The concept of inequality arises in various contexts and there is remarkable interest in its measurement. Estimation of the shape parameter, Lorenz curve and Gini-index for power function distribution using Bayesian method is discussed in the present article. Bayes estimators have been developed under squared error loss function as well as under LINEX loss function. We demonstrate the use of the proposed estimation procedure with the U. S. income data for the period 1913-2010. Our proposed Bayesian estimators are compared using a Monte Carlo simulation study with the maximum likelihood estimators proposed by
Belzunce et al. (1998).