Abstract: One of the modern government's basic functions is to satisfy all residents' need for public goods. Hence,in contrast to other commodities, the government will be motivated to intervene the supply system of public goods once the firms which compete spontaneously in the market fail to cover all the residents' public needs. So, how can the government decide whether to intervene according to the results of market spontaneous competition? What is the standard for the government when choosing an intervention approach? How will the intervention affect the consumers' surplus in the market? Much remain to be discussed on these issues. Given the lack of literature on this issue, the government and the market coverage factor into the vertical competition structure is introduced to study how should the government makes intervention decisions in market competition. Our study differs from other similar research on vertical competition structure inmaking the market coverage factor endogenous by considering the effect of government intervention on the range of the uncovered market. The results show that:first, the boundary setting of government intervention depends on the market features of consumers' willingness to pay and firms' willingness to produce; second, the two market features also determine the feasibility range of the two intervention approaches, the subsidy approach and the proprietary approach, which implies thatthe government should make intervention decision matched for the two features' range, otherwise, the intervention could fail due to mismatch; third, to maximize the consumers' surplus, the government should choose the strategy of subsidizing high-quality firm in subsidy approach of the strategy of following high-quality firm in proprietary approach.Our theoretical findings provide not only the abstract logic in intervention decision for the government, but also practical application in reality. In real market of public goods, the government can subsidize the high-quality firm when the uncovered market is caused by the firms' low willingness to produce, and follow the high quality firm when the uncovered needs for public goods is pressing.

Key words: government's intervention, market coverage, government'sproprietary trading, fiscal subsidy, subgame perfect Nash equilibrium