Bert Willems

will give a presentation on

Multi-product Supply Function Equilibria

Abstract:

We solve for Nash equilibria in a procurement auction with two heterogeneous divisible goods. There are (dis)economies of scope in production and goods could be substitutes or complements for the procurer. Before demand is realized, each firm offers a vector of supply functions where supply of a good depends on the prices of both goods. This is related to the organisation of the product-mix auction and electricity markets with complex bids. We show that outcomes are not influenced by bundling of the goods. For quadartic costs and linear demand, we can use this property to transform the multi-product problem into an equivalent set of separated single-good markets, which can be analysed independently. We show that Lerner and pass-through tensors can be used to characterise mark-ups and welfare losses in a multi-product market. Eigenvalues of the tensors are fundamental properties of the multi-product market, as they do not depend on bundling.