Procurement with Asymmetric Information About Fixed and Variable Costs

• Author: RICK ANTLE,PETER BOGETOFT
• DOI: http://doi.org/10.1111/1475-679X.12236
• Date: 01 December 2018
• Published date: 01 December 2018

DOI: 10.1111/1475-679X.12236

Journal of Accounting Research

Vol. 56 No. 5 December 2018

Printed in U.S.A.

Procurement with Asymmetric

Information About Fixed and

Variable Costs

RICK ANTLE

∗AND PETER BOGETOFT

†

Received 25 November 2015; accepted 4 June 2018

ABSTRACT

We investigate optimal rationing of resources and organizational slack when

a principal procures from an agent with private information about fixed and

variable costs. We study the problem in a two-period setting with persistent

types and investigate how the optimal rationing and slack depend on whether

production increases or decreases over time. We find that rationing in a dy-

namic model with persistent types is extra costly, since thetypes that are elimi-

nated in period 1 might have been attractive in period 2. The cost of rationing

increases with the variability of production. If production levels are increasing

(decreasing), the principal will be cautious when eliminating types with low

variable (fixed) costs in period 1, since these types are particularly profitable

in period 2. When production is more stable over time, harsher rationing can

be applied in period 1, followed by less harsh rationing, if any, in period 2.

JEL codes: C72; C76; D21; L24; M41

Keywords: cost accounting; fixed and variable costs; production contract-

ing; dynamic model; resource rationing; organizational slack; contracting;

cost functions; production management; managerial accounting

∗Yale School of Management; †Copenhagen Business School.

Accepted by Haresh Sapra. We appreciate the very insightful and constructive comments

received from participants in the Yale SOM Faculty Seminar and the Copenhagen Business

School Department of Economics Brown Bag Seminar, as well as from the referees of this

journal. The comments have had a profound impact on the paper.

1417

CUniversity of Chicago on behalf of the Accounting Research Center,2018

1418 R.ANTLE AND P.BOGETOFT

1. Introduction

It is widely acknowledged that, in many organizations, information about

product costs is dispersed. Typically, theoretical studies of how the disper-

sion of cost information affects the design of incentive systems, communi-

cation alternatives, and the allocation of resources in organizations have

assumed that a less informed principal contracts with a better informed

agent and have concentrated on cost information that is one-dimensional.

This paper keeps the focus on a less informed principal contracting with

a better informed agent, but expands the focus to dispersed informa-

tion about a linear cost structure that has both a fixed and a variable

component.

This added structure is irrelevant in a one-period problem because all

that matters is the total production cost. In a two-period model, however,

the cost structure can matter because observation of the production and

total cost in the first period does not resolve all the principal’s uncertainty

in the second, even if the cost structure is constant across periods: different

combinations of fixed and variable costs could lead to the same first-period

total costs. Intuitively, this allows the agent to extract extra information

rents. In particular, the historical experience can be portrayed as stemming

from a variety of fixed and variable components in ways that benefit the

agent. When production is to be expanded, prior costs can be portrayed as

predominately variable. When production is to be contracted, they can be

portrayed as largely fixed.

We assume—for most parts of the paper—that forgoing production in

the first period eliminates the possibility of producing in the second, per-

haps because the agent has moved on to another job. Therefore, the prin-

cipal’s behavior in the first period affects his welfare both directly, because

valuable output is produced in the first period, and indirectly, because the

first period “prescreens” the types of agents available for production in

the second period. This might lead the principal to screen fewer types

in the first period of a two-period setting, relative to the one-period case,

in order to preserve opportunities in the second period.

The principal’s behavior in the second period involves the standard one-

period tradeoff between the probability of production and the profit mar-

gin, but that determination is done using the distribution of costs induced

by the principal’s and agent’s choices in the first period. In this sense, the

principal learns from the first period and acts optimally contingent on that

knowledge in the second.

To gain intuition, it is useful to distinguish between two types of changes

that can occur between the first and second periods: changes involving the

quantity of production, which drives costs, and changes involving the value

of production, which directly impacts the principal’s welfare. The simplest

case is when the production level does not change but the value of the pro-

duction does. When the production level is fixed, so is the distribution of

total costs. Hence, the principal faces the problem of sequentially rationing

PROCUREMENT WITH ASYMMETRIC INFORMATION 1419

in the same underlying total cost distribution. The optimal outcome in this

case depends on the value of the production in the two periods. When pro-

duction becomes less valuable over time, for example, because the market

becomes saturated or the principal is involved in price discrimination, the

dynamics are particularly simple. The principal will solve each of the two

periods as a single period screening problem. If on the other hand, pro-

duction becomes more valuable over time, rationing must be less harsh in

period 1, since types that are eliminated in period 1 are not available to

produce in period 2.

When the production level changes over time, the optimal strategy is

more complicated. When production changes, so does the distribution of

total costs. The fixed costs are most important when production is low, and

the variable costs play a larger role when production is high. Either way,

the principal must sequentially ration in evolving type distributions, and

his choice in period 1 affects the distribution he faces in period 2.

We show that any increase or decrease in production in period 2 leads

the principal to allow more organizational slack in period 1 and to ration

more aggressively in period 2. The intuition in this case is twofold. First,

as discussed above, rationing is generally more costly in period 1 because

it reduces the types available in period 2. Second, and more intricate, the

types the principal prefers differ over time. When production increases,

for example, the principal prefers an agent with relatively lower fixed costs

in the first period and relatively lower variable costs in the second period.

This makes myopic single-period rationing extra costly when production

changes.

To sum up, the main contribution of this paper is that, in a dynamic set-

ting with persistent types, it shows how the structure of the optimal incen-

tive scheme depends on the variability of production over time when the

underlying total costs are driven by a structure with both fixed and variable

components.

The outline of the paper is as follows. In section 2, we discuss the liter-

ature most closely related to the specific problem we study. In section 3,

we introduce the basic setting, and we formulate the contract design prob-

lem in section 4. In sections 5 and 6, we discuss the optimal contract char-

acteristics in the static and dynamic contexts. In addition to the general

characterizations of the optimal contracts, we study a few special cases

and some numerical examples. We investigate second-period rationing in

more detail in the uniform case in section 7. We sketch some applications

and testable implications in section 8. A final discussion is provided in

section 91.

1In an earlier working paper version of the paper available from the authors on request,

we also discuss different extensions of our model. In particular, we relax the assumptions that

(1) the production levels y1and y2and the values V1and V2are exogenously given and that

(2) agents are myopic (or face limited liability constraints within periods).