SPRs generate two kinds of good. First, SPRs can keep oil price from soaring at supply interruption; second, SPR drawing rights enable the owners to be more competitive for the released SPR oil and thus give them advantages at supply interruption. The first good benefits all oil consumers and excludes none from enjoying it at bearable cost, so for it we have the name “public good”, which is typically a kind of Samuelson’s pure public goods [4]. The second good can easily exclude any one by price biding, so for it we have the name “private good”.

Two government types are defined as and where is the number of the oil consumers, is the size of the GSPR the government need build, is the aggregate utility function of GSPR as pure public good while is the aggregate utility function of the pre allocated GSPR drawing right, is the GSPR’s total cost, is the anticipated duration between the time 0 and the next supply interruption, and is the real rate incorporating factors of the oil price’s long run trend. The difference between the two governments is that under GSPR is purely financed by public expenditure, while under GSPR is financed not only by public expenditure but also by the private bids for the GSPR drawing rights before the construction of GSPR. For the governments, assumptions 1-3 are arranged.

Assumption 1: Bothand know the function, which is concave and continuously increasing on.

Assumption 2: knows, and knows both and.

Assumption 3: As net oil importer, both and maximizes the aggregate consumer surplus, which means must hold for, and must hold for.

Consumers are willing to pay for GSPR because they have expected an oil supply interruption which may endanger their welfare and this danger may cost them more than GSPR does. As price takers under the current oil market condition, oil consumers know well that only collective actions can deter the soaring oil price. Economies of scale provide a main rationale for considering public infrastructure provision [5]. GSPR projects have extraordinary economies of scale, and the total GSPR cost would be unacceptably high if construction actions have been taken separately rather than collectively.

Let stand for consumer i’s utility function of GSPR as public good, and stand for consumer i’s utility of his/her GSPR drawing right, stand for consumer i’s payment for GSPR, stand for i’s proportional share of the total cost pie of the GSPR, and. For the consumers, assumptions 4-6 are arranged.

Assumption 4: is concave and continuously increasing on; is concave and continuously increasing on;, and.

Assumption 5:;, where and.

Assumption 6: There exists certain so that in, while in,.

It can be inferred that is also continuously increasing on. However, there is free-riding problem in the provision of public good and it’s rather difficult to overcome this problem by decentralized mechanisms, so for simplicity we assume that under the government’ authority, the society’s propensity to free-ride has been wiped out. Under this circumstance, the government can optimally decide the size of the GSPR as public good and the distribution of the corresponding cost. The rationale of the last sentence of assumption 6 is, if is always larger than, GSPR should never be built; and, that is always larger than is impossible.

We introduce the multiplier to further clarify the difference between the concepts of GSPR as public good and that of the GSPR drawing right. If there exists and only exists one so that the cost of the GSPR as public good is and that of the GSPR drawing right cost is, the GSPR as public good and the GSPR drawing right are clearly separated. Under this circumstance, becomes the coordinate of i’s share of the public good cost and that of the drawing right cost, , subject to and.

Many examples, such as panic buying of fuel in 1973 oil crisis [6], panic buying of fuel in Hurricane Katrina [7], panic buying of salt in Japan’ s nuclear crisis [8] and so on, suggest that consumer hoarding (or panic buying) may happen at supply interruption. According to the economic explanation given by [9], panic buying can be interpreted as the distortion of demand curve. When supply interruption happens, demanders are expected to value the supply unusually high and get less elastic to price, hence the demanders may suffer greater surplus loss. For the possibility of panic buying, assumption 7 is arranged.

Assumption 7: The announced supply interruption distorts the price elasticity of the aggregate demand. The degree of the distortion is decreasing on the size of the strategic inventory held at the immediate convenience of the consumers.

Suppose that the oil supply interruption is expected to take pace at time and policies of GSPR are required to make at time 0. Currently, no GSPR drawing right has been pre allocated and the GSPR oil is sold to the market at, the instant market price of time, which means at time 0, is regarded as 1. In other words, the current government is typically the kind of. Our proposal is requiring the government to transform from to.

More specifically, consumers and at time 0 are proposed to sign a contract which specifies: at time consumer i is allowed to buy amount of GSPR stock at the price, where is the market price at the contracting time point, provided that at time 0 consumer i pays a fair part of the total GSPR cost. To differentiate the GSPR under from the normal commercial oil stocks, we emphasize that the drawing rights also can only be executed at the government announced oil supply interruption.

By incentive improvement we meant that under the proposed mechanism, consumers will enable the government to build a lager GSPR by contributing more. Under, there exists one and only one so that and. Given the GSPR of size, all consumers will pay less for GSPR as public good for is definitely less than. Therefore, the aggregate marginal utility curve under intersects the marginal cost curve to the right (on the vertical line) of the point where the marginal utility curve under intersects the marginal cost (on the vertical line), as Figure 2 shows. Thus, the government is required to build a GSPR of size, and the total expenditure is which is obviously larger than. Thus, the incentive improvement has easily been proved.

From Figure 2, it can also be easily inferred that the significance of the incentive improvement depends on the scale of: the smaller the the larger the, which means if the consumers value GSPR drawing rights more, the incentive improvement would be more significant.

In order to deepen the understanding of the incentive improvement, we proceed with a simple numerical example.

Suppose, , and respectively the consumers’ utility functions are:

.

It can be inferred that, under this market the aggregate utility function of the GSPR as public good is, and that of the GSPR drawing right is

.

Under, and the optimal is determined by Equation (1) according to the principle “marginal utility equals marginal cost”.

and, the cost distribution among the consumers is determined by Equation (2).

By solving the combination of Equation (1) and Equation (2), we can obtain that, under, , the total expenditure on the GSPR is 3.60, and the cost distribution is in terms of proportions, or the consumers need pay 0.60, 1.20 and 1.80 respectively.

Under, and the optimal is determined by Equation (3).

and, the cost distribution among the consumers is determined by Equation (4).

By solving the combination of Equation (3) and Equation (4), we can obtain that, under, , , the total expenditure on the GSPR as public good is 4.81 and the total expenditure on the GSPR drawing rights is 3.86, and the cost distribution of the GSPR as public good is in terms of proportions or in terms of monetary values; the cost distribution of the GSPR drawing rights is in terms of proportions or in terms of monetary values; and,. We can see that there has been a very significant improvement since is more the twice of and all together the consumers will spend more income under then the twice of that under.