Monetizing Intelligence: Advertising and Subscription Design on LLM Platforms

1. Introduction

• The central design problem is balancing ad revenue that can fund service against advertising’s reduction of user value and the incentives to pay for higher tiers.The introduction motivates this trade-off with potential output interference, weakened trust, and privacy concerns.Source: §1 · pp. 1–2
• Advertising can fund useful service for consumers excluded under pure subscription, while weaker middle plans let the platform raise prices for unchanged ad-free service.Some fully advertised users gain utility, while users on partially advertised and ad-free plans lose relative to pure subscription.Source: §1 · p. 3
• A moderate advertising cap can maximize consumer surplus by improving lower-tier service while preserving some advertising revenue to finance quality.The identified outcome can outperform both unrestricted advertising and a complete ban.Source: §1 · p. 3
• Cheaper compute can raise service quality and reduce advertising intensity, yet sufficiently large efficiency gains can raise total advertising revenue above its initial level.Higher capability can increase the advertising value of users who continue to see ads, outweighing revenue lost when others see fewer ads.Source: §1 · p. 3
• Advertising-funded upgrades can first create a useful quality tier for low-valuation consumers, then bring all groups to the same quality ceiling and full ad exposure, causing tiers to merge.Otherwise identical plans cannot sustain different prices because consumers choose the cheaper one.Source: §1 · pp. 3–4
• The platform jointly chooses response quality, advertising intensity, and price because quality affects both user value and advertising returns, while ads reduce the value of service.These interactions connect provision at the bottom of the menu to prices and utility for users on other plans, including ad-free users.Source: §1 · p. 4

2. Literature Review

• Monopoly-screening and nonlinear-pricing work provides the framework, while two-sided platform and digital-goods studies examine participation, access, usage, and advertising exposure.The paper differs by jointly choosing costly service quality and advertising exposure for each plan, with quality affecting both subscription payments and advertising revenue.Source: §2 · p. 4
• Advertising-financed media research studies how advertising interacts with participation, content provision, and pricing, whereas this paper makes consumer-specific quality a central design choice.Allocating capability changes the service delivered, advertising returns, and the plan’s attractiveness to other users.Source: §2 · p. 5
• Existing AI-platform models study token budgets, service caps, ad auctions, ad placement, or ad timing, but do not combine consumer screening through quality, ad intensity, and price as this paper does.Related empirical and computational studies document commercial value in adjacent AI settings but do not directly identify how raising supplied quality changes advertising returns.Source: §2 · p. 5
• Closest related models separately examine ad-disutility menus, quality investment or quality-dependent nuisance, and endogenous consumption with fixed content quality.This paper brings both quality-linked advertising returns and advertising-related loss of user value into a single screening problem.Source: §2 · pp. 5–6
• The paper jointly chooses costly response quality, advertising intensity, and price because quality affects advertising returns and advertising reduces the value users obtain from quality.Improving one plan also changes its attractiveness as an alternative elsewhere in the menu, linking quality provision to information rents and prices, including on ad-free plans.Source: §2 · p. 6

3. Model

• A monopolistic LLM platform chooses each plan’s quality, advertising intensity, and price, with quality costly to produce and advertising both generating revenue and reducing effective quality.Consumers select their preferred plan or leave the platform.Source: §3 · p. 6

3.1. Consumers

• Consumers privately know their marginal valuation of effective quality, and advertising can make positive-quality service profitable for types excluded under pure subscription.The virtual-value threshold captures the screening cost that can outweigh subscription returns for lower types in the pure-subscription benchmark.Source: §3.1 · pp. 6–7

3.2. Platform’s Instruments

• Each menu plan specifies supplied quality, ad intensity, and a subscription price; quality may represent model choice, inference effort, or usage capacity.An example platform menu trades ad exposure against payment or fewer daily free messages.Source: §3.2 · p. 7

3.3. Quality Production

• Higher quality requires computational resources, and the model represents this with an increasing, strictly convex cost function and a technological quality ceiling.Convexity is motivated by model routing or additional reasoning effort; the ceiling is linked to efficient quality in an ad-free benchmark.Source: §3.3 · p. 8

3.4. Consumer Utility

• Consumers value effective quality after advertising-related degradation, and advertising weakly reduces the marginal value of supplied quality.The baseline uses one private type for both quality valuation and the loss from reduced effective quality, with no separate dimension of private ad aversion.Source: §3.4 · p. 9

3.5. Advertising Revenue

• Advertising revenue has diminishing marginal returns to ad intensity, while positive ad exposure earns more revenue when supplied quality is higher.The model treats the quality-driven advertising premium as an assumption motivated by platform practices, not as a directly established causal relationship.Source: §3.5 · pp. 9–10

3.6. Mechanism Design Problem

• The platform maximizes subscription and advertising revenue net of quality costs subject to incentive compatibility and individual rationality.It publicly commits to the menu, consumers privately know their types and choose a plan or the outside option, and the revelation principle gives a direct-mechanism representation.Source: §3.6 · p. 10

3.7. Main Specification

• The main specification uses uniformly distributed types and quadratic compute costs; advertising reduces effective quality proportionally, while revenue includes quality-linked and quality-independent components.Parameter restrictions preserve an endogenous ad-free premium tier, and lower compute-cost parameter values expand the quality ceiling.Source: §3.7 · pp. 11–12

4.1. Reduction to Virtual Surplus

• Incentive compatibility makes each type’s utility depend on effective quality available to lower types, reducing the platform’s problem to maximizing expected virtual surplus subject to monotonicity.Individual rationality and nonnegative payments imply U(0) = 0.Source: §4.1 · p. 12

4.2. Virtual Advertising Profit

• Virtual advertising profit combines ad revenue with the value lost through degraded service, offset by lower information rents when a plan is less attractive to higher types.For non-positive virtual values, rent savings weakly outweigh lost willingness to pay; for positive virtual values, willingness-to-pay losses dominate.Source: §4.2 · p. 13

4.3. Pointwise Optimization

• For types with non-positive virtual value, full advertising is optimal, and quality is positive when the quality-driven ad premium offsets the negative virtual value.Some consumers below the median therefore receive positive quality despite receiving zero quality under pure subscription; when λ = 0, no below-median type receives positive quality.Source: §4.3 · p. 14
• As type rises, the platform moves from full advertising toward reduced ad loads and ultimately removes ads for the highest types.For non-positive virtual types, baseline ad profitability can support full advertising even at zero quality; the quality-driven premium can separately make positive quality profitable.Source: §4.3 · pp. 14–15

4.4. Characterization of the Optimal Mechanism

• The optimal menu has up to four segments: zero-quality full-ad service, positive-quality full-ad service, partial-ad service, and ad-free service.The highest types receive pure-subscription monopoly quality, no advertising, and the menu’s highest subscription prices.Source: §4.4 · p. 15
• Relative to pure subscription, fully advertised positive-quality plans can raise quality, while middle plans provide less quality; allocations are implementable without ironing.The zero-quality, fully advertised limiting plan gives consumers zero utility while earning baseline advertising revenue.Source: §4.4 · p. 16

5.1. Quality Responses to Ad Degradation (δ)

• Greater δ expands positive-quality entry and raises supplied quality for positive-quality below-median fully advertised types.The quality increase requires λ > 0; with λ = 0, below-median users continue to receive zero quality.Source: §5.1 · pp. 17–18
• For medium types, greater δ raises quality under a light ad load, lowers it under a heavy load, and has no first-order effect at one-half.For types who remain fully advertised above the median, quality falls; for those remaining ad-free, quality is unchanged.Source: §5.1 · pp. 17–18

5.2. Divergent Pricing: Baseline Ad Profitability (¯r)

• Higher baseline ad profitability leaves low-type prices unchanged, lowers medium-type prices, and raises ad-free high-type prices despite unchanged quality.Deteriorated lower tiers reduce the information rent needed to retain ad-free users, permitting a higher price for the same allocation.Source: §5.2 · p. 19

5.3. Consumer Utility and Aggregate Welfare

• Some positive-quality low types gain, every medium type loses, and the ad-free top can face a higher price for unchanged service.When λ ≤ 1 − δ, all positive-quality low types in the stated interval gain; when λ > 1 − δ, only a subset gains and utility at θ1 is below the benchmark.Source: §5.3 · p. 21
• Utility polarization does not require strictly convex quality costs when costs are linear and the technological ceiling is independently fixed.In that case quality becomes a boundary choice, yet advertising and information-rent effects can still generate polarization.Source: §5.3 · p. 21
• Hybrid monetization raises social welfare throughout the regular region, even when aggregate consumer surplus falls.Consumer surplus depends on whether gains at the bottom exceed losses above; social welfare also includes advertising revenue and quality costs.Source: §5.3 · pp. 21–22
• The comparison assumes platform operation and does not establish consumer outcomes relative to platform exit.If fixed infrastructure costs make pure subscription unprofitable, its optimized menu may not be an attainable market alternative.Source: §5.3 · p. 22

6.1. Advertising Caps and Consumer Surplus (¯α)

• At (δ,λ, r̄) = (0.9, 0.5, 0.18), CS(0.78) ≈ 0.04898 > CS(0) ≈ 0.04167 > CS(1) ≈ 0.03155, so every maximizing cap is strictly interior at this instance.Caps can produce non-monotonic consumer surplus: preserving some ad-funded quality while limiting degradation can outperform both a ban and unrestricted advertising. Tighter caps can eventually weaken quality funding enough to reduce surplus.Source: §6.1 · pp. 23–25, Figure 4 · p. 23

6.2. Compute Efficiency, Service Quality, and Advertising (β)

• As compute costs fall, optimal quality weakly rises, advertising intensity weakly falls, every type’s utility and platform profit weakly increase, and the ad-free segment expands.Fully advertised users receive more capability without a change in ad load, while the partial-ad middle receives higher quality and fewer ads.Source: §6.2 · pp. 25–26
• Despite weakly lower ad intensity for every user, some β̂ ∈ (0,1) yields aggregate advertising revenue Rtotal(β̂) > Rtotal(1).Higher quality raises advertising value per remaining interaction; the fixed-mass, fully advertised low-type segment’s quality-linked revenue grows as β falls under the expanding ceiling.Source: §6.2 · p. 26

Appendix A.5 examines whether this gain survives diminishing advertising returns to quality.

• With diminishing advertising returns to quality, reducing β from 1 to 0.5 raises aggregate advertising revenue by about 3.6% while weakly reducing intensity for every type.The increase is not guaranteed for arbitrary concave premiums.Source: Appendix A.5 · pp. 26–27

7. An Extension: When Service Tiers Converge

• In the three-type extension, stronger advertising returns produce a 2–3–2–1 sequence of positive-quality tiers, ending in universal pooling when λ ≥ λU.When groups share the same quality and advertising exposure, they require the same price; universal pooling has all groups receiving (q*, α*) = (q̄, 1).Source: §7 · pp. 27–28

8. Conclusion

• A consumer-surplus gain from a cap does not necessarily raise social welfare, and the tier-convergence result concerns a monopolistic platform that commits to its menu.Other forms of differentiation may still support separate marketed plans.Source: §7 · p. 28, §8 · pp. 29–30

Appendix A: Model Extensions; A.1. Mixed Ad Degradation

• The extensions vary advertising-return and user-value specifications, and the mixed-degradation exercise adds quality-independent nuisance alongside quality-proportional ad degradation.The supplied passages describe these extensions’ scope but do not report their detailed comparative results.Source: Appendix A · p. 33, §A.1 · p. 33

A.1. Mixed Ad Degradation

• Under mixed ad degradation, the optimum has four segments when θm > 0; its lowest segment can use costly quality only to offset nuisance, leaving zero effective quality.When δn < εS, the boundary pool and adjacent positive-effective-quality segment remain fully ad-supported. Baseline comparative statics persist only locally for sufficiently small additive nuisance.Source: §A.1 · pp. 33–34

A.2. Correlated Ad Degradation: A Diagnostic

• The correlated-degradation diagnostic preserves baseline quality-distortion, ad-profitability, and utility-polarization results within each sensitivity state, but does not solve joint screening.Higher ad profitability lowers interior effective quality and preserves the rent-extraction force that raises prices for remaining ad-free users in each statewise benchmark.Source: §A.2 · p. 35

A.3. Positive Ad Utility

• With positive direct ad value, equilibrium thresholds, allocations, and consumer utilities match the baseline after replacing λ with λ + η.The matching value can be extracted through subscription payments without changing information rents; within-segment price responses to ad profitability also carry over.Source: §A.3 · p. 36

A.4. Type-Dependent Ad Monetization

• With type-dependent ad monetization, the baseline structure, non-monotonic quality distortion, and utility polarization persist under the restriction preserving an ad-free premium tier.Higher baseline ad profitability lowers interior effective quality and locally raises prices for remaining ad-free users, but no global sign is asserted for interior prices.Source: §A.4 · p. 36

A.5. Concave Quality-Driven Advertising Premium

• With a concave premium, the mechanism retains fully advertised low types, partially advertised middle types, and ad-free high types, with a zero-quality segment when the lower threshold is positive.Concavity changes the quality conditions and leaves thresholds implicit rather than closed form.Source: §A.5 · pp. 37–38
• As quality rises, the marginal premium h′(q) and average premium h(q)/q decline; the former governs quality provision and the latter helps determine whether service remains ad-supported.The comparison is within the same concave specification and does not order its advertising returns against the linear benchmark.Source: §A.5 · pp. 37–38
• Reducing β from 1 to 0.5 weakly reduces advertising intensity for every type while aggregate advertising revenue rises from 0.078968 to 0.081803.This bounded, strictly concave-premium example illustrates the revenue reversal but is not a result for arbitrary concavity.Source: §A.5 · p. 39

A.6. Reduced-Form Competition Diagnostic

• Under the reduced-form objective Π + κCS, the quality and local divergent-pricing mechanisms persist, while all full-ad low types gain only if λ ≤ (1−κ)(1−δ).Without that condition, an interval of low types gains while medium and high types lose relative to pure subscription at the same κ.Source: §A.6 · pp. 39–40

B.1. Discussion of Assumptions

• The analysis combines general structural results with closed-form comparative statics under a uniform-quadratic, multiplicative baseline; its conclusions are not established for purely additive nuisance.The paper presents the framework as a broader theory of ad-supported digital platforms, with LLM platforms as a leading application rather than an exclusive setting.Source: §B.1 · pp. 41–43
• Consumer screening maintains one private type that governs both quality valuation and ad sensitivity; independent or negatively correlated preferences remain outside the established results.The paper says a genuinely two-dimensional model remains open.Source: §B.1 · p. 41
• Full commitment licenses the screening reduction, while the welfare effect of imperfect commitment is left unresolved; the competition extension likewise excludes strategic interaction.Ex post ad expansion could deepen losses, but reputational discipline or weakened ad-free-tier credibility could instead lead the platform to concede rents.Source: §B.1 · p. 42
• The competition diagnostic models rent pass-through, not strategic platform interaction, and therefore does not establish competing platforms’ price levels or advertising policies.It preserves a conditional comparison: higher baseline ad profitability lowers prices for users remaining partially ad-supported and raises them for users remaining ad-free.Source: §B.1 · p. 42

B.2. Supplementary Exhibits

• Under market regularity, a low quality-driven advertising premium leaves a positive-measure lowest-type interval at zero quality, while a high premium eliminates that interval except at the boundary.The bounds also sustain an endogenous premium ad-free segment; Appendix C.1 considers parameters outside them.Source: §B.2 · p. 43
• The comparative-statics notes report that a higher advertising return lowers prices for users remaining partially advertised and raises prices for users remaining ad-free.Quality is unchanged at the median full-ad type and to first order at the interior half-ad-load cutoff.Source: §B.2 · p. 43, Table EC.2 · p. 43
• Strictly convex quality costs support smooth, type-dependent quality adjustments, but utility polarization can persist under linear costs with threshold-based quality choices.With linear costs, the platform chooses maximum feasible quality when marginal virtual benefit exceeds cost, and zero otherwise.Source: §B.2 · p. 44
• At the illustrated parameters, an interior cap raises effective quality for many low types relative to the unregulated menu, whereas a complete ban leaves the bottom without positive quality.For the ad-free top, effective quality matches under the cap and unregulated menu, but utility differs because lower plans change information rents.Source: §B.2 · p. 44, Figure EC.1 · p. 44
• At θM = 2/3 and δ = 0.8, the illustrated configuration lies on a knife-edge where type M reaches the full-ad corner as type L begins receiving positive quality.For θM above δ/[2(2δ −1)], type M instead has an interior ad load before reaching the full-ad corner; the number of positive-quality tiers is unchanged.Source: §B.2 · p. 45, Table EC.3 · p. 45

C.1. Equilibrium Structure under Extended Parameter Spaces

• Outside market regularity, stronger advertising returns can remove the positive-measure ad-free segment, and a sufficiently large quality-driven premium can push quality to its ceiling.When λ ≥ 2 − δ, all types receive maximum quality with full advertising; utility gains then depend on degradation, and high types can lose when δ > 3/4.Source: §C.1 · pp. 46–47

C.2. Advertising Caps and Social Welfare

• A marginal tightening from the unregulated benchmark can raise social welfare only under extreme ad-induced degradation and within an intermediate interval of the quality-driven premium.This is a local comparison: it does not establish that a larger tightening or the globally optimal cap raises welfare.Source: §C.2 · pp. 47–48

C.3. Equilibrium under Compute Efficiency

• The extension maintains θ ∼ U[0,1], g(q,α) = q(1 − δα), and the ceiling convention q̄ = 1/β, so the feasible quality ceiling expands as compute becomes more efficient.The cost function is c(q) = βq²/2, with β ∈ (0,1].Source: §C.3 · p. 48
• The compute-efficiency characterization preserves the baseline ordering of advertising regimes, leaves the first two thresholds unchanged, and makes the ad-free threshold depend on β.The threshold for positive quality does not depend on β.Source: §C.3 · pp. 48–49
• Lower compute costs raise positive quality; among users remaining partially advertised, the platform reduces ad intensity and the ad-free segment expands as its threshold falls.The zero-quality-segment condition is unchanged: it has positive measure if λ < 1 − δ, only θ = 0 at equality, and is empty if λ > 1 − δ.Source: §C.3 · p. 49

D.1. Proof of Lemma 1

• The proof strategy reduces the mechanism problem to virtual surplus and verifies implementability by showing effective quality is non-decreasing across types.The virtual value is v(θ) = θ − [1 − F(θ)]/f(θ), and the allocation must also satisfy the original bounds.Source: §D.1 · p. 51, §D.4 · pp. 52–53

D.3. Proof of Proposition 1

• For θ ≤ 1/2, the optimal ad load is full; positive quality can nevertheless reach some negative-virtual-value users because advertising returns rise with quality.With λ > 0, some users just below θ = 1/2 receive strictly positive quality.Source: §D.3 · p. 51

D.4. Proof of Theorem 1

• The optimal allocation uses thresholds separating zero-quality, full-ad, interior-ad, and ad-free regimes, with the ad-free threshold below 1 when baseline ad profitability is below δ − λ.The induced effective quality is non-decreasing, so the allocation is incentive compatible without ironing.Source: §D.4 · pp. 52–53

D.5. Proof of Proposition 2

• As degradation rises, the zero-quality threshold shifts left, upgrading types between the old and new cutoffs; full-ad quality rises below the median and falls above it.Within the interior-ad segment, quality falls under a heavy ad load, rises under a light load, and is locally unchanged at αint = 1/2; ad-free quality is unchanged.Source: §D.5 · p. 53

D.6. Proof of Proposition 3

• Fully advertised low types have locally unchanged prices because their quality and ad load do not depend on baseline advertising profitability.The comparison is local: it does not assert a universal price sign for finite changes that move a consumer across a threshold.Source: §D.6 · pp. 53–54
• Prices for users remaining in the partial-ad segment strictly decrease as baseline advertising profitability rises, because their effective quality declines.The result applies within the open interior segment.Source: §D.6 · p. 54
• Users remaining ad-free keep their allocation, but their information rent falls as medium-type effective quality declines, producing a strict price increase.Their own effective quality is unchanged; the rent effect comes from the rest of the menu.Source: §D.6 · pp. 53–54

D.7. Proof of Proposition 4

• Some fully advertised low types gain relative to pure subscription, but the advantage disappears by the partial-ad threshold and only a subset of positive-quality low types gains when λ > 1 − δ.Types receiving zero quality and type θ = 0 retain zero utility.Source: §D.7 · p. 55
• All medium types and high types strictly lose utility relative to pure subscription because medium-tier effective quality is lower and high types inherit that loss.The medium-type loss follows from ad-supported effective quality growing more slowly with type.Source: §D.7 · p. 55
• Hybrid monetization strictly raises aggregate social welfare relative to pure subscription throughout the regular parameter region.The proof compares the profit gain with the virtual-surplus difference at the bottom of the type support; subscription payments cancel in aggregate welfare.Source: §D.7 · p. 56
• Within the regular region, aggregate social welfare also strictly increases with the quality-driven advertising premium.This comparative static holds while the mechanism remains in that region.Source: §D.7 · p. 56

D.8. Proof of Proposition 5

• In the region described by the proof, marginal tightening reduces consumer surplus.The supplied passage does not state the region's full parameter condition.Source: §D.8 · p. 57
• When the stated condition holds, marginally tightening the unregulated cap raises consumer surplus, so the cap of 1 cannot maximize it.Only positive-quality fully advertised types contribute to this first-order effect.Source: §D.8 · pp. 56–57
• CS(0.78) ≈ 0.04898 exceeds CS(0) ≈ 0.04167 and CS(1) ≈ 0.03155, so an interior cap strictly beats both endpoints in this instance.Because a consumer-surplus maximizer exists, every maximizer here is interior; the strict comparisons extend to a neighborhood of the instance.Source: §D.8 · p. 57

D.9. Proof of Corollary EC.2

• For λ ≤ 1 − δ, marginal tightening reduces welfare throughout the positive-quality, fully advertised branch.The proof includes the boundary case λ = 1 − δ.Source: §D.9 · p. 58
• For λ > 1 − δ, marginal tightening raises welfare exactly under the parameter condition stated in the proof.This condition applies when all fully advertised types receive positive quality.Source: §D.9 · p. 58
• The local welfare-improvement possibility is confined to extreme degradation, and a boundary gain alone does not establish a globally optimal cap.The proof places the threshold near δ ≈ 0.957 and notes that comparison with the total-ad-ban endpoint is still needed.Source: §D.9 · p. 58

D.10. Proof of Theorem EC.4

• Under the generalized cost function, zero-quality types receive full advertising; positive-quality types move from full ads to interior ads and then ad-free service as type rises.The full-ad branch ends at θ1, while the ad-free branch begins at θ2,β; the interior solution joins both continuously.Source: §D.10 · pp. 58–59

D.11. Proof of Proposition 6

• As β decreases, quality weakly increases and advertising intensity weakly decreases across user types.For medium types, quality strictly rises and ad intensity strictly falls; high-type quality also strictly rises while remaining ad-free.Source: §D.11 · p. 59
• Consumer utility weakly increases as β falls because quality raises value and advertising intensity lowers it.The proof also establishes that maximized platform profit weakly increases, since a mechanism feasible at higher β remains feasible at lower β.Source: §D.11 · pp. 59–60
• The ad-free premium segment expands as β falls, because the cutoff θ2,β shifts left.The cutoff is increasing in β, and the interior and ad-free branches meet continuously at that threshold.Source: §D.11 · pp. 59–60

D.12. Proof of Proposition 7

• Lower β weakly reduces advertising intensity for every user, including users who switch from the medium segment into the ad-free segment.The medium-type intensity falls, while the ad-free threshold shifts left as β decreases.Source: §D.12 · p. 60
• On a positive-measure low-type segment, advertising remains fully loaded while quality rises as β falls, increasing the λqα component of advertising revenue.These types remain below the technological quality ceiling, and their per-type advertising revenue includes λϕ(θ)/β.Source: §D.12 · p. 60
• Sufficiently lower β can raise aggregate advertising revenue above its initial level despite reducing ad intensity.The proof establishes this as an existence result using the positive-mass fully advertised segment.Source: §D.12 · p. 60

D.13. Proof of Proposition 8

• The allocation structure yields 2-3-2-1 tiers as λ rises, with middle and high types pooling before all types pool.Middle and high types share the same quality, advertising, and price in the two-tier range; at λU all types pool.Source: §D.13 · pp. 62–63

D.14. Proof of Theorem EC.1

• When δ_n < ε_H, advertising thresholds are ordered and interior allocations are unique; effective quality is nondecreasing, so no ironing is required.The proof also shows that the zero-effective-quality boundary is optimized at full advertising under δ_n < ε_S ≤ ε_B.Source: §D.14 · pp. 63–64

D.15. Proof of Proposition EC.1

• For sufficiently small δn, on compact subsets away from thresholds, medium-type prices decrease and ad-free prices increase with r̄; some low types gain and some high types lose relative to pure subscription.Source: §D.15 · p. 65

D.16. Diagnostic Calculations for Correlated Ad Degradation

• In both degradation states, full-ad quality rises for θ < 1/2 and falls for θ > 1/2, while the cutoff shifts leftward.These are state-contingent diagnostics that hold the virtual type fixed and omit cross-state incentive constraints.Source: §D.16 · p. 65
• In both correlated-degradation states, lower interior effective quality preserves premium price increases, while low types gain and premium types lose.The high-degradation state becomes more likely as user type rises, reinforcing the relevance of ad-induced distortion for high-valuation users.Source: §D.16 · p. 66

D.17. Proof of Proposition EC.2

• When ad value shifts the effective parameter to λ+η, higher ad profitability lowers partial-ad prices, leaves full-ad prices unchanged, and raises prices for locally ad-free users.These price responses hold in the effective regular region.Source: §D.17 · p. 66

D.18. Proof of Proposition EC.3

• With type-dependent ad degradation, low types gain while medium and high types lose, preserving utility polarization.Low types with positive effective quality gain; high types remain ad-free but inherit the utility loss accumulated across the interior segment.Source: §D.18 · p. 67

D.19. Proof of Theorem EC.2

• With concave ad-funded upgrades, the optimal menu retains zero-quality full-ad, interior-ad, and ad-free segments, with allocations implementable through monotone effective quality.The proof establishes global optimality across segments and constructs incentive-compatible transfers.Source: §D.19 · pp. 68–69

D.20. Proof of Proposition EC.4

• For sufficiently small a, baseline quality responses, divergent medium- and high-type price effects, and utility polarization persist away from thresholds and sign-switching loci.High types remain ad-free, so their quality is unaffected by δ.Source: §D.20 · pp. 69–70

D.21. Proof of Corollary EC.1

• For small a, the corollary’s proof combines allocation convergence with bounds keeping both convergence errors below ε in its revenue comparison.The supplied passage does not expose the complete revenue expression or comparison.Source: §D.21 · p. 70

D.22. Proof of Theorem EC.3

• With type-dependent preferences, the model replaces 2θ−1 with vκ(θ), and the final virtual cutoff remains below one for every κ∈[0,1].The cutoff ordering follows when r̄<δ−λ.Source: §D.22 · p. 70

• As δ rises, the lower threshold is weakly decreasing; where its underlying cutoff is positive, its derivative is negative.Source: §D.23 · p. 70
• Interior quality falls under heavy ad loads and rises under light loads, while ad-free quality is unaffected.Source: §D.23 · p. 70
• For a locally ad-free user, allocations stay fixed but the user receives less information rent from below, so price rises; no sign is asserted for finite threshold crossings.Source: §D.23 · p. 71
• All full-ad low types gain exactly when the boundary utility gap is zero, which holds when a zero-quality segment exists, λ ≤ (1−κ)(1−δ).Source: §D.23 · p. 71