AN-011: Static welfare arithmetic

Intuition (plain-language)

Translate the price effect into welfare: the waste from a higher-cost supplier winning, plus the extra cost of raising public funds to pay the bill. At λ=0.30 that is about 29% of the open price in ordinary goods — and a planner would need to value SME profits at 2.42× ordinary money to call it worth it. On Group 65 alone, R$38–89M a year.

Question

What is the per-auction static welfare cost of the full SME-only set-aside, decomposed into real allocative waste and fiscal distortion? And what SME welfare weight would a planner need to apply to be indifferent between the set-aside and the open regime?

Design

• Sample: structural cells from AN-010 — non-pharma standardized; pharma boundary case.
• Variation: counterfactual policy regime \(V_0\) (full SME-only) vs \(S_1\) (open).
• Specification: Loss(\(V_0\)) = DWL\(_{\mathrm{alloc}}\) + \(\lambda \cdot (p^{V_0} - p^{S_1})\), where DWL\(_{\mathrm{alloc}} = c_{(1)}^{V_0} - c_{(1)}^{S_1}\). The first term is real allocative waste (the winner has a higher production cost under the set-aside); the second is the fiscal distortion at the marginal cost of public funds \(\lambda = 0.30\) baseline.
• Implied SME welfare weight \(\omega\) solves \(\omega \cdot \text{transfer} = \text{DWL}_{\mathrm{alloc}} + \lambda \cdot \Delta_{\mathrm{gov}}\).
• Bootstrap CIs from v7-jpube-tight/scripts/56_welfare_bootstrap.R.
• Outcomes: \(\Delta_{\mathrm{gov}}\), DWL\(_{\mathrm{alloc}}\), \(\lambda \cdot\) MCPF, total Loss / \(p^{S_1}\), implied weight \(\omega\).

Results

From v8-jpube/output/values.tex. All shares of reference price \(p^{S_1}\); \(\lambda = 0.30\) baseline (Ballard-Shoven-Whalley).

	Non-pharma	Pharma (boundary)
\(\Delta_{\mathrm{gov}}\) (payment increase)	0.247	0.298
DWL\(_{\mathrm{alloc}}\) (allocative waste)	0.148	0.207
\(\lambda \cdot \Delta_{\mathrm{gov}}\) (MCPF distortion)	0.074	0.089
Total loss / \(p^{S_1}\)	28.9%	44.8%
Bootstrap lower endpoint	20.5%	34.9%
Implied SME welfare weight \(\omega\)	2.42	2.61

Pharma magnitudes are larger but inherit additional model sensitivity — treated as a boundary case (AN-016).

Annualized on Group 65 alone: R\(38–89M per year (US\)11–25M) across the 30–70% adherence range (v7-jpube-tight/scripts/57_welfare_adherence_sensitivity.R).

Output: macros in v8-jpube/output/values.tex; paper table tab_welfare_policy_v8 in §5.

Interpretation

The set-aside is costly on both welfare margins: the contract is assigned to a higher-cost supplier (real allocative waste) and the government pays more (fiscal distortion at \(\lambda\)). The implied welfare weight of 2.42 means a planner must value SME producer surplus at $2.42 of welfare to find the full set-aside optimal — a number that should be benchmarked against the other welfare weights implied elsewhere in the planner's revealed preferences.

The R\(38–89M annual range comes from the SME-eligible adherence-rate sensitivity across the **30–70%** range reported in the paper, against a Group-65 annual reference outlay of ~R\)345M (non-pharma) and ~R\(363M (pharma). The headline is meaningful because it is one product group of a single state's R\)13B procurement platform.

Confidence: yellow. The welfare arithmetic inherits the structural decomposition's restrictions (H:ipv-clock-admissible) and the \(\lambda=0.30\) benchmark (Ballard-Shoven-Whalley). Sensitivity to \(\lambda\) is reported in paper §5. The non-pharma reading is the load-bearing claim; pharma is boundary.

Follow-ups

• \(\lambda\) sweep: report welfare loss at \(\lambda \in \{0.10, 0.20, 0.30, 0.50\}\) as a sensitivity table.
• Distributional incidence of the set-aside redistribution: v7-jpube-tight/scripts/60_distributional_incidence.R shows the SME-side gain distribution; documenting it as a standalone AN would expose the within-SME concentration of the transfer.
• Comparison to literature welfare weights from corporate tax or SME subsidy programs (e.g., Hendren 2020 MVPF benchmarks): the implied weight of 2.42 is only meaningful relative to the planner's other revealed weights.