# Economic Classroom Experiments/Network Externalities

Consumers with different private valuations enter a market with positive externality, where the value of the commodity to each is increasing in the number of others who buy it; the predicted equilibrium is reached where consumers buy when their private valuations exceed a common threshold.

## Overview

Any level

None

Any

### Intended learning outcomes

1. Network externalities.

## Computerized Version

There is a computerized version of this experiment available on the Exeter games site.

You can quickly log in as a subject to try out this group participation experiment, by pretending to be one of the original participants in a real session. You may also find the sample instructions helpful.

### Abstract

Students play together in a single large group as consumers who must simultaneously decide whether or not to buy a commodity. The price of the commodity is the same for all and is common knowledge. The value of the commodity to each consumer is equal to that consumer's private value multiplied by the proportion of other consumers who decide to buy. Private values are uniformly distributed across a known interval.

This is an example of a positive network externality, where the entry of additional consumers into a market has a beneficial effect on those who already possess the commodity, e.g. the market for fax machines, which are only useful if there are enough other people you can send a fax to.

### Discussion of Likely Results

One should only buy the good if the expected value is above the price E[n*V]>=p (where n is the proportion of others buying the good). There are multiple equilibria. One equilibrium has no one buying the good. For instance, if no one buys a fax a machine, then you shouldn't buy a fax machine E[0*V]<p.

In the default setup, the price is £2.40 and the private values are uniformly distributed in the interval [£0.00, £10.00]. Here there is another equilibrium with a positive n. Those deciding to buy the good have should have V such that E[n]V>p. In words, they each decide to buy when for private values above a common threshold value V=p/E[n]. What should that value be? The proportion of others who buy is approximately (10-V)/10, so each consumer is indifferent between buying and not buying when V(10-V)/10=2.4, which has solutions for V=4 and V=6. When V=4, this is the success equilibrium where 60% of the consumers buy the good. When V=6, it is in an unstable equilibria, which one can call the "tipping point". If people with values of 5.9 start buying it then, the object would be a hit, that is, it will go to the equilibrium with V=4. This is because the proportion of those buying it is now (10-5.9)/10=0.41 and p/0.41=2.4/0.41=5.85. So those with values above 5.85 will start buying the good. Repeating this calculation (an infinite number of times) one will arrive at V=4.