Demand Uncertainty and Resale Price Maintenance

By Nariu, Tatsuhiko; Flath, David | Contemporary Economic Policy, October 2000 | Go to article overview

Demand Uncertainty and Resale Price Maintenance


Nariu, Tatsuhiko, Flath, David, Contemporary Economic Policy


TATSUHIKO NARIU [*]

When retailers must commit to shipment quantities prior to resolution of demand uncertainty manufacturer stipulation of a minimum retail price is likely to be profitable for the manufacturer and not damaging to the retailers. The reason is simple: If demand turns out to be low, the unfettered market-clearing price can lie below the price that maximizes total sales revenue. A minimum retail price that is binding in the low-demand state can thus increase total revenue even though it saddles retailers with unsold merchandise. The ubiquity of full reimbursement for returns in Japan, even though it is in theory merely a second-best way of achieving minimum retail price stipulations, reveals important aspects of manufacturer maintenance of retail prices having to do with enforcement problems, the allocation of risk-bearing, and economic incentives. These aspects of resale price maintenance (RPM) are relevant to the normative evaluation of the special exemptions for RPM that Japan's Fair Trade Commission has long m aintained but is now phasing out. (JEL D42, D81, K21, L42)

I. INTRODUCTION

Several authors have recently noticed that when retailers must commit to shipment quantities prior to resolution of demand uncertainty, manufacturer stipulation of a minimum retail price is likely to be profitable for the manufacturer and not damaging to the retailers. [1] The logic of this is quite simple: If demand turns out to be low, the unfettered market-clearing price can lie below the price that maximizes total sales revenue. A minimum retail price that is binding in the low-demand state can thus increase total revenue even though it saddles retailers with unsold merchandise. In the following paragraphs, we first develop a simple algebraic example that, among other things, exposes the close correspondence between this argument and analysis of the peak-load pricing problem. We then discuss some considerations bearing on the manufacturer's choice among the different ways of curbing price discounting by independent retailers. We also offer some specific empirical examples from Japan in which the argument may apply. Finally, we discuss the social welfare implications of prohibitions against price maintenance in low-demand states, again based on our algebraic example.

II. AN ALGEBRAIC EXAMPLE

We start with the algebraic example that ties this new rationale for price maintenance to the phenomenon known as peak-load pricing and that is also the basis for some other points. Let the linear demand curve for some good have vertical intercept Y, and let the demand curve have slope -[b.sub.H] with probability [theta], and slope -[b.sub.L] with probability 1 - [theta], where [b.sub.L] [greater than] [b.sub.H]:

price = {[p.sub.H] = Y - [b.sub.H][x.sub.H], with probability = [theta]

[p.sub.L] = Y - [b.sub.L][x.sub.L], with probability = (1 - [theta]).

Suppose that a risk-neutral and vertically integrated manufacturer must produce before realization of the stochastic demand just described. Suppose further that the unit cost equals c. The manufacturer solves the problem

max expected profit

=[theta](Y - [b.sub.H][x.sub.H])[x.sub.H] + (1 - [theta])

x(Y - [b.sub.L][x.sub.L])[x.sub.L] - cQ,

s.t. [x.sub.H] [less than or equal to] Q, and [x.sub.L] [less than or equal to] Q.

The manufacturer will not allow the price to fall below the revenue maximizing level Y/2 even if it results in some output remaining unsold. But the self-imposed price floor of Y/2 is only binding for some combinations of the parameters c/Y, [theta], [b.sub.L] and [b.sub.H]. Specifically, if ([b.sub.L] - [b.sub.H])/[b.sub.L] [greater than or equal to] c/(Y[theta]), then the firm maximizes its expected profit by producing (Y - c/[theta])/2[b.sub.H], but only selling the smaller amount Y/2[b.sub.L] at the price Y/2 in the low demand state, while selling all at the price (Y + c/[theta])/2 in the high-demand state. …

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