Allocation of Public Resources: A Knapsack Problem

If Singapore (or the world) were to sustain a massive peace time fuel shock and we're left with imports amounting to 5% necessary to fuel daily demand for the foreseeable future, who are we to allocate this to? Should we operate a free market and literally auction the fuel to the highest bidder (say with a generalized second-price auction)? That would be efficient in the sense defined by an economist, where the one who has the highest value for the fuel gets it. The fallacy is, this is possibly sub-optimal given that the transacted price is maximized but not the end-to-end economic output.

The high bidding CEO necessarily has had his wealth built on the backs of others. Not to discount his skills, his high value skills require a functioning operation with sufficient scale to generate real returns that "justify" his pay. In order to keep society running, we'd best allocate the fuel first to the buses that get people to work and the trucks the get commodities where they need to be processed.

In terms of resource allocation, the socially optimal solution is not, as the freshman economists are taught, to allocate to those with the highest value for the good as signified by willingness and ability to spend via the free market. Instead it is socially optimal to allocate each unit to the activity that brings the most marginal benefit to society as a whole. This is a knapsack problem of sorts.

Note that I'm not saying that rewards should be allocated in this fashion. I'm neither blindly communist nor blindly laissez faire free market crusader-ish. As a "full employment approximation", rewards should be commensurate with the difference between what is achievable with and individual and what is achievable without. This is in perfect accord with the above discussion: rewards to an individual should relate to the value that the person brings.

Allocation of public resources is a tough knapsack-type problem where the contribution of an element depends on the other elements in the basket. Still it is straightforward that some elements are in any optimal solution associated with resource levels low and high. These correspond to economic necessities: food security, transport, housing and education. These needs should be filled first before allocating resources to the more fanciful.

On this account, I think Singapore has done very well with food security and education. It has succeeded with transport and housing (With the latter, most of the griping is from people wanting more.) Yet, there is significant room for improvement for the transport and housing situation, which might be partially characterized by the saying "a monopoly is a license to steal". I'll comment on this in future.