Abstract: This paper studies the auction problem of divisible goods. First, a uniform price auction mechanism of divisible goods with variable supply is proposed under three conditions, i.e., every buyer submits a nonincreasing continuous demand function, the seller and all buyers are risk neutral and the seller uses the strategy of variable supply(let the supply as a function of price). Second, the information incentive and effectiveness of allocation are analyzed, and the seller's optimal supply strategy and the buyers' bidding strategies are discussed. Third, this auction mechanism is generalized under the condition of the risk neutral buyers, risk averse buyers and risk seeking buyers coexist in an auction. Meanwhile, several more general equilibrium results are also educed about auction under a uniform price. Finally, this auction mechanism is applied to analyze and evaluate the validity for the free allocation of total permitted pollution discharge capacity in the environmental planning of Wuhan City Circle in Hubei Province, China. The validity evaluation result of free allocation is obtained by analyzing the statistical data of SO₂ in 9 cities of Wuhan City Circle. Combining with the actual background, several improved strategies on free allocation method and current sewage application system are also given.

Key words: divisible goods, uniform price auction, variable supply, environmental planning