Subsidy given by the government for production is common to develop renewable energy enterprises. This article establishes a duopoly model including renewable energy enterprises and traditional energy enterprises based on market with both complete information and asymmetric information. A generalized consumer surplus (GCS) function is defined, and the assumption that the government maximizes generalized consumer surplus is provided. To identify the cost of enterprises precisely, the government gives incentive compatibility constraint. Firstly, this article found that optimal subsidy for renewable energy enterprises positively correlates with its cost under complete information. Secondly, under asymmetric information, the optimal subsidy values increase with the probability of firms with high costs. Thirdly, renewable energy enterprises may hide their cost to maximize their profits when the difference between subsidies for renewable energy enterprises with disparate cost is too large or too small. Finally, a mechanism to induce enterprises' truth based on incentive compatibility constraints is offered. Under this circumstance, a suggestion is provided that government should choose to screen the cost information of the enterprises or to maximize generalized consumer surplus as the preferred target. (C) 2016 Elsevier Ltd. All rights reserved.