service-price-optimization

#area/zhaw/dps/theory

Service price optimization

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$c$ : Variable cost
$r$ : Price
$y (r) = a - b \cdot r$ : Linear demand function

Continuous demand function with one segment

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$r^{*}$ : Price optimum to maximize profit

r^{*} = \frac{a + b c}{2 b}

$Π (r^{*})$ : Maximum profit

Π (r^{*}) = \frac{(a - b c)^{2}}{4 b}

Continuous demand function with 2 segments

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$r_{1}^{*}, r_{2}^{*}$ : Price optimum per segment to maximize profit

r_{1}^{*} = \frac{2 a + b c}{3 b} r_{2}^{*} = \frac{a + 2 b c}{3 b}

$Π (r_{1}^{*}, r_{2}^{*})$ : Maximum profit

Π (r_{1}^{*}, r_{2}^{*}) = \frac{(a - b c)^{2}}{3 b}

Continuous demand function with individual segments

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$Π^{*}$ : Maximum profit

Π^{*} = \frac{(a - b c)^{2}}{2 b}

Segmentation

Mechanism to ensure that customers with a high willingness to pay are not included in the low-price segment

Time: Time between purchase and consumption, Time of consumption, Delivery period
Location: Country/City or consumption, place of consumption
Flexibility: Changes/Cancellations, place
Groups: Age, status, memberships
Variants: Upgrades, downgrades, versions