Designing investment subsidies around demand, capacity and a shared budget

One budget, different investment decisions

In Optimal Subsidy Design for Productive Investment across Markets, Alexandros Pavlis develops a mathematical framework for supporting productive investment when demand is uncertain and expansion cannot be reversed. The preprint, dated November 3, 2026, presents theoretical results and numerical illustrations rather than an empirical evaluation of a subsidy programme.

The model contains several separate markets, each served by one risk-neutral monopolist. Goods cannot substitute for one another, and productive capacity cannot move between markets. Each producer chooses output and can repeatedly expand capacity, paying an installation cost per unit minus any subsidy.

Demand evolves randomly through a continuous diffusion process. A regulator commits to a subsidy schedule that depends on each market’s demand state, anticipating how the producer will respond. The objective combines weighted consumer surplus, producer profits and a separate benefit from installed capacity, while accounting for the excess resource cost of raising public funds.

That additional capacity benefit represents value not already captured in the modeled consumer surplus and profits. The paper gives preparedness and infrastructure advantages as possible interpretations; it does not estimate their magnitude.

Solve for investment, then recover support

The central technique reverses the apparent policy-design problem. Instead of searching directly over subsidy schedules, the analysis first identifies investment boundaries: rules separating situations in which a producer waits from those in which it expands.

Under the paper’s assumptions, the producer’s optimal response is to expand enough to reach a demand-dependent capacity target whenever necessary. Because investment is irreversible, subsequent falls in demand do not reduce installed capacity. The optimal capacity process therefore depends on the highest demand reached so far, as well as initial capacity.

Pavlis then rewrites the regulator’s stochastic problem as a deterministic optimization over these boundaries. An integral formula recovers subsidies that implement the resulting investment decisions.

The preprint establishes existence of optimal schedules and uniqueness of the induced investment policy from the specified initial states, subject to its assumptions. This is not a claim that every part of the subsidy schedule is uniquely determined: schedules can differ in demand regions where no investment occurs from those initial conditions.

A common budget multiplier links otherwise separate market-level calculations. Together with the excess financing cost, it acts as a penalty on subsidy spending. A tighter binding budget increases this penalty and reduces aggregate expected discounted expenditure. Once the budget is sufficiently large to stop binding, additional funding leaves the optimal investment policy unchanged.

Why support can fall—or initially rise

Without additional capacity benefits, the constructed optimal subsidies are nonincreasing in demand. Under a sufficiently high spending penalty, support ends entirely above a market-specific demand threshold.

A simpler special case produces constant subsidies: additional capacity benefits are absent, the excess cost of raising public funds is zero, and the budget is large enough to implement the unconstrained optimum. The result is conditional, not a general recommendation for flat support.

Positive capacity benefits can change the pattern. The paper shows that subsidies initially rise and then decline when the spending penalty is sufficiently small. Its numerical examples also illustrate this hump-shaped support at selected positive penalties. Thus, valuing installed capacity separately can justify increasing support over an initial range of demand, but does not imply that subsidies should always increase.

The numerical illustrations also distinguish subsidy rates from fiscal allocation. In examples varying installation costs, higher costs produce larger per-unit subsidies but smaller expenditure shares. The relevant spending calculation includes both the timing and scale of induced expansion—not simply the amount offered for each unit.

What the budget does not guarantee

The shared constraint limits expected discounted subsidy expenditure. It is not a requirement that spending remain below a fixed cash ceiling on every possible demand path.

That distinction matters for correlated demand shocks. Holding individual demand dynamics and initial states fixed, the paper finds that correlation does not change optimal schedules or the regulator’s value in this model. Correlation can nevertheless change the distribution of aggregate expenditure.

The conclusions also depend on committed policies, separate monopoly markets, irreversible expansion and technical restrictions on demand dynamics and capacity benefits. They provide a structured account of incentive design under those conditions, not evidence that the same schedules would be optimal in competitive or interconnected markets.