The economic world is full of patterns, many of which exert a profound influence over society and business. One of the most contentious is the distribution of wealth. Way back in 1897, an Italian engineer-turned-economist named Vilfredo Pareto discovered a pattern in the distribution of wealth that appears to be every bit as universal as the laws of thermodynamics or chemistry. The present paper proposes some Bayes estimators of shape parameter of Pareto income distribution in censored sampling. Asymmetric LINEX loss function has been considered to study the effects of overestimation and underestimation. For the prior distribution of the parameter involved a number of priors including one and two-parameter exponential, truncated Erlang and doubly truncated gamma have been contemplated to express the belief of the experimenter s/he has regarding the parameter. The estimators thus obtained have been compared theoretically and empirically with the corresponding estimators under squared error loss function, some of which were reported by Bhattacharya et al. (1999).