The Effects of Reforming the Chinese Dual-Track Price System

Appendix 1: Proofs

Proposition 1

From (7), (x_p + x_mx)dp — x_mxdp + x_m(p — p)dx = xpdp. Hence, using (3) to
eliminate xp , we have

dp
dpx

x_m x

(18)

(19)

S — (x — xx)xm — x^s_p

dp _ -(p — p)xm

dxx S — (x — xx)xm — x^s_p

Proposition 2

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

dP
dpx

=dp+
dpx

—+—
dpx x

xx dp

^p')CX)2 ^xp dp.

(20)

By assumption,

∈p

p dx

= ^pττ< 0,
x dp

(21)

⁶P

p dx^s

= ——> 0.
x^s 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.