Foreign Direct Investment and Unequal Regional Economic Growth in China

where

«1 = 1/(1 - c(Y))

(6)

c(Y) - the marginal propensity to consume is a function of the real per
capita income

Other variables could be included to explain the investment multiplier, e.g. the
marginal (inland) propensity to invest, the marginal propensity to import etc.
Therefore c is here an “aggregate” marginal propensity to consume. The functional
form for estimation of the investment multiplier was, after relative and absolute
income

«1 = α_io ^- a_nDY

«1 = βo ^- β1Y1

(7)
(7a)

where the expected sign of β₁ is negative while β₀ is positive.

The point of departure for discussing β now becomes

GI = γo + Y1 DY
GY = α_o + a₁GI
«1 = «10 ^- O11^dy

(8)

(9)

(10)

Now the distribution of growth on regions is described by a second degree polynomial

DGY = ( (X1oY1 - (X11Yo )DY - (X11Y1DY2

(11)

The coefficient γ₁ is here crucial because it indicates to which degree the investment
growth is unequally distributed in relation to the income distribution

Equal growth as a function of γ₁ is found by solving

⁽ɑɪoɪɪ ^- ɑɪɪɪo ^{)DY -} «11Y1DY2 = ⁰

(12)

The condition for an equal regional growth at an unequal distributed DFI is for a
given “aggregate” consumption function is now given by

Y1 = «11Yo^/( «1o ^- «11^DY)

(13)