In this paper, we interpret the community question answering websites on the
StackExchange platform as knowledge markets, and analyze how and why these
markets can fail at scale. A knowledge market framing allows site operators to
reason about market failures, and to design policies to prevent them. Our goal
is to provide insights on large-scale knowledge market failures through an
interpretable model. We explore a set of interpretable economic production
models on a large empirical dataset to analyze the dynamics of content
generation in knowledge markets. Amongst these, the Cobb-Douglas model best
explains empirical data and provides an intuitive explanation for content
generation through concepts of elasticity and diminishing returns. Content
generation depends on user participation and also on how specific types of
content (e.g. answers) depends on other types (e.g. questions). We show that
these factors of content generation have constant elasticity---a percentage
increase in any of the inputs leads to a constant percentage increase in the
output. Furthermore, markets exhibit diminishing returns---the marginal output
decreases as the input is incrementally increased. Knowledge markets also vary
on their returns to scale---the increase in output resulting from a
proportionate increase in all inputs. Importantly, many knowledge markets
exhibit diseconomies of scale---measures of market health (e.g., the percentage
of questions with an accepted answer) decrease as a function of number of
participants. The implications of our work are two-fold: site operators ought
to design incentives as a function of system size (number of participants); the
market lens should shed insight into complex dependencies amongst different
content types and participant actions in general social networks.Comment: The 27th International Conference on World Wide Web (WWW), 201