Comprehensive Study Notes: Pricing Strategies and Price Optimization

Strategic Pricing Approaches

  • Cost-Plus Pricing:

    • Methodology: Calculates total production costs—comprising variable costs, fixed overhead, and a required return on capital—and applies an administrative percentage mark-up.
    • Departmental Ownership: Typically managed and enforced by the finance department.
    • Strategic Orientation: Focuses exclusively on internal accounting costs while ignoring market competition and customer willingness to pay.

  • Market-Based Pricing:

    • Methodology: Establishes product prices based exclusively on the prevailing prices set by direct competitors.
    • Departmental Ownership: Favored and executed by the sales department.
    • Strategic Orientation: Functions as an operational necessity for smaller market participants lacking market power and serves as an effective mechanism for entering established markets, though it disregards internal cost structures and individual customer value perceptions.

  • Value-Based Pricing:

    • Methodology: Sets prices based on the perceived value that the offering provides to each target customer segment, aiming to configure customized pricing for distinct buyers.
    • Departmental Ownership: Spearheaded and championed by the marketing department.
    • Strategic Orientation: Prioritizes customer value perceptions and utility above internal costs and immediate competitor benchmark prices.

  • Comparative Assessment of Pricing Paradigms:

    • Value-Based Strategy: Grounded in customer valuation; disregards internal production costs and competitor pricing; driven by marketing objectives.
    • Market-Based Strategy: Grounded in competitive market dynamics; disregards internal cost structures and specific customer perceptions; driven by sales objectives.
    • Cost-Plus Strategy: Grounded in internal cost metrics; disregards competitive moves and customer willingness to pay; driven by financial control objectives.

The Value-Price-Cost Framework and Taxonomy of Value

  • The Fundamental Value Hierarchy:
    • V=Value to Customer (Exchange or Economic Value)V = \text{Value to Customer (Exchange or Economic Value)}: The total economic ceiling a buyer places on a product.
    • P=Price (Reference Value)P = \text{Price (Reference Value)}: The monetary amount demanded by the seller.
    • C=Costs of ProductionC = \text{Costs of Production}: The aggregate fixed and variable expenses incurred to produce the product or deliver the service.
    • V−P=Consumer Surplus (Differentiation Value)V - P = \text{Consumer Surplus (Differentiation Value)}: The net economic benefit retained by the customer beyond the purchase price, consisting of monetary and psychological components.
    • P−C=Profit Margin (Contribution Margin)P - C = \text{Profit Margin (Contribution Margin)}: The producer surplus retained by the seller per transaction.

Diagram of the Value, Price, and Cost relationship showing Consumer Surplus and Profit Margin

  • Taxonomy of Customer Values (Nagel, Logan, & Zale, 2011):
    • Use Value: The holistic utility and qualitative satisfaction experienced by the consumer through the consumption of a product or service.
    • Exchange (Economic) Value: The absolute maximum willingness to pay (WTP\text{WTP}) exhibited by a customer, formally defined as:         Exchange Value=Reference Value+Differentiation Value\text{Exchange Value} = \text{Reference Value} + \text{Differentiation Value}
    • Reference Value: The pricing baseline set by the customer's best available alternative product among competing market offerings.
    • Differentiation Value: The quantitative worth of attributes that distinguish the offering from competitive alternatives, representing the net benefits delivered above the competitive reference price.
    • Monetary Value: The tangible cost reductions, financial savings, or income enhancements that directly accrue to the customer as a consequence of using the offering.
    • Psychological Value: The innate emotional, status-driven, or subjective fulfillment realized by the customer through product possession or engagement.

Value-Based Segmentation and Rate Fencing

  • Implementation Steps for Value-Based Segmentation (Nagel, Logan, & Zale, 2011):

    • Determine foundational segmentation criteria by differentiating buyer purchase behaviors and perceived benefits.
    • Identify discriminating value drivers that serve as primary purchase motivators.
    • Evaluate operational constraints and strategic advantages, including cost profiles, operational efficiency, and internal resource limits.
    • Define primary and secondary customer segments based on differentiation criteria.
    • Formulate comprehensive segment profiles containing specific operational needs, demographic data, and behavioral attributes.
    • Construct targeted pricing metrics and enforceable rate fences for each distinct segment.

  • Operational Typology of Rate Fences:

    • Definition: Structural barriers configured to permit consumers to self-segment into distinct market tiers based on their willingness to pay, consumption behaviors, and operational needs.
    • Physical Rate Fences: Differentiations tied directly to tangible characteristics, including geographic location, room view, and physical amenities.
    • Product-Line Rate Fences: Price divisions linked to categorical product tiers, such as deluxe and top-of-the-line classifications versus standard economy classifications.
    • Controlled-Availability Rate Fences: Restrictions based on qualification criteria, including coupon possession, guest or property geographic location, and specific distribution channels.
    • Buyer-Characteristic Rate Fences: Tiered pricing designated for specific consumer categories, including senior citizens, children, and recognized institutional group affiliations.

  • Pricing Menu Architecture and Fencing Rules:

    • Single Unified Rate: Setting a uniform price across all inventory units (e.g., identical pricing for every hotel room).
    • Tiered Rates by Product Type: Structuring distinct prices strictly according to unit specifications and product grades.
    • Fenced Discount Rates: Offering reduced tariffs contingent upon customer adherence to specific operational hurdles.
    • Advance Reservation Rules: Requiring bookings to be finalized within fixed advance purchase horizons, typically 33, 77, 1414, 2121, or 30 days30\,\text{days} prior to arrival.
    • Refundability Conditions: Establishing graduated terms ranging from non-refundable rates to percentage-based refunds, fixed monetary cancellations, or unconditional 100% refunds.
    • Modification Provisions: Enforcing varying change limits, ranging from zero change allowances, date-shifting allowances preserving the original room-night duration, unlimited modifications without refund, to fully flexible change policies.
    • Duration and Timing Criterias: Mandating specific stay patterns, including weekday versus weekend utilization and minimum Length of Stay (LOS\text{LOS}) thresholds.

  • Systemic Limits to Price Differentiation:

    • Imperfect Segmentation: The operational impossibility of isolating the exact willingness to pay for every individual buyer, necessitating the construction of segments calibrated such that the average willingness to pay diverges between groups.
    • Cannibalization: The risk where high-willingness-to-pay buyers circumvent pricing barriers to access discounts intended exclusively for price-sensitive tiers.
    • Arbitrage: The commercial vulnerability where secondary intermediaries purchase inventory at discounted price points and resell to high-willingness-to-pay consumers below prevailing market prices, capturing the margin.

The Price-Response Function and Market Sensitivity

  • Definition of the Price-Response Function:

    • Represents the specific demand curve facing an individual enterprise rather than the aggregate macroeconomic demand of the entire market sector.

  • Mathematical Characteristics of a Standard Price-Response Function:

    • Non-negativity: Price is bounded such that p≥0p \ge 0.
    • Continuity: Demand d(p)d(p) forms an unbroken, differentiable function across every defined price point pp.
    • Monotonically Downward Sloping: Quantity demanded is inversely related to price (dd(p)dp<0\frac{dd(p)}{dp} < 0), meaning that a lower price generates higher demand.

  • Theoretical and Practical Exceptions to Downward-Sloping Demand:

    • Giffen Goods: Conceptualized by Scottish economist Sir Robert Giffen, identifying inferior baseline subsistence goods where an increase in price induces an increase in quantity demanded due to overwhelming income effects.
    • Price as a Quality Proxy: Scenarios where consumers lack complete information and use higher prices as an indicator of superior product craftsmanship, reliability, or safety.
    • Veblen Goods and Conspicuous Consumption: Formulated by American economist Thorstein Veblen, describing prestige and luxury goods where higher prices enhance social status, exclusivity, and subjective appeal, increasing demand.

  • Market Contexts:

    • Perfect Competition: An individual firm acts as a pure price taker, confronting a horizontal demand schedule at the prevailing market price; any price charged above market causes demand to fall to zero.
    • Typical Differentiated Market: An individual firm possesses pricing power and faces a downward-sloping demand curve, where incremental price variations systematically alter demand.

  • Measuring Price Sensitivity: Slope of the Price-Response Function:

    • Mathematical Formulation:         Slope=ΔDΔP=D2−D1P2−P1\text{Slope} = \frac{\Delta D}{\Delta P} = \frac{D_2 - D_1}{P_2 - P_1}
    • Economic Meaning: Expresses the absolute marginal change in quantity demanded resulting from a one-unit change in currency price.
    • Worked Sensitivity Example:
      • Baseline price P1=$52P_1 = \$52 generates demand D1=10,000 unitsD_1 = 10{,}000\,\text{units}.
      • Adjusted price P2=$53P_2 = \$53 generates demand D2=9,800 unitsD_2 = 9{,}800\,\text{units}.
      • Calculation:             Slope=9,800−10,000$53−$52=−2001=−200 units / $\text{Slope} = \frac{9{,}800 - 10{,}000}{\$53 - \$52} = \frac{-200}{1} = -200\,\text{units / \$}
    • Application Example: Small Group Hospitality Reservations:
      • Historical baseline: Price P1=£89P_1 = £89 yields group demand D1=240 roomsD_1 = 240\,\text{rooms}.
      • Price increase: Price P2=£94P_2 = £94 causes demand to decline to D2=200 roomsD_2 = 200\,\text{rooms}.
      • Calculation:             Slope=200−24094−89=−405=−8 rooms / £\text{Slope} = \frac{200 - 240}{94 - 89} = \frac{-40}{5} = -8\,\text{rooms / £}

Price Elasticity of Demand

  • Formulation and Calculation of Arc Elasticity:

    • Mathematical Definition:         Ed=−Demand at New Price−Demand at Current PriceDemand at Current PriceNew Price−Current PriceCurrent Price=−ΔD/D1ΔP/P1E_d = -\frac{\frac{\text{Demand at New Price} - \text{Demand at Current Price}}{\text{Demand at Current Price}}}{\frac{\text{New Price} - \text{Current Price}}{\text{Current Price}}} = -\frac{\Delta D / D_1}{\Delta P / P_1}
    • Worked Calculation:
      • For P1=$52P_1 = \$52 with D1=10,000 unitsD_1 = 10{,}000\,\text{units}, and P2=$53P_2 = \$53 with D2=9,800 unitsD_2 = 9{,}800\,\text{units}:             Ed=−9,800−10,00010,00053−5252=−−0.02152=−−0.020.01923≈1.04E_d = -\frac{\frac{9{,}800 - 10{,}000}{10{,}000}}{\frac{53 - 52}{52}} = -\frac{-0.02}{\frac{1}{52}} = -\frac{-0.02}{0.01923} \approx 1.04

  • Core Properties of Price Elasticity:

    • Localized Validity: Similar to the linear slope, arc elasticity is strictly valid for marginal price shifts around the current price point.
    • Dimensionless Metric: Unlike slope, elasticity is unit-free, enabling direct comparisons across currencies (\, €€, CHF\text{CHF}) and physical units (kg\text{kg}, tons\text{tons}, rooms\text{rooms}).
    • Temporal Adjustment: Differentiates short-term elasticity from long-term elasticity, reflecting how consumer substitution, contractual commitments, and behavioral habits adapt over time.

  • Ski Resort Lift Pass Application:

    • Current State: Average sales D1=140 passes / dayD_1 = 140\,\text{passes / day} at ticket price P1=CHF 65/dayP_1 = \text{CHF}\,65 / \text{day}.
    • Estimated Parameter: Elasticity Ed=1.25E_d = 1.25.
    • Proposed Strategy: Reduce ticket price by 15.4%15.4\% down to P2=CHF 55/dayP_2 = \text{CHF}\,55 / \text{day}.
    • Anticipated Demand Shift:         ΔD%=Ed×∣ΔP%∣=1.25×15.4%=19.25%\Delta D\% = E_d \times |\Delta P\%| = 1.25 \times 15.4\% = 19.25\%ΔD=140×0.1925=26.95≈27 passes / day\Delta D = 140 \times 0.1925 = 26.95 \approx 27\,\text{passes / day}
    • New Sales Volume:         D2=140+27=167 passes / dayD_2 = 140 + 27 = 167\,\text{passes / day}

  • Lulu Hotel Comprehensive Elasticity Analysis:

    • Initial Data: At P1=$120P_1 = \$120, demand D1=310 roomsD_1 = 310\,\text{rooms}; at P2=$150P_2 = \$150, demand D2=250 roomsD_2 = 250\,\text{rooms}.
    • Slope of the Response Function:         Slope=250−310150−120=−6030=−2 rooms / $\text{Slope} = \frac{250 - 310}{150 - 120} = \frac{-60}{30} = -2\,\text{rooms / \$}
    • Point Elasticity from Baseline:         Ed=−250−310310150−120120=−−6031030120=−−0.193550.25≈0.774E_d = -\frac{\frac{250 - 310}{310}}{\frac{150 - 120}{120}} = -\frac{-\frac{60}{310}}{\frac{30}{120}} = -\frac{-0.19355}{0.25} \approx 0.774
    • Elasticity Interpretation: Demand is price-inelastic (Ed<1.0E_d < 1.0), meaning that percentage changes in price result in proportionally smaller percentage changes in quantity demanded.
    • Demand Adjustment from Price Reduction ($140\$140 to $125\$125):
      • Price change: ΔP=125−140=−$15\Delta P = 125 - 140 = -\$15.
      • Using the constant slope m=−2 rooms / $m = -2\,\text{rooms / \$}:             ΔD=Slope×ΔP=−2×(−15)=+30 rooms\Delta D = \text{Slope} \times \Delta P = -2 \times (-15) = +30\,\text{rooms}
    • Demand Adjustment from Price Increase ($120\$120 by 10%10\% to $132\$132):
      • Price change: ΔP=132−120=+$12\Delta P = 132 - 120 = +\$12.
      • Using constant slope: ΔD=−2×12=−24 rooms\Delta D = -2 \times 12 = -24\,\text{rooms}.
      • Alternatively, applying arc elasticity: ΔD%=−0.774×10%=−7.74%\Delta D\% = -0.774 \times 10\% = -7.74\%, yielding ΔD=−0.0774×310≈−24 rooms\Delta D = -0.0774 \times 310 \approx -24\,\text{rooms}.

Mathematical Modeling of Price-Response Functions

  • Linear Price-Response Model:

    • Equation:         d(p)=D−mpd(p) = D - mp
    • Parameters:
      • DD: Maximum possible demand / total market capacity when price is zero (d(0)=Dd(0) = D).
      • PP: Satiating price / reservation cutoff where demand drops to zero (d(P)=0d(P) = 0).
      • mm: Price sensitivity parameter (m>0m > 0), representing the constant slope magnitude m=DPm = \frac{D}{P}.
      • pp: Actual price charged.
      • d(p)d(p): Actual quantity demanded at price pp.
    • Behavioral Assumption: The price-response function is strictly linear when the willingness to pay (WTP\text{WTP}) of the target market is uniformly distributed, meaning equal shifts in price yield identical shifts in demand.

  • Linear Modeling Calibration Example:

    • Input Data: Maximum single-room market capacity D=4,000 roomsD = 4{,}000\,\text{rooms}, satiating price P=€550P = €550.
    • Sensitivity Coefficient Calculation:         d(P)=0  ⟺  D−mP=0  ⟺  m=DP=4,000550≈7.27 rooms / €d(P) = 0 \iff D - mP = 0 \iff m = \frac{D}{P} = \frac{4{,}000}{550} \approx 7.27\,\text{rooms / €}
    • Calibrated Function:         d(p)=4,000−7.27pd(p) = 4{,}000 - 7.27p
    • Expected Demand at p=€400p = €400:         d(400)=4,000−(7.27×400)=4,000−2,908=1,092 roomsd(400) = 4{,}000 - (7.27 \times 400) = 4{,}000 - 2{,}908 = 1{,}092\,\text{rooms}

  • Point Price Elasticity Formulations:

    • General Calculus-Based Formulation:         Ed=−d′(p)⋅pd(p)E_d = -\frac{d'(p) \cdot p}{d(p)}         where d′(p)d'(p) represents the first derivative of the demand function with respect to price.
    • Linear Price-Response Point Elasticity:
      • Given d′(p)=−md'(p) = -m and d(p)=D−mpd(p) = D - mp:             Ed=−(−m)⋅pD−mp=mpD−mpE_d = -\frac{(-m) \cdot p}{D - mp} = \frac{mp}{D - mp}
    • Point Elasticity Evaluation at p=€400p = €400:         Ed=7.27×4004,000−(7.27×400)=2,9081,092≈2.66E_d = \frac{7.27 \times 400}{4{,}000 - (7.27 \times 400)} = \frac{2{,}908}{1{,}092} \approx 2.66

  • Logit Price-Response Model:

    • Behavioral Foundations: Models market environments where consumer willingness to pay follows a normal distribution rather than a uniform distribution.
    • Curve Geometry: Exhibits a sigmoidal S-shape, showing lower price sensitivity at extremely low and high prices, with peak sensitivity across middle-tier price ranges.

Logit Price-Response function displaying a sigmoidal S-curve shape

Single-Product Price Optimization

  • Mathematical Objective Formulation:

    • Maximize total contribution margin m(p)m(p):         max⁡pm(p)=(p−c)⋅d(p)\max_{p} m(p) = (p - c) \cdot d(p)         where pp represents unit price, cc denotes incremental marginal cost per unit, and d(p)d(p) represents quantity demanded.

  • Rule I: First-Order Optimality Condition:

    • Differentiate the contribution function with respect to price and set equal to zero:         m′(p)=ddp[(p−c)⋅d(p)]=0m'(p) = \frac{d}{dp}\left[(p - c) \cdot d(p)\right] = 0m′(p)=d′(p)(p−c)+d(p)=0m'(p) = d'(p)(p - c) + d(p) = 0
    • Optimality condition:         d(p∗)=−d′(p∗)(p∗−c)d(p^*) = -d'(p^*)(p^* - c)

Total contribution curve plotted against price showing maximum contribution at optimal price p*

  • Closed-Form Solution for Linear Demand:

    • Substitute d(p)=D−mpd(p) = D - mp and d′(p)=−md'(p) = -m:         D−mp∗=−(−m)(p∗−c)=m(p∗−c)D - mp^* = -(-m)(p^* - c) = m(p^* - c)D−mp∗=mp∗−mcD - mp^* = mp^* - mc2mp∗=D+mc2mp^* = D + mcp∗=D+mc2mp^* = \frac{D + mc}{2m}
    • Given that Dm=P\frac{D}{m} = P (satiating price), the equation simplifies to:         p∗=P+c2p^* = \frac{P + c}{2}
    • Core Economic Implication: When willingness to pay is distributed uniformly, the contribution-maximizing optimal price is the exact midpoint between the unit incremental cost cc and the satiating price PP.

  • Rule II: Elasticity Optimality Condition:

    • Rearrange the first-order condition d′(p)(p−c)+d(p)=0d'(p)(p - c) + d(p) = 0:         −d′(p∗)(p∗−c)=d(p∗)-d'(p^*)(p^* - c) = d(p^*)−d′(p∗)⋅p∗d(p∗)=p∗p∗−c-\frac{d'(p^*) \cdot p^*}{d(p^*)} = \frac{p^*}{p^* - c}
    • The left side defines point price elasticity EdE_d, while the right side equals the reciprocal of the contribution margin ratio:         CM Ratio=p∗−cp∗  ⟹  1CM Ratio=p∗p∗−c\text{CM Ratio} = \frac{p^* - c}{p^*} \implies \frac{1}{\text{CM Ratio}} = \frac{p^*}{p^* - c}
    • Rule: At the optimal price point p∗p^*, the price elasticity of demand equals the reciprocal of the contribution margin ratio:         Ed=p∗p∗−c=1CM RatioE_d = \frac{p^*}{p^* - c} = \frac{1}{\text{CM Ratio}}

  • Single-Product Hotel Optimization Application:

    • Operational Parameters: Maximum potential market D=28,100 guestsD = 28{,}100\,\text{guests}, satiating price P=$750P = \$750, incremental unit cost c=$50/guestc = \$50 / \text{guest}, uniform willingness to pay.
    • Determination of the Price-Response Function:         m=DP=28,100750≈37.4667 guests / $m = \frac{D}{P} = \frac{28{,}100}{750} \approx 37.4667\,\text{guests / \$}d(p)=28,100−37.47pd(p) = 28{,}100 - 37.47p
    • Optimal Room Price Calculation:         p∗=P+c2=750+502=8002=$400p^* = \frac{P + c}{2} = \frac{750 + 50}{2} = \frac{800}{2} = \$400         (Alternatively: p∗=28,100+(37.4667×50)2×37.4667=28,100+1,873.3374.9333=$400p^* = \frac{28{,}100 + (37.4667 \times 50)}{2 \times 37.4667} = \frac{28{,}100 + 1{,}873.33}{74.9333} = \$400)
    • Annual Demand, Revenue, and Contribution at p∗=$400p^* = \$400:
      • Expected demand:             d(400)=28,100−(37.4667×400)=28,100−14,986.67=13,113.33 guestsd(400) = 28{,}100 - (37.4667 \times 400) = 28{,}100 - 14{,}986.67 = 13{,}113.33\,\text{guests}
      • Expected annual revenue:             R = p^* \times d(p^*) = \400 \times 13{,}113.33 = \5,245,333.335{,}245{,}333.33
      • Expected total annual contribution:             \text{CM} = (p^* - c) \times d(p^*) = (\$400 - \$50) \times 13{,}113.33 = \350 \times 13{,}113.33 = \4,589,666.674{,}589{,}666.67

Multi-Segment Price Differentiation Dynamics

  • Economic Mechanics of Price Differentiation:
    • Price differentiation replaces a uniform single price with segmented prices designed to extract consumer surplus and serve price-sensitive buyers below the unsegmented price.
    • Revenue generated per segment: Ri=di×piR_i = d_i \times p_i.
    • Contribution margin generated per segment: CMi=di×(pi−ci)\text{CM}_i = d_i \times (p_i - c_i).

Price differentiation graph showing revenue and profit areas under linear demand

  • Resort Case Study: Unsegmented Baseline:

    • Market Parameters: Linear demand function d(p)=23,500−6.71pd(p) = 23{,}500 - 6.71p, incremental cost c=$700c = \$700 per holiday package.
    • Satiating Price Calculation:         P=23,5006.71≈$3,502.24P = \frac{23{,}500}{6.71} \approx \$3{,}502.24
    • Single-Price Optimal Strategy:         p^* = \frac{P + c}{2} = \frac{3{,}502.24 + 700}{2} = \frac{4{,}202.24}{2} = \2{,}101.12 \approx \2,1002{,}100
    • Baseline Performance Metrics:
      • Unsegmented demand:             d(2,100)=23,500−(6.71×2,100)=23,500−14,091=9,409 holidaysd(2{,}100) = 23{,}500 - (6.71 \times 2{,}100) = 23{,}500 - 14{,}091 = 9{,}409\,\text{holidays}
      • Baseline contribution:             \text{CM} = (\$2{,}100 - \$700) \times 9{,}409 = \1{,}400 \times 9{,}409 = \13,172,60013{,}172{,}600
    • Uncaptured Market Opportunity: Market research identifies potential tourists willing to pay more than $700\$700 but less than the unsegmented price of $2,100\$2{,}100.

  • Two-Segment Optimization via Rate Fencing:

    • Structural Fence Criteria: The resort defines two distinct segments based on willingness to pay, separated by a fence threshold at WTP=$1,500\text{WTP} = \$1{,}500.
    • Segment 1 Analysis (High WTP: WTP≥$1,500\text{WTP} \ge \$1{,}500):
      • Demand function: d(p1)=23,500−6.71p1d(p_1) = 23{,}500 - 6.71p_1.
      • Valid for p1≥$1,500p_1 \ge \$1{,}500, bounding maximum segment demand at:             d(1,500)=23,500−(6.71×1,500)=23,500−10,065=13,435 holidaysd(1{,}500) = 23{,}500 - (6.71 \times 1{,}500) = 23{,}500 - 10{,}065 = 13{,}435\,\text{holidays}
      • Optimal pricing for Segment 1 remains at p1∗=$2,100p_1^* = \$2{,}100.
      • Segment 1 sales volume: 9,409 holidays9{,}409\,\text{holidays}.
      • Segment 1 total contribution: $13,172,600\$13{,}172{,}600.
    • Segment 2 Analysis (Moderate WTP: \700 \le \text{WTP} < \1,5001{,}500):
      • Demand function: d(p2)=10,065−6.71p2d(p_2) = 10{,}065 - 6.71p_2 (reflecting demand between $700\$700 and $1,500\$1{,}500, where 6.71×1,500=10,0656.71 \times 1{,}500 = 10{,}065).
      • Segment 2 satiating reservation price: P2=$1,500P_2 = \$1{,}500.
      • Segment 2 optimal price:             p2∗=P2+c2=1,500+7002=2,2002=$1,100p_2^* = \frac{P_2 + c}{2} = \frac{1{,}500 + 700}{2} = \frac{2{,}200}{2} = \$1{,}100
      • Segment 2 sales volume:             d(1,100)=10,065−(6.71×1,100)=10,065−7,381=2,684 holidaysd(1{,}100) = 10{,}065 - (6.71 \times 1{,}100) = 10{,}065 - 7{,}381 = 2{,}684\,\text{holidays}
      • Segment 2 incremental contribution:             \text{CM}_2 = (p_2^* - c) \times d(p_2^*) = (\$1{,}100 - \$700) \times 2{,}684 = \400 \times 2{,}684 = \1,073,6001{,}073{,}600

Segment 2 linear demand curve with intercept at 10,065 and price cutoff at 1,500

  • Consolidated Profit Impact of Price Differentiation:
    • Total differentiated contribution:         CMtotal=CM1+CM2=$13,172,600+$1,073,600=$14,246,200\text{CM}_{\text{total}} = \text{CM}_1 + \text{CM}_2 = \$13{,}172{,}600 + \$1{,}073{,}600 = \$14{,}246{,}200
    • Net incremental financial gain: Implementing rate fences to serve the second market segment captures an additional $1,073,600\$1{,}073{,}600 in contribution profit compared to the unsegmented single-price strategy.