Privilege and corruption: The problems of China's socialist market economy - New Perspectives on Transition Economics: Asia

American Journal of Economics and Sociology, The, Jan, 2002 by Shuntian Yao

IV

A Free Market Economy

WE FIRST CONSIDER an ideal society in which every individual is allowed to choose her occupation freely. As a result, a decision plan of individual i is [d.sup.i] = ([l.sup.i.sub.1], [l.sup.i.sub.2], [l.sup.i.sub.3]; [x.sup.i.sub.1], [x.sup.i.sub.2], [x.sup.i.sub.3], [y.sup.i.sub.1], [y.sup.i.sub.2], [y.sup.i.sub.3]), where is [l.sup.i.sub.j] the amount of labor she allocates for good j's production, [x.sup.i.sub.j] is the amount of good j she sells and [y.sup.i.sub.j] is the amount of good j she buys. The following constraints must be satisfied:

[l.sup.i.sub.1] [greater than or equal to] 0, [l.sup.i.sub.1] [l.sup.i.sub.2] [l.sup.i.sub.3] [less than or equal to] 1; 0 [less than or equal to] [x.sup.i.sub.j] [less than or equal to] [q.sup.i.sub.j], j = 1,2;

[y.sup.sub.j] [greater than or equal to] 0, [p.sub.1][y.sup.i.sub.1] [p.sub.2][y.sup.i.sub.2] [p.sub.3][y.sup.i.sub.3] [less than or equal to] [p.sub.1][x.sup.i.sub.1] [p.sub.2][x.sup.i.sub.2] [p.sub.3][x.sup.i.sub.3] (*)

where [q.sup.i.sub.j] ([q.sup.i.sub.3] now represents the amount of the administrative produced) are as defined in equations (2) and (3) with all the variables having a superscript i. Obviously when we use the notation in equation (2) for [q.sup.i.sub.1] and [q.sup.i.sub.2], the above-mentioned constraints imply that [s.sup.i.sub.1] 1[s.sup.i.sub.2] [less than or equal to] max{0, c([l.sup.i.sub.3] - b)} - [x.sup.i.sub.3] [y.sup.i.sub.3]. The final consumption of i can be computed by [Z.sup.i.sub.j] = max {0,([l.sub.j] - a) [S.sup.i.sub.j [alpha]]} - [X.sup.i.sub.j] [ky.sup.i.sub.j], j = 1,2. Thus i achieves a utility of u([Z.sup.i.sub.1], [Z.sup.i.sub.2]) = [Z.sup.i.sub.1] [Z.sup.i.sub.2].

A Walrasian equilibrium of such an economy is defined as a price vector p ([p.sub.1], [p.sub.2], [p.sub.3]) and a decision plan [d.sup.i] for every individual i in the population, such that (a) given p, [d.sup.i] maximizes the utility of i when she is allowed to choose among all feasible decision plans ([l.sup.i.sub.1], [l.sup.i.sub.2], [l.sup.i.sub.3]; [x.sup.i.sub.1], [x.sup.i.sub.2], [x.sup.i.sub.3], [y.sup.i.sub.1], [y.sup.i.sub.2], [y.sup.i.sub.3]) satisfying (*), and (b) the excess demand of every good is less than or equal to zero: [[integral].sub.[0,1]] [y.sup.i.sub.j] [less than or equal to] [[integral].sub.[0,1]] [x.sup.i.sub.j], j = 1,2,3.

It is not difficult to establish the following:

Proposition 1. In our model with ex ante identical individuals and freedom of choice of professions, every individual must achieve the same equilibrium utility. Moreover, when the transaction efficiency is sufficiently close to 1 in any Walrasian equilibrium of the economy, the equilibrium utility is [U.sup.*] = [k.sup.1 [alpha]][(1 - a).sup.2][C.sup.2[alpha]] [(1 - b).sup.2[alpha]] [[alpha].sup.2.[alpha]] [(1 - [alpha]).sup.2-2[alpha]]/4. In particular, when a = 0.2, b = 0.5, c = 10, [alpha] = 0.1, we have [U.sup.*] = [0.115226k.sup.1.1].

The proof of this proposition is given in the Appendix.