J_{33} = {\frac{\partial \dot{b}}{\partial b}}_{(u , α , h , b , r *)}$	i−g _x	>0 or<0
$J_{41} = {\frac{\partial \dot{r}}{\partial u}}_{(u , α , h , b , r *)}$	$\frac{(g_{x} + δ) \cdot μ \cdot [s - (g_{x} + δ)]}{g_{x} \cdot [s + m - (g_{x} + δ)]}$	>0 or <0
$J_{44} = {\frac{\partial \dot{r}}{\partial r}}_{(u , α , h , b , r *)}$	−g _x	<0

Jacobian Element	Analytic Form	Signal
$J_{11} = {\frac{\partial \dot{u}}{\partial u}}_{(u , α , h , b , r *)}$	$- (g_{g} + δ) \cdot (1 - \frac{μ}{s + m - g_{g} - δ})$	+,0,−
$J_{12} = {\frac{\partial \dot{u}}{\partial h}}_{(u , α , h , b , r *)}$	−1	−
$J_{21} = {\frac{\partial \dot{h}}{\partial u}}_{(u , α , h , b , r *)}$	$μ \cdot (g_{g} + δ)$	+
$J_{31} = {\frac{\partial \dot{b}}{\partial u}}_{(u , α , h , b , r *)}$	$- \frac{μ \cdot (g_{g} + δ) \cdot [τ \cdot (1 - π) - (s + m - g_{g} - δ)]}{(i - g_{g}) \cdot (s + m - g_{g} - δ)}$	+,0,−
$J_{32} = {\frac{\partial \dot{b}}{\partial h}}_{(u , α , h , b , r *)}$	−1	−
$J_{33} = {\frac{\partial \dot{b}}{\partial b}}_{(u , α , h , b , r *)}$	i−g _g	+,0,−
$J_{41} = {\frac{\partial \dot{r}}{\partial u}}_{(u , α , h , b , r *)}$	$- \frac{μ \cdot (1 + \frac{δ}{g_{g}}) \cdot m}{s + m - g_{g} - δ}$	+,0,−
$J_{44} = {\frac{\partial \dot{r}}{\partial r}}_{(u , α , h , b , r *)}$	−g _g	−

Parameter	Interval	Parameter	Interval
μ	[0;1]	s	[0;1]
u _n	[0;1]	m	[0;1]
g _g	[0;0.1]	i	[0;0.1]
g _x	[0;0.1]	τ	[0;1]
δ	[0;0.1]	π	[0;1]
v	2.5	α ₀	0.5

Parameter	Value	Parameter	Value
μ	0.30 and 0.42	s	0.40
u _n	0.90	m	0.20
g _g	0.07	i	0.05
g _x	0.06	τ	0.30
δ	0.05	π	0.30
v	1.11	α ₀	0.50

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