Optimal Growth in Two-Sided Markets

47 Pages Posted: 19 Jan 2019

See all articles by Zhen Lian

Zhen Lian

Cornell University - Samuel Curtis Johnson Graduate School of Management

Garrett van Ryzin

Cornell Tech; Lyft, Inc.

Date Written: January 4, 2019

Abstract

We develop a theoretical model of optimal growth in two-sided markets. The model posits that market output (number of transactions) is a function of the stock of sup- ply and demand. This market output is modeled using a Cobb-Douglas production function, which can have increasing or decreasing returns to scale. The supply and demand stock levels follow a growth model in which the rate of growth at each point in time is a function of both the surplus each side of the market receives and the attrition of supply and demand (supply and demand lifetimes). The surplus can be apportioned between the two sides of the market by changing the price paid to sellers and the price charged to buyers, which we assume the platform controls. Through these price levers, the platform can pay subsidies to one or both sides of the market. We investigate the behavior of optimal market growth, including the point at which the market becomes self-sustaining and the long-run optimal size of the market. We characterize the optimal balance between supply and demand as the market size grows and determine optimal subsidy policies that maximize discounted total pro t. For the case of both increasing and decreasing returns without price constraints, we show the optimal policy is to grow using an impulse of subsidy spending (a "subsidy shock") to move the market immediately to its optimal long-run size. This result is consistent with the "race to growth" observed in many two-sided markets like ride-sharing.

Keywords: two-sided market, optimal growth, market balance, sharing economy

Suggested Citation

Lian, Zhen and van Ryzin, Garrett, Optimal Growth in Two-Sided Markets (January 4, 2019). Available at SSRN: https://ssrn.com/abstract=3310559 or http://dx.doi.org/10.2139/ssrn.3310559

Zhen Lian

Cornell University - Samuel Curtis Johnson Graduate School of Management ( email )

Ithaca, NY 14853
United States

Garrett Van Ryzin (Contact Author)

Cornell Tech ( email )

2 W Loop Rd
New York, NY 10044
United States

Lyft, Inc. ( email )

San Francisco, CA

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