Equilibrium Pricing of Semantically Substitutable Digital Goods

TL;DR

This paper develops a market model and proves the existence of equilibrium prices for semantically substitutable digital goods, extending economic theory to digital markets and ensuring welfare properties.

Contribution

It introduces a new market model for semantically substitutable digital goods and proves the existence of equilibrium prices within this framework.

Findings

Existence of equilibrium prices proven using Kakutani's fixed point theorem.

Fundamental theorems of Welfare Economics are extended to this digital goods market.

Market allocations remain socially fair and efficient despite digital nature.

Abstract

The problem of arriving at a principled method of pricing goods and services was very satisfactorily solved for conventional goods; however, this solution is not applicable to digital goods. This paper studies pricing of a special class of digital goods, which we call {\em semantically substitutable digital goods}. After taking into consideration idiosyncrasies of goods in this class, we define a market model for it, together with a notion of equilibrium. We prove existence of equilibrium prices for our market model using Kakutani's fixed point theorem. The far reaching significance of a competitive equilibrium is made explicit in the Fundamental Theorems of Welfare Economics. There are basic reasons due to which these theorems are not applicable to digital goods. This naturally leads to the question of whether the allocations of conventional goods are rendered inefficient or "socially unfair" in the mixed economy we have proposed. We prove that that is not the case and that in this sense, the intended goal of Welfare Economics is still achieved in the mixed economy.