On the private provision of public goods

The main idea: allowing the private provision of some public services by peculiarities in contract design. 

0. Posts on this blog are ranked in decreasing order of likeability to myself. This entry was originally posted on 27.11.2022, and the current version may have been updated several times from its original form.

0.1 This is an expanded and translated version of what I’ve written elsewhere for the specific application of city parking. I think it generalises pretty well.

1 The problem

1.1 Assume you wish to provide a service that is beleaguered by positive externalities to the degree that no private provider would ever fund the service, as they could only capture a small part of the true value it would provide.

1.2 An immediate example would be a rail line between two major cities, which increases the property values in both by orders of magnitude more than you can ever charge by way of ticketing. As I’m using this as just an example, ignore the obvious solution of selling the line plus land around the stations here, as similar solutions do not come by as easily in other applications.

1.3 If you’d like to avoid the public operation of the line for reasons of well-known inefficiencies, a first-order solution would be to build the line publicly and then auction it off to the highest bidder, so that the actual operation is private. Given the discrepancy between true value and ticketing revenue, the sale would most likely be a loss-making operation, but (within broad limits) profits are not the point for the public purse which can capture part of the true value of the line through taxes.

1.4 The problem with this solution though is the inverse relationship between ridership and total (inc. externalities) value, whereby the more you charge in tickets, the less the ridership, and the greater the impact on the positive externality.

1.5 Fully privatizing the line could well result in a profit-maximising owner setting such prices as to leave part of the capacity unused (classic monopoly problem), as long as the total revenue is maximised. Nothing wrong with this in principle, but in such application the real value is the unseen, not the ticketing revenue, and such a real but unseen value of the line is majorly impacted.

1.6 Examples that could be argued to fit this model include (off the top of my head) public transport, road infrastructure, sewage and energy transmission systems, city parking and quite a few more.

1.7 What all of these scenarios have in common is that there seems to be no way to calculate the real value-maximising price and quantity mix, but the answer feels like its lower and higher respectively than what a private provider would find in their interest to go for.

1.8 We can still provide such services privately though if we take care to construct an appropriate mix of incentives for such a private provider. Neither of the two ideas floated below is a fully satisfactory solution to the issues caused by extensive externalities, as neither allows for the market to calculate the quantity of the service that is offered. Still, both allow the calculation of an efficient price for a pre-set quantity, and thus I’d argue that they - and especially the second proposal - are still major steps in direction of the efficient provision of public goods.

2 The first, less satisfactory solution

2.1 Keeping with the rail example, you build the rail line publicly and then auction it off to private operators. But bids are not solicited in the form of prices to pay (indeed, no price will be paid for the acquisition at all) but instead of prices that the provider will charge to the public: the lowest price wins. A pre-set portion of the revenue is paid back to the government, which can be packaged into a bond format and sold off separately to the broader market.

2.2 In theory, bidders have an incentive to bid the price that matches the sum of their operations cost, market profit rate and portion withheld by the government, with the winner being he who can operate the line at the lowest cost. No one would price such as to leave unused capacity (empty seats) except as dictated by operations cost.

2.3 A major issue with the model would be the tendency for people to overestimate how efficiently they can run the line, with the process resulting in a bankrupt provider a few years down the path. A closely related point is the lack of flexibility, as once you set the winning (lowest) price, there is no way to change it even though conditions change all the time.

2.4 You could have the winner buy back in the open market all bonds issued under 2.1, thus giving them the option to set whichever price they’d like, but this could be an expensive endeavour for a provider who’d be strapped for cash almost by design.

2.5 Further, once you do this and buy back the liability, the whole unorthodox contract design becomes good for nothing, and the issue with potential overcharging emerges again.

2.6 I don’t have a solution to this major issue, which is why this approach is my least favourite, as it seems to be ill suited to long-term operations.

2.7 Other minor issues would be the challenge of determining who among the bidders is actually providing the lowest price, as in practice there are dozens of types of tickets available: peak, day off-peak, night, pre-paid, etc. Which option is to be compared?

2.8 The issue would probably be ameliorated to a reasonable degree by having bids be public and giving bidders the option to change their submission as many times as needed within the bidding window, which I’d expect would lead to bids being continuously adjusted towards a market optimum. So, not a huge issue but worth mentioning.

3 The second, more satisfactory solution

3.1 Soldiering on with the rail example, you build the rail line publicly and then auction it off to private providers, in a normal auction where the highest price provided to you wins. But the contract stipulates a minimum capacity (the actual seating capacity of the line) and any part of this being found empty (allegedly on account of overpricing) would cause the operator to pay to the government the price of that empty seat: you pay me the ticket of any empty seats on the train (see 3.61 on the number of seats thus contracted for). In the same fashion as before, this liability is packaged in a bond format and sold off separately.

3.2 If we assume X to be the price that would maximise the revenue of the operator whilst leaving some capacity empty, and X - Y to be the price that ensures full occupancy of the railcars, I’d expect the winner to charge X - some portion of Y, if not X - Y in full.

3.3 The same minor issue as earlier applies, with it not being immediately obvious which price the operator is to pay back for an empty seat (pre-paid or at-the-gate ticket), but here this is an even more minor issue, with a solution just needing to be specified in advance.

3.4 Another minor issue would be the need for some sort of real-time measure of occupancy, not a huge challenge in this day and age, I think.

3.5 Otherwise, note how this design is much more flexible than the previous one, where the operator has full rights to amend their prices as they see fit, allowing for long-term operation and true ownership of the line.

3.6 Indeed, the design could be a bit too flexible, as the operator could still go out and buy back the bond issued under 3.1 if this is the profit-maximising move, thus invalidating the whole point of the design. I’m not sure whether allowing or disallowing this would be optimal.

3.61 Yet a further bit of flexibility could be engineered by allowing the bidders under 3.1 to bid a combination of purchase price and guaranteed quantities, to see if there's and obvious inflection point at some quantity other than foreseen by the government. Maybe 500 passengers per day on the line connecting two villages is a bit unfeasible, eh?

3.7 It is worth noting that you could, in principle, run a fully socialist economy in this way, with the state building everything and setting production quantities by five-year plans and outsourcing the efficient operation of the plan to the market. It’d still be a mess in terms of calculation as you still set quantities centrally, but the prices being charged would be much closer to optimal and meaningful.

3.8 In principle, reliance on the prices could even lead to the gradual improvement of the quantities scheduled in time, in a matter similar to - but probably much better behaved than - what was foreseen by market socialism.

3.9 Indeed, the open trade of bonds as per 3.1 would appear to give this economy the chance to organically privatise itself, or portions thereof.

3.10 I’d think a bit more about the implications of such an economy if I didn’t have a better option for those elites who seek socialism. Except that a heavily-modified version of this mechanism could conceivably be used to manage virtual companies set up within a business large enough that internal accounting is not quite able to calculate on the basis of rational prices.