A Note on Quantity versus Price Risk and the Theory of Financial Intermediation

Abstract

MODELING THE BEHAVIOR OF financial intermediaries under conditions of uncertainty has a long and varied history.1 Moreover, it continues to be a topic of considerable interest because appropriate public policy decisions depend, in part, on the assumed characteristics of firms participating in the market. One central point of debate, as presented by Sealey [3], involves the potentially contrasting behavioral implications associated with assuming that intermediaries are price setters in their deposit markets, as opposed to quantity setters operating under conditions of perfect competition. He addresses, among other things, the important question of whether the supply of financial intermediation is altered by the inclusion of quantity risk. Sealey argues that, in contrast to earlier work by Pyle [1], one cannot determine how the degree of association between asset rates and the quantity of deposits influences the amount of lending by intermediaries. The purpose of this note is twofold. First, we provide conditions under which the ambiguity between Sealey's and Pyle's works may be resolved. Second, we argue that the results from the two models are symmetric. We use symmetry here to denote the fact that the conditions on association that, for example, discourage intermediation are the same in both models when viewed in the context of revenues and costs. However, the two frameworks require opposite conditions on the association between rates and quantities to achieve identical results concerning the relationship between revenues and costs. The approach used involves constructing a scenario that makes the Sealey model almost identical to that used earlier by Pyle except for the rate versus quantity setting issue. We then show that a positive association between asset rates and the quantity of deposits actually discourages lending but promotes the gathering of more deposits. We then provide a rationale for why this is consistent with Pyle's conjecture that a negative association discourages intermediation in the pure rate-uncertainty case. Interestingly, we also argue that, while a negative association will promote lending by depository intermediaries under certain conditions, the result in this case is generally ambiguous, as is the case when a positive association is analyzed in the Pyle model. The paper is structured as follows. In Section I, we present the basic model, derive our results, and discuss their implications. Section II contains concluding remarks.