To sell public or private goods

Abstract

Traditional analysis takes the public or private nature of goods as given. However, technological advances, particularly related to digital goods such as non-fungible tokens, increasingly make rivalry a choice variable of the designer. This paper addresses the question of when a profit-maximizing seller prefers to provide an asset as a private good or as a public good. While the public good is subject to a free-rider problem, a profit-maximizing seller or designer faces a nontrivial quantity-exclusivity tradeoff, and so profits from collecting small payments from multiple agents can exceed the large payment from a single agent. We provide conditions under which the profit from the public good exceeds that from a private good. If the cost of production is sufficiently, but not excessively, large, then production is profitable only for the public good. Moreover, if the lower bound of the support of the buyers' value distribution is positive, then the profit from the public good is unbounded in the number of buyers, whereas the profit from selling the private good is never more than the upper bound of the support minus the cost. As the variance of the agents' distribution becomes smaller, public goods eventually outperform private goods, reflecting intuition based on complete information models, in which public goods always outperform private goods in terms of revenue.

Keywords: Bilateral trade; Mechanism design; Non-fungible token (NFT); Public goods; Revenue maximization.

Fig. 1

Illustration of the public allocation rule g and the region of trade for the public good when $n=2$

Fig. 2

Allocation by type vector realization for $n=2$, $c=0$, and uniformly distributed values on [0, 1]. In the case of a private allocation, the good is allocated to the buyer with the higher value

Fig. 3

Revenue by type vector realization for $n=2$, $c=0$, and uniformly distributed values on [0, 1]. The dashed lines are contour lines, with the arrow indicating the direction of increasing revenue

Fig. 4

Allocation rule for $n=2$, $c=0$, and values distributed over [0, 1] according to $F_a$ with $a=2$

Fig. 5

Revenue by type vector realization with $n=2$, $c=0$, and values distributed over [0, 1] according to $F_a$ with $a=2$

Fig. 6

Virtual type functions and inverse demand $P(q)=F^{-1}(1-q)$ for distributions in the family of reserve kinked distributions. Panel (a) shows the concave case with $b_1=1/2$ and $b_2=1$, where public provision dominates, and panel (b) shows the convex case with $b_1=2$ and $b_2=1$, where private provision dominates

Fig. 7

Intermediary profits and maximum transformation costs in the setup with two-sided private information. Panel (a): intermediary profits under private provision and under public provision when transformation costs are zero. Panel (b): maximum transformation cost $\overline{k}$ that a profit-maximizing intermediary would be willing to incur and the range of transformation costs (shaded region) that a profit-maximizing designer would be willing to incur to transform the good from private to public. Assumes that the seller’s and buyers’ types are uniformly distributed on [0, 1]