In this paper, we aim to explore the influence of budget constraint privatization policy in the context of mixed duopoly to examine whether privatization policy is dependent upon the unionization structure with labour productivity difference. We showed that, when the unions put equal weights on the wages and the numbers employment, the social welfare pre-privatization is always higher than the one post-privatization regardless of the type of unionization; the government should not privatize the public firm, and nationalization policy should be retained because it will provide a higher rent for the union. Furthermore, union(s) opposes the privatization policy in the presence of budget constraint and union structure.