Slides10_Dynamic_Pricing

Slides10_Dynamic_Pricing - The Information Economy Dynamic...

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The Information Economy Dynamic Prices 1
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Peak Load Pricing 2 Suppose a firm has zero marginal cost, with capacity K Broadband capacity, cell phone towers, number of tickets Capacity costs z per unit to build. There are two periods (or two equally likely states) Period L demand is low, p L (q) Period H demand is high, p H (q) Firm chooses q L , q H and K to maximize profits = q L p L (q L ) + q H p H (q H ) zK subject to q L ,q H ≤ K Lagrangian: choose q L , q H and K to maximize L = q L p L (q L ) + q H p H (q H ) zK + L [K-q L ] + H [K-q H ]
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Peak Load Pricing 3 Solution FOCs for q L ,q H and K: MR L (q L *)= L , MR H (q H *)= H , z = L + H Optimal capacity: K*=q H * Idea: Charge capacity when constraint binds. Two cases: 1. Constraint slack in period L (big difference in demands) 2. Constraint binds in period L (small difference in demands) Price in H higher for two reasons (a) The demand is higher, (b) Charging more of the capacity Examples: cheap evening calls and Christmas flights
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1. Constraint Slack in Period L (q L *<q H *) 4 Optimal quantities: MR L (q L *)=0, MR H (q H *)= z
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2. Constraint Binds in Period L (q L *<q H *) 5 Optimal quantities: q L *=q H *, MR L (q L *)= L , MR H (q H *)= z- L
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Revenue Management 6 A firm has K tickets to sell Airline seats, hotel rooms, advertising slots Customers arrive over time Customers have value v unknown to firm How should firm set prices over time? If lower price then: (a) sell to marginal agents today (b) make less revenue from inframarginal agents (c) lose opportunity to sell tomorrow
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Revenue Management: Example 7 Example: one item to sell (K=1)
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Slides10_Dynamic_Pricing - The Information Economy Dynamic...

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