Ensuring sufficient online inertia is key to maintaining the security of system frequency when there is a high penetration of renewable energy in the system. The establishment of an inertia auxiliary service market is an effective means of achieving this. Therefore, with integrating synchronous inertia response into paid service, a pricing clearing model considering the minimum synchronous inertia is built, and a discrete variable relaxation method is proposed to transform the clearing model into a convex optimization problem. Then, based on the marginal cost pricing method and the Lagrange duality principle, a shadow price corresponding to the minimum synchronous inertia requirement constraint is extracted to evaluate its economic value and price the inertia service. Finally, taking the improved IEEE 39-bus and IEEE 118-bus systems as examples, the existence mechanism of the synchronous inertia shadow price, the numerical influencing factors and the benefits of the synchronous units are discussed in detail. The results show that it is necessary and urgent to build an inertia auxiliary service market in a power system which has a high proportion of new energy. Consequently the proposed method and simulation are able to provide guidance for the establishment of such an inertia auxiliary services market.