Intermediated surge pricing

• Published date: 01 January 2020
• Author: Sushil Bikhchandani
• DOI: http://doi.org/10.1111/jems.12332
• Date: 01 January 2020

J Econ Manage Strat. 2020;29:31–50. wileyonlinelibrary.com/journal/jems © 2019 Wiley Periodicals, Inc.

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Received: 28 August 2018

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Revised: 2 September 2019

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Accepted: 9 September 2019

DOI: 10.1111/jems.12332

ORIGINAL ARTICLE

Intermediated surge pricing

Sushil Bikhchandani

Anderson School of Management, UCLA,

Los Angeles, California

Correspondence

Sushil Bikhchandani, Anderson School of

Management, UCLA, Los Angeles 90095‐

1481, California.

Email: sbikhcha@anderson.ucla.edu

Abstract

Although Uber and Lyft are known for their flexible “surge pricing,”they are

surprisingly rigid in another way: each firm takes a constant percentage of

passenger fare whether or not there is a surge. In this paper, I investigate the

possible reasons for, and the impact of, this rigidity. I study a market in which a

profit‐maximizing intermediary facilitates trade between buyers and sellers. The

intermediary sets prices for buyers and sellers, and keeps the difference as her

fee. Optimal prices increase when demand increases, that is, shifts right. If a

demand increase is due to an increase in the number of ex ante symmetric

buyers, then the intermediary’s optimal percent fee decreases. If, instead, a

demand increase is due to a reduction in the elasticity of demand, then the

intermediary’s optimal percent fee increases. In either case, if the intermediary

keeps a constant percent fee regardless of shifts in demand, as is the case with

Uber and Lyft, then surge pricing (i.e., the ratio of price during high demand to

price during low demand) is amplified on one side of the market and

diminished on the other side.

KEYWORDS

intermediation, monopoly and monopsony, pricing

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INTRODUCTION

I investigate pricing in an intermediated market for immediate delivery of a product. Of particular interest is the

variation in the intermediary’s optimal revenue share with fluctuations in demand. Intermediaries such as Uber and

Lyft provide a motivating example. Uber’s (and also Lyft’s) superior matching technology reduces search costs for car

drivers and passengers. Uber sets a price (per mile) that passengers pay and takes a fixed percent of the passenger fare

from each transaction that it mediates. Uber monitors local demand and supply conditions in real time. While Uber

responds to sharp increases in demand by raising price, it keeps the same percent fee at each demand level. Thus, the

payment that a car driver receives is a fixed percent of the payment made by the passenger. Conceivably, if Uber were to

reduce its percent fee when many passengers enter the market, such as during rush hour, it may increase profits by

enticing more drivers to enter the supply pool. At other times when passengers are few but have a greater willingness‐

to‐pay, such as late at night or after a severe snowstorm, it may be profitable for Uber to increase its percent fee while

charging passengers more. In either case, the flexibility afforded by not having the payment by a passenger and the

payment to a driver in lock step may have an impact on price increases during periods of high demand.

I explore these questions in a simple market model with a monopolist intermediary who sets prices for buyers and

sellers. The focus is on how optimal prices and the intermediary’s optimal revenue share

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vary with changes in demand,

especially when there is some inflexibility in the prices set by the intermediary.

In the model, an intermediary facilitates trade between a large number of buyers and sellers. Search costs for buyers

and sellers are larger than the gains to trade; hence without the intermediary there is (essentially) no trade. This is the

case in several markets that have experienced extraordinary growth after recent advances in digital technology enabled

intermediaries to reduce search costs. Each buyer’s value and each seller’s cost for the product are private information.

Consequently, the intermediary does not have the ability to price discriminate between buyers or between sellers. It is

optimal for the intermediary to set a price for all buyers and a price for all sellers. As there are a large number of buyers

and sellers, it is optimal for each buyer and seller to act as a price‐taker. The intermediary keeps the difference between

the buyer price and the seller price in each trade.

The technological advances that have reduced search costs and enabled better matches between buyers and sellers

have also made it easier for the intermediary to monitor demand and supply and adjust prices accordingly. Not

surprisingly, the optimal prices charged to buyers and paid to sellers increase as demand increases—also known as

surge pricing. However, the optimal share (i.e., percent fee) of the intermediary may increase or decrease depending on

the nature of the increase in demand.

The intermediary’s role consists of two interlinked parts: it acts as a monopolist in its interactions with buyers and as

a monopsonist in its interactions with sellers. The marginal cost of the intermediary monopolist is determined by the

intermediary monopsonist, while the marginal revenue of the intermediary monopsonist is determined by the

intermediary monopolist. The ratio of the optimal buyer price to the optimal seller price charged by the intermediary

equals the product of the gross mark‐up of the intermediary acting as a monopolist and the gross mark‐down of the

intermediary acting as a monopsonist. Thus, the change in the intermediary’s optimal percent fee after an increase in

demand depends entirely on the elasticities of demand and supply through their effects on the gross mark‐up and on

the gross mark‐down, respectively.

A constant percent fee for the intermediary that does not change with demand conditions is rarely optimal. I

consider two types of changes in demand which are somewhat orthogonal in nature. First, the demand curve may shift

because a larger number (mass) of buyers enter the market; in effect, buyers are replicated without changing the

distribution of buyer values.

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This leads to an outward rotation of the demand curve about the vertical intercept.

Second, the demand curve may shift because the distribution of buyer values becomes less elastic but the number of

buyers does not change. This leads to an outward rotation of the demand curve about the horizontal intercept. Of

course, a shift in demand may be due to both factors causing the new demand curve to lie completely above the old one.

However, it is useful to analyze separately the impact of these two factors as they have opposite effects on the

intermediary’s optimal revenue share.

For a large enough increase in buyer mass, the optimal percent fee of the intermediary decreases. Reducing the

intermediary’s percent fee draws more sellers in, thereby increasing the number of trades and making it optimal for the

intermediary to capture a smaller fraction of this larger pie.

If, instead, a positive change in demand is entirely due to a large reduction in demand elasticity and the buyer mass

remains the same, it is optimal for the intermediary to increase its percent fee (as well as increase buyer and seller

prices). As there is no increase in buyer mass, there is less incentive to draw more sellers into the market. Consequently,

the sellers’share of the pie decreases after a reduction in demand elasticity.

Uber extracts the same fraction of the pie, charging a constant percent fee

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regardless of the level of demand. This

inflexibility in pricing results in a match between demand and supply that is less than optimal for the intermediary.

Under a constant percent fee, the number of transactions is less than optimal (for the intermediary, when compared

with flexible percent fees) when the buyer mass is high and it is greater than optimal when the buyer mass is low. In

contrast, if the demand change is due to a change in elasticity, then under a constant percent fee the number of

transactions is greater than optimal when demand is inelastic and less than optimal when demand is elastic.

Apart from being suboptimal, a constant percent fee amplifies the surge in prices on one side of the market and

diminishes the surge in prices on the other side of the market. To see this, consider a scenario where high and low

demand periods are determined by a change in the mass of buyers. In the absence of a constant percent fee constraint, it

is optimal for the intermediary to reduce its percent fee when buyer mass increases. Under a constant percent fee

constraint, the intermediary will charge a fee that is smaller than optimal during low demand and greater than optimal

during high demand. This in turn leads to an even higher buyer price during high demand and an even lower buyer

price during low demand, compared with optimal prices with a flexible percent fee. Consequently, the surge in buyer

prices is amplified. A constant percent fee also diminishes the surge in seller prices in response to an increase in the

mass of buyers.

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BIKHCHANDANI