The Effects of Reforming the Chinese Dual-Track Price System



Appendix 1: Proofs

Proposition 1

From (7), (xp + xmx)dp — xmxdp + xm(p — p)dx = xpdp. Hence, using (3) to
eliminate xp , we have

dp
dpx


xm x

(18)

(19)


S — (x — xx)xm — xsp

dp _    -(p — p)xm

dxx   S — (x — xx)xm — xsp

Proposition 2

Differentiating (6) w.r.t. px , we then obtain 15

dP
dpx

=dp+
dpx

1

—+—
dpx x

xx   dp

p')CX)2 xp dp.

(20)

By assumption,

∈p

p dx

= pττ< 0,
x dp

(21)

6P

p dxs

= ——> 0.
xs dp

(22)

15We use brackets with superscript 2, (x)2 to define x square function. The superscript 2

without brackets represents variables for the type-2 household.

27



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