/

C^'D— 3A United States

Department of

Agriculture

nZÁL

Technical

Bulletin

Number 1867

An Economic Research Service Report

Nonfarm Input Pri^St

Price IVIarglns, an(|^ '

Consumer Food Prices

A. J. Reed

J. S. Clark
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Nonfarm Input Prices, Price Margins, and Consumer Food Prices. By A. J. Reed and

J. S. Clark. Food and Rural Economics Division, Economic Research Service, U.S.

Department of Agriculture. Technical Bulletin No. 1867.

Abstract

The U.S. Department of Agriculture's Economic Research Service (ERS) often bases its

analyses of retail food and farm prices on a traditional, fixed-input proportions framework.

We review the implications of fixed- and variable-proportions production for food and

farm price analysis in this report. Based on this review, one would expect significantly

different price predictions, and the empirical results presented confirm this expectation.

This bulletin recommends more consideration be given to price analyses based on

variable-proportions models.

Keywords: Retail-to-farm price margins, variable proportions, fixed proportions.

Acknowledgments

The authors express appreciation to Wanda-Reed Rose for preparation of the graphs,

Sharon Lee for editing the bulletin, and to Anne Pearl for the cover design. The authors

also express appreciation to Dr. Michael Wohlgenant for comments and discussion of the

material in this bulletin.

Washington, DC 20036-5831 March 1998
Contents

Summary iii

Introduction 1

Measures of Retail-to-Farm Price Margins 2

Retail-to-Farm Price Margins and Fixed Proportions 3

Retail-to-Farm Price Margins and Variable Proportions 3

Effect of Input Prices on Retail Food Prices 4

Changes in Consumer Food Prices and Fixed Proportions 5

Changes in Consumer Food Prices and Variable Proportions 7

Empirical Analyses 13

Effects of Shift in Consumer Demand 13

Effects of Shift in Farm Supply 15

Effects of Shift in Nonfarm Input Price 16

Conclusions 17

References 18

Appendix 19
Summary

Nonfarm inputs in food production have become increasingly important in today's more industrialized

food sector. For example, the cost of labor, energy, packaging, advertising, and transportation account for

over 75 percent of the cost of food products. Changes in the vertical coordination of raw agricultural

inputs to final food products have raised the question of whether food markets are efficient, or whether

farm producers and food consumers bear the welfare loss associated with inefficient markets. At the heart

of this question is an economic analysis of food, farm, and nonfarm input prices.

Such analyses have traditionally been based on the assumption that food producers fix the proportion of

farm and nonfarm inputs in each unit of food output regardless of changes in relative input prices.

However, the restrictions accompanying this assumption have often been refuted empirically. The

theoretical and empirical comparisons of fixed- and variable-proportions frameworks further call into

question the applicability of the perfectly competitive, fixed-proportions framework to the analysis of food

and farm price data. The more general, variable-proportions framework explains why, in competitive

markets, increases in consumer prices are not fully passed through to farmers, why nonfarm input price

increases lead to widening price spreads, why an expanding farm supply results in farm prices falling

more than retail prices, and how firms in a perfectly competitive industry could earn positive longrun rents.

The conclusions reached here may lay the groundwork for a reconsideration of the traditional methods of

food and farm price analyses.

Ill
Nonfarm Input Prices, Price Margins, and

Consumer Food Prices

A. J. Reed and J. S. Clark

Introduction

Labor, energy, packaging, advertising, and transportation account for over 75 percent of the total retail cost

of food. The relatively small and declining portion of farm ingredients used in today's food products may

serve to mitigate increases in farm prices and widen the spread between the consumer's price and farm

prices.

Analysts faced with the question "What happens to food prices and to retail-to-farm price margins when

nonfarm input prices change?" require a market framework that relates the value of inputs used in food

production to the value of final food products. A critical aspect of any such framework is the specification

of the production function for food.

Production functions are either fixed or variable proportions. Associated with each is a definition of retailto-farm price margins and a relationship between input prices and consumer food prices. The different

definitions and different relationships are attributed to different theories of input productivity implied by

each class of production function. In fixed-proportion functions, input productivity remains unchanged

because input proportions remain unchanged. In variable-proportion functions, input productivity changes

as relative input levels change. In fixed-proportion functions, a change in an input price effects no change

in the input's productivity because it has no effect on input proportions. In variable-proportion functions, a

change in an input price alters input proportions and the productivity of all inputs. Not surprisingly, the

effect of input price changes, consumer trends, or other market changes on food and farm prices depends

on whether analysts view food as produced in fixed- or variable-proportions technology.

To see the differences in slightly more detail, consider a simple market in which an industry produces a

consumer food product using a single farm commodity, and two or more nonfarm inputs, one of which is

arbitrarily referred to here as energy. Assume further that food consumption is fixed and exogenous and

the market is competitive. Consider the effect of a 1-percent increase in the price of energy on consumer

and farm-level prices under a fixed- and a variable-proportion production function.

If food production is represented by a fixed-proportion function, a 1-percent increase in the price of energy

results in a percentage increase in the marginal cost equal to the cost share of energy. In a competitive

market, then, the percentage increase in the consumer food price equals energy's cost share. If consumer

demand for the food product is predetermined, farm prices remain unchanged and the widening retail-tofarm price spread reflects only the increase in the retail food price. Retail and farm price analyses by U.S.

Department of Agriculture's Economic Research Service (USDA, ERS) are often based on a fixedproportions framework, for example, Hanson, Robinson, and Schlüter (1993) and Elitzak (1996).

If, on the other hand, food production is represented by a variable-proportion function and if energy costs

rise by 1 percent, the industry will respond by reducing its proportions of more expensive energy inputs
and increasing its proportions of less expensive inputs. Because the variable-proportions industry uses

proportionately more of the relatively less expensive inputs than does the fixed-proportions industry, one

would expect that the increase in the marginal cost of food production and the retail price of food to be less

in a variable-proportions industry than it would be in a fixed-proportions industry. In addition, any change

in the proportion of farm inputs used will affect the industry's demand for farm inputs and alter farm

prices. The direction of change in the demand for farm inputs and, hence, the direction of change in the

farm price is, in general, ambiguous because the farm input can complement or substitute for the nonfarm

inputs. One would expect changing market conditions to affect consumer food prices and spreads between

retail and farm prices differently under variable and fixed proportions.

Traditionally, food price analyses have been based on a fixed-proportions assumption. Despite both the

theoretical and empirical developments made in advancing the variable-proportions approach by

Wohlgenant (1989), Wohlgenant and Haidacher (1989), and Wohlgenant (1997), some economists object

to applying variable proportions to food price analysis. The objection is maintained despite the fact that

virtually any category of the Consumer Price Index for food is a composite price of numerous products,

each of which uses different proportions of farm and nonfarm inputs. Altering the production mix of final

products effectively alters the industry's input proportions (Wohlgenant, 1989). The objection to variable

proportions is also maintained despite the failure of fixed proportions to explain the stylized fact that

consumers pay higher markups for higher-retail-priced food items (George and King, 1971, p. 58).

Finally, the objection to a variable-proportions approach remains despite observed declines in farm shares,

widening retail food-to-farm price spreads, and consumer trends toward purchasing more highly processed

food products both at home and away from home.

Interpreting price relationships in the food and agricultural sector is crucial for sound economic policy

analysis, since questions of market power, captive supplies, and welfare loss often accompany a price

analysis. The empirical results associated with the fixed- and variable-proportions models suggest that the

restrictions associated with the fixed-proportions assumption may lead to biased retail-to-farm price

analysis and to misleading conclusions regarding market efficiency and competitiveness.

Measures of Retail-to-Farm Price Margins

In competitive markets, the retail-to-farm price margin is the retail value that consumers are willing to pay

for nonfarm inputs in their food products; and it is the contribution to marginal costs food producers pay to

attract nonfarm inputs into food production. While price margins respond to exogenous changes in

nonfarm input prices, they also respond to shifts in consumer demand or farm supply. Estimates of price

or marketing margins are sometimes interpreted as summary measures of welfare loss or gain. For

example, a pattern of widening margins might be interpreted as food producers' charging consumers

higher prices and paying farmers lower prices than they would in competitive markets. However, if

markets are efficient, widening margins merely reflect a réévaluation of nonfarm inputs by both consumers

and food producers.

ERS computes estimates of marketing margins based on a fixed-proportion production function and no

consumer price response. This section formally justifies ERS's computation and introduces an alternative

measure based on variable-proportions production.
Retail-to-Farm Price Margins and Fixed Proportions

ERS computes fixed-proportions estimates of marketing margins, farm value, and farm value share

(Elitzak, 1996). To justify the computations, consider the simplified case of an industry that produces food

output, ß, using fixed proportions of farm input, F, labor input, A^, and energy input, £, so the production

function is

ß = min(F/a, Nib, Elc) (1)

where a, b, and c are the input-output coefficients of the farm, labor, and energy inputs, respectively. If p^

is the farm price, w is the wage, and /^^is the energy price, the cost equation is C = p^F + wN + pß. The

cost function associated with equation 1 is (0 /7^ + ¿7 w + c p^Q. Both the average and marginal cost

functions are

C

AC = — = a pj, + b w + c p^.

In this case, if markets are efficient, the retail price of food, p^^, is equal to average cost, and the marketing

margin is

M = b w + c p^ = p^ - a pj,. (2)

If equation 1 represents the production function for food, ERS's estimates of farm value, app, and farm

value share, applp^, are based on equation 2 and represent valid measures of economic value. Equation 2

suggests that consumer and farm-level prices and an input-output coefficient are the only data required to

compute retail-to-farm price margins.

Retail-to-Farm Price Margins and Variable Proportions

Variable-proportions production offers an alternative measure of marketing margins. In contrast to

equation 1, food production is assumed to follow Q = g(F,N,E), in which the production function, g, has

continuous, positive, and declining marginal products that depend on levels of all inputs. The optimization

problem is min^^^ ppF+wN+pß+\[Q^- g(F,N,E)],v/herc Q^ represents an exogenous level of food output

and in which the Lagrangian multiplier, X, represents the marginal cost (MC) of food production.

PF W PF

The solution to the problem satisfies X = MC = — = — = —s. This set of conditions states that at the

^1 ^2 <^3

cost minimum point, the MC of increasing output using the farm input equals the MC associated with

using either the labor or energy input. In this example, if the firm chose to increase output using all three

inputs, the increment to cost would be (Silberberg, 1978)

g^F + ^2^ + gß g^F + ^2^ + gß g^F + ^2^ + gß (3)
where gj, g2, and g^ are the marginal products of the farm, labor, and energy inputs, respectively. The

conditions necessary for cost minimization reveal that at the cost minimum point, the marginal cost of

production is the same regardless of whether firms increase production using any one input or using all

inputs.

Equation 3 is useful for computing a variable-proportions, retail-to-farm price margins. If markets are

efficient, equation 3 implies

wN PE^

M = + = Pj^

g^F + gj^ + gß gß + ^2^ + gß

í

^ gxF + ^2^ + g^E]

Pr (4)

The problem of implementing equation 4 empirically is with evaluating the marginal product schedules, gy,

g2, and g^. The use of equation 4 requires an explicit specification of the production function, g. If,

however, g exhibits constant returns to scale (CRS), g can be expressed as ß = g^F + gj^ + gßl and

equation 4 simplifies to

The term

' L

Q

Pp in equation 4 represents farm value, and the term ÍM1 represents the farm value

share associated with variable proportions production. In principle, these two estimates could replace the

fixed-proportions estimates of farm value and farm value share currently reported by ERS. Furthermore,

variable-proportions estimates of retail-to-farm price margins described by equation 5 are more general

than the estimates described by equation 2. The difference between equations 2 and 5 involves the

transformation of the farm price to its retail-equivalent value. If production is fixed proportions, equation

2 indicates the parameter a is used for this transformation, so the transformation is invariant to changes in

relative input prices. If production is variable proportions, the random variable F/Q is used for this

transformation, and because F/Q depends on relative prices, the transformation of the farm price to its

retail-equivalent value depends on relative prices. With margins based on a variable-proportions model,

retail-equivalent farm prices could change even if farm prices remain unchanged.

The problem with basing estimates of retail-to-farm price margins on variable proportions is the lack of

direct observations on food production or consumption. USDA's consumer disappearance data are not

appropriate since disappearance data reflect farm-level transactions. However, despite the lack of direct

observations on final food consumption, it is possible to establish empirical estimates of the relationships

between retail food prices and farm and nonfarm input prices.

Effect of Input Prices on Retail Food Prices

An important aspect of food price analysis is evaluating the effect of changes in input prices on consumer

food prices. Any price response generally depends on the simultaneous responses of consumers, food

producers, and farmers. This section provides a comparative-static analysis of a fixed- and a variableproportions model. The comparative-static analysis is mainly graphical, with a minimal appeal to
mathematical formulas. Wohlgenant (1989) and Wohlgenant and Haidacher (1989) provide a more formal

comparative static analysis of the variable-proportions model.

Changes in Consumer Food Prices and Fixed Proportions

ERS uses two fixed-proportions models to compute estimates of how changes in input prices affect retail

food prices. In both models, industry production is fixed proportions and the firms are identical. The

assumption that consumers do not respond to retail prices and food producers do not respond to relative

input prices greatly simplifies the comparative static analyses. Elitzak (1996) and Hanson, Robinson, and

Schlüter (1993) describe related versions of fixed-proportions models used for price analysis.

In the basic fixed-proportions model, the effect of a change in an input price on retail food price is found

by setting the retail price equal to the average cost function. Therefore, in a three-input example, one has

a pp + b w ^ c p^

where (again) the parameters a, Z?, and c are input-output coefficients for the farm, labor, and energy

inputs, respectively, and ppy w, and p^ are prices for farm, labor, and energy inputs, respectively.

Expressing this relationship in terms of percentage changes gives

PR = ^F PF " ^N PN -^ h PE

or

PR

PR

(6)

where the notation, z* = dz/z and where Sp-, Sj^, and s^ represent cost shares of the farm, labor, and energy

inputs, respectively. Equation 6 states that the percentage change in the retail price of a food product is a

weighted sum of the percentage changes in the price of the inputs used in food production, with cost shares

serving as weights. Equation 6 states that when an input price changes in a fixed-proportions framework,

the product of the percentage change in the input price and the cost share of the input is passed on to

consumers in the form of higher food prices.

Figure 1 sketches the comparative statics of an energy price increase in the fixed-proportions model when

consumer demand is exogenous. The figure depicts the familiar L-shaped isoquants in the labor-energy

plane. The slopes of the straight-line isocost functions represent the relative prices of labor and energy.
ON Figure 1

Energy price increase, fíxed proportions, and no

consumer response

Energy

Q

Labor

Energy price rises relative to

wages.

TZ Output

Energy price increase raises

average costs.
As the price of energy rises relative to the wage, the isocost Une rotates counterclockwise, but the L-shaped

isoquants imply that the industry does not alter its input proportions. In fixed-proportions production, the

substitution effect is always zero.

Figure 1 also depicts the perfectly horizontal average cost function, AC associated with all fixedproportions models. Because fixed-proportions production imposes constant returns to scale on

production, average cost functions are always perfectly horizontal. When the price of energy increases,

average cost rises from AC to AC and retail price rises from p^^ to pj^'. Associated with ERS's fixedproportions models is the feature of a predetermined consumer demand schedule. Figure 1 depicts a

perfectly inelastic consumer demand function denoted as D. The feature of a predetermined consumer

demand impUes that an increase in an industry's average cost leads to higher food prices but no consumer

response to higher food prices and, therefore, no change in industry output. The zero output effect implies

that if the price of energy rises, the industry's demand for farm ingredients as well as farm prices remains

unchanged. Price analyses generated by ERS's fixed-proportions models embody neither consumer nor

food producer response to changes in an energy (or any other input) price.

Changes in Consumer Food Prices and Variable Proportions

In contrast to ERS's fixed-proportions models, its variable-proportions framework embodies both

consumer and food producer responses to relative price changes. Furthermore, the model is a longrun

model, not necessarily in the sense that adjustments take a long time, but in the sense that it accounts for

the adjustment of an industry's capital in the form of entry and exit of firms.

ERS's variable-proportions model was constructed by Wohlgenant (1989) and Wohlgenant and Haidacher

(1989). A key feature of the Wohlgenant and Haidacher (WH) model, distinguishing it from textbook

neoclassical models, is that it accounts for nonidentical firms as proposed by Panzar and Willig (1978).

Hence, the WH model embodies the important feature that in competitive markets an industry can earn

competitive rents in the long run.

The easiest way to understand the comparative statics of the WH model is to consider the comparative

statics of a competitive equilibrium under the assumptions of variable proportions and identical firms.

Then relax the restriction of identical firms according to Panzar and Willig (1978). We review these

analyses in figures 3-5, using an increase in the price of energy as an example.

In these three analyses, firms receive the same retail price, p^, for each unit of food they produce. Industry

production is denoted as Q. The industry uses levels of the farm ingredients, F, labor, A^, and energy, E,

for which all firms pay the same farm price, Pf,, wage, w, and the price of energy, p^. In this version of the

WH model, the supply of farm ingredients is predetermined, and labor and energy are perfectly elastically

supplied. It is maintained that all input and output markets are perfectly competitive. The initial setup of

the model is displayed in figure 2, showing the industry's downward-sloping demand function for energy

and a perfectly elastic-supply-of-energy function. The price of energy rises from p^ to p^' as energy supply

contracts from S^ to 5^'. The illustration of the industry's smooth-shaped labor-energy isoquants shows

that food is produced according to a variable-proportions production function. In the three analyses, the

initial level of the food industry's output is Qj and the initial level of the exogenously supplied farm input

isF,.

Since industry production is variable proportions, its response to an increase in the price of energy can be

decomposed into two parts. The first part holds industry output constant. As figure 2 illustrates, when the
Figure 2

Model setup: Variable proportions

Energy Labor

Energy

Energy price rises.

Energy

Industry substitutes

labor for energy.

Farm

Industry's demand

for farm input

changes.
price of energy rises, the industry reduces its proportion of the energy input by moving from point AtoB

along the production isoquant associated with output Qj,

When the energy price rises, the amount by which the industry adjusts its demand for energy, holding

output constant, is the substitution effect. Vertical arrows suggest the substitution effect alone will shift an

industry's demand for farm ingredients, D^, and alter farm prices. More specifically, with output held

constant, an increase in the price of energy will shift the demand for farm inputs outward if the farm and

energy inputs are net substitutes and shift the demand for farm inputs inward if they are net complements.

The demand for other nonfarm inputs will also change, but the price remains unchanged as nonfarm inputs

are perfectly elastically supplied. The second part of an industry's response is the output effect. The

magnitude and direction of the output effect depends on the entry and exit of firms, on whether firms are

marginal or inframarginal firms, and whether the energy input is normal or inferior. In a discussion

leading up to the WH model, there are three cases.

In the first case, an industry, consisting of identical firms that can enter and exit the industry without cost,

produces food output in which the energy input is a normal factor of production. As a normal factor, the

industry uses more (less) energy when it increases (decreases) production. Equivalently, as a normal input,

an increase in the price of energy implies an increase in the industry's marginal cost of production. Figure

3 presents a graphical analysis of higher energy prices in this first case.

Initially, the typical firm faces longrun average costs, LAC, earns zero longrun profits, and produces output

qj. The firm also faces shortrun marginal costs, denoted as SMC, and associated with its SMC is the

industry's shortrun (quasi) supply function, SS, shown in figure 3. The industry's longrun supply of

output, LS, intersects the consumer demand schedule, D, at point A. The market clears output Qj at the

retail price Pj.

When the price of energy rises, the typical firm's longrun average cost also rises. This is shown as a shift

from LAC to LAC\ Because energy is a normal input, firms' marginal costs also rise from SMC to SMC\

effecting some increase in the industry's shortrun quasi-supply function. The increase in the price of

energy raises firms' longrun average costs above the initial output price, Pj. Since firms do not cover their

longrun average costs and because entry and exit are costless, the higher energy price forces firms to exit

the industry.

Firm exit has two implications. First, firm exit reduces shortrun industry supply. Second, since the

industry's longrun supply schedule is upward sloping, the exit of firms and the reduction of supply releases

costly resources and lowers the cost structure of the firms remaining in the industry. For the firms

remaining, the longrun average cost falls from the initial increase (that is, LAC) to LAC" and a firm's

shortrun marginal cost falls from the initial increase (that is, SMC) to SMC'\ Corresponding to SMC is

the shortrun industry supply function, S"S'\ At point B, S"S" intersects the consumer demand function D

at price P2. At price P2, the typical firm remaining in the industry produces output level ^2- Since firms

earn zero longrun profits, the equilibrium is stable and point B represents one point on the new longrun

supply function LS".

In this first case, an increase in the price of energy leads to a contraction of the longrun supply function

from LS to LS'\ a reduction in industry supply from Qj to Q2, and an increase in the retail price from Pj to

Consider the second case in which energy is used by identical firms to produce food output but energy is
Figure 3

Effect of higher energy prices when energy is normal and

fírms are identical

Before firm exit,

firms earn negative

profits.

The exit offirms

alters firms' costs.

QQ Output

Industry output falls

and food prices rise.
Figure 4

Effect of higher energy prices when energy is inferior

and fîrms are identical

?"?S'

Output

Before firm exit,

firms earn negative

profits.

The exit offirms

alters firms' costs.

Industry output falls

and food price rises.
an inferior factor of production. As an inferior factor, less energy is used when an industry produces more

output. Equivalently, as the price of energy rises, the marginal cost of production decreases. Inferior

factors relate to the relative position of production isoquants (Silberberg, 1978, p. 198). The classic

example of an inferior input is unskilled labor. As a firm expands production, it may use more skilled

labor and other inputs in place of unskilled labor. It is important to note that fixed-proportions production

excludes inferior factors, while variable-proportions production allows for factors to be only locally

inferior. Furthermore, classifying a factor as normal or inferior depends on the number of other factors

considered in an analysis. For example, factors might be considered normal if analyzed within an

aggregate framework of two factors, but might be classified as inferior when incorporated within a

disaggregate analysis of multiple factors.

Figure 4 depicts the effect of an increase in the price of energy for the case in which energy is inferior and

firms are identical. As before, the industry's longrun supply of output, L5, intersects the consumer demand

schedule, D, at point A, and ßy and Py denote the initial longrun, market-clearing output quantity and

output price. Initially, the typical firm produces output level q¡ at the point where shortrun marginal cost,

SMC, equals Fy. The firm initially earns zero longrun profits since its longrun average cost, LAC, also

equals P¡. Corresponding to the firm's SMC schedule is the industry's shortrun (quasi) supply function,

SS, which intersects the consumer demand schedule D at a point on the longrun supply schedule LS.

When the price of energy rises, the firm's longrun average cost rises from LAC to LAC\ Because energy is

an inferior factor, however, each firm's shortrun marginal cost falls from SMC to SMC\ Corresponding to

this decHne is the expansion of the industry's shortrun quasi-supply function from SS to S'S\ However,

the intersection of S'S' with the demand schedule D is not stable because firms earn negative longrun

profits as the initial output price, P¡, falls below longrun average cost LAC\ As in the previous analysis,

firms exit the industry.

As in the previous case, firm exit reduces industry supply and releases costly resources. The longrun

average cost of the typical firm that remains rises to LAC (< LAC) and produces ^2 units of output.

Associated with firms' shortrun marginal cost, SMC'\ is the new, shortrun industry supply function S''S".

Since firms earn zero profits at ^2» the intersection of S"S" with the consumer demand schedule D at point

B represents a point on a new longrun supply function, LS'\ Figure 4 suggests that if firms are identical,

an increase in the price of energy when energy is an inferior factor leads to a contraction of the longrun

industry supply from Qj to Q2 and an increase in output price from Pj to P2.

The longrun result that higher nonfarm input prices lead to higher competitive food prices regardless of

whether energy is a normal or inferior factor owes to the assumption that all firms are marginal firms. In

the WH model, however, some firms are marginal and some are inframarginal. Inframarginal firms hold

fixed assets, such as location or entrepreneurial capacity (Friedman, 1976; Panzar and Willig, 1978), that

provide them with a cost advantage over marginal firms. The introduction of inframarginal firms may alter

the relationship between nonfarm input prices and retail food prices.

Today's pork industry may be viewed as an industry consisting of both marginal and inframarginal firms.

Recent changes in the vertical coordination among firms in the Southeast may reflect an entrepreneurial

capacity that exceeds the capacity of firms in the Midwest. The WH model provides insight into why one

would expect the two groups of firms to respond differently to changing market conditions.

12
The simplest structure is one in which an industry consists of two groups of firms. The first group consists

of identical marginal firms, and the second consists of identical inframarginal firms. The group of

marginal firms responds to changes in input price according to figure 3 (for a normal factor) or figure 4

(for an inferior factor). In either case, an increase in the price of an input leads the group of marginal firms

to reduce supply, placing upward pressure on consumer prices.

The longrun response of the group of inframarginal firms to an input price increase is different. If the

input is normal, the marginal cost of inframarginal firms rises, but firms do not exit because longrun

average costs are below the output price (that is, their fixed assets earn rents). The increase in marginal

costs, however, induces inframarginal firms to produce less so that both the inframarginal and marginal

firms reduce supply and retail food prices unambiguously rise.

If the input is inferior, the industry response is less clear because the response of marginal and

inframarginal firms places opposite pressure on retail food prices. Figure 5 illustrates the response of

inframarginal firms when the price of the inferior energy input rises. Point A represents the initial industry

equilibrium in which the group of inframarginal firms produces Qj units of output at price Pj, and the

typical inframarginal firm produces qj units of output. At the point SMC = Py, inframarginal firms earn

positive rents (since Pj >LAC at qj) because of the fixed asset. Associated with SMC is the industry's

shortrun (quasi) supply function, SS. When the price of an inferior input rises, firms' longrun average

costs rise from LACio LAC\ but firms' shortrun marginal costs fall from SMC to SMC\ The group of

inframarginal firms expands shortrun industry supply from SS to 5'5". While longrun average costs rise,

inframarginal firms do not exit the industry. The reduction in marginal cost expands the supply of the

inframarginal firm from q¡ to ^2» and the supply of the group of inframarginal firms rises from Q¡ to Q2.

The change in total industry supply is ambiguous: the response of marginal firms reduces industry supply,

and the response of inframarginal firms increases industry supply. Hence an increase in the price of an

inferior factor has an ambiguous effect on consumer prices.

The conceptual analyses presented in this section indicate that estimates of both the magnitude and

direction of changes in retail- and farm-level prices depend on assumptions regarding the production

function for food.

Empirical Analyses

Retail food prices and farm prices change for three very general reasons. First, consumer demand

functions shift either because of a change in consumer preferences or because of a change in an exogenous

variable such as income. Second, the supply of farm ingredients changes, inducing a shift in the farm

supply function. Third, the supply of nonfarm inputs changes, causing nonfarm input prices to change.

This section presents empirical estimates of changes in retail food prices and farm prices associated with

shifts in consumer demand, farm supply, and nonfarm input prices. Our results suggest that the magnitude

and direction of price changes depend on whether food production is modeled as fixed- or variableproportions.

Effects of Shift in Consumer Demand

Table 1 reports estimates of the percentage change in the ratio of the retail-to-farm price caused by an

exogenous, 1-percent increase in the industry's retail price. The retail price is exogenous because it is

caused by an exogenous upward shift in consumer demand with no consumer substitution among other

13
Figure 5

Effect of higher energy prices on inframarginal firms

when energy is inferior

^1 ^2

Inframarginal firms earn

rents and expand

production as marginal

costs fall.

LS'

Q Q Output

Output rises exerting

downward pressure

on food prices.
retail food products. Wohlgenant (1994) analyzed the effect of such a change when studying the

transmission of shifts in consumer demand on farm prices. The results reported in table 1 suggest that the

effect of an exogenous change in consumer demand very much depends on whether food is assumed to be

produced according to fixed- or variable-proportions production.

The fixed-proportions results suggest that an exogenous expansion of consumer demand leads to a

narrowing of the price spread in percentage terms. If input proportions are fixed, a 1-percent exogenous

increase in retail price causes the farm price to increase by the inverse of the farm share. Fixed-proportions

production implies that farm prices rise by more than retail prices and reflects a full-pass through of a retail

price increase to farm prices.

The variable-proportions results suggest that shifts in consumer demand are less than fully passed through

to the farm sector. The results suggest that as consumers increase demand, farm prices rise and the farm

ingredients used in food production become relatively more expensive than nonfarm inputs. Given

variable-proportions production, food producers reduce the proportion of the relatively more expensive

farm ingredients used in food. The results in table 1 suggest that under variable proportions, producers'

demand for farm ingredients rises but by less than it would under fixed proportions. Under variable

proportions, farm prices rise by less than retail prices and widen with increases in consumer demand.

More specifically, table 1 suggests that for five of the eight industries, an exogenous increase in consumer

demand leads to a widening of spreads in percentage terms. For the beef, pork, and poultry industries, the

predicted decline in the spread is less than the decline predicted by fixed proportions. That higher retailto-farm price spreads result from rising retail prices is a corollary of the empirical finding that consumers

pay higher markups for higher priced retail food products (George and King, 1971).

Effects of Shift in Farm Supply

Table 1 reports estimates of the percentage change in the retail price and retail-to-farm price ratio caused

by a 1-percent increase in farm supply. The results suggest that under variable proportions, an increase in

farm supply causes a smaller reduction in the retail price and a smaller spread between the retail and farm

price than it would under fixed proportions. The differences are attributed to differences in the elasticity of

an industry's demand for farm ingredients implied by fixed- and variable-proportions production.

An increase in farm supply leads to a reduction in the marginal cost of food production and food prices and

an expansion of industry output. To induce the industry to employ the additional farm supply, marketdetermined farm prices fall. The magnitude by which farm prices fall depends on whether food is

produced in fixed or in variable proportions.

If production is fixed proportions, the ratio of nonfarm-to-farm inputs remains constant for any level of

output. For a given fixed ratio, the market's farm price will fall some to induce the industry to employ the

additional farm supply. If, on the other hand, production is variable proportions, any decline in the farm

price will be accompanied by an increase in demand for farm ingredients and an increase in farm price.

Hence, the decline in farm price caused by an expanding farm supply is less under variable proportions

than it is under fixed proportions. The estimates reported in table 1 reflect this difference as farm prices

fall by less and price spreads widen by less under variable proportions than under fixed proportions.

15
Table l-Comparisons of fixed- and variable-proportions estimates

Retail food price Retail-to-farm price

1-percent

exogenous change in:

Fixed

proportions

Variable

proportions

Fixed

proportions

Variable

proportions

Consumer food price:

Beef and veal

Pork

Poultry

Eggs

Dairy

Processed fruits and vegetables

Fresh fruit

Fresh vegetables

Farm supply:

Beef and veal

Pork

Poultry

Eggs

Dairy

Processed fruits and vegetables

Fresh fruit

Fresh vegetables

Nonfarm input price:

Beef and veal

Pork

Poultry

Eggs

Dairy

Processed fruits and vegetables

Fresh fruit

Fresh vegetables

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

-1.2878

-1.5470

-1.3748

-10.718

-4.7438

-3.2103

-8.4962

-4.4924

0.35

0.45

0.48

0.38

0.53

0.80

0.68

0.67

Percent change

1.0 -0.5385

1.0 -0.8182

1.0 -0.9231

1.0 -0.6129

1.0 -1.1277

1.0 -4.000

1.0 -2.1250

1.0 -2.0303

0.8802 0.6934

1.1277 1.2658

1.2765 1.2690

4.0010 6.5692

0.7616 5.3494

0.4906 12.841

0.8181 18.054

0.7958 9.1208

0.3722 -0.1885

0.4185 -0.3682

0.2054 -0.4431

0.7954 -0.2329

0.9394 -0.5976

1.0203 -3.2000

0.9461 -1.4450

1.0205 -1.3603

-0.0517

-0.3254

-0.7859

0.3978

0.6582

0.9333

1.0199

0.4632

0.4743

0.9227

1.1787

2.4528

0.8597

-0.3245

-0.6543

1.6157

0.3386

0.4755

0.7331

0.1244

0.0688

0.0411

-0.0145

-0.0429

Effects of Shift in Nonfarm Input Price

Table 1 also reports estimates of the percentage change in the ratio of retail-to-farm prices caused by a 1-

percent increase in the Food Marketing Cost Index (FMCI). The FMCI (Elitzak, 1996) represents the

average price of an aggregate nonfarm input used in food production. In both the fixed- and variableproportions models, an increase in the FMCI causes an increase in the marginal cost of food production, an

increase in the retail price of food, and a reduction in the quantity of food consumed. In the fixed- and

variable-proportions models, the food-producing sector reduces supply. The major difference between the

models is the adjustment in the demand for farm ingredients.

Since the farm input is normal in both models, the industry's demand for farm ingredients falls as

production falls. To induce an industry to use less farm ingredients, farm prices rise. Under the fixedproportions model, the percentage increase in the farm price exceeds the percentage increase in the retail

food price, as the percentage change in the retail-to-farm price ratio declines. Because variable-proportions

16
producers can change their proportion of farm ingredients, farm prices may rise by less than fixed

proportions to induce the same decrease in the demand for the farm ingredients. This effect is reflected in

table 1 as farm prices rise by less than retail prices.

Conclusions

Economic theory suggests consumer demand shifts and shifts in farm and nonfarm input supply affect

retail-food and farm-level prices. This report reminds readers that the assumption regarding the production

function for food greatly affects the economic analysis of such shifts. While food and farm price analyses

are often based on the fixed-proportions production function, this bulletin repeats the warning of previous

studies (for example, Wohlgenant and Haidacher, 1989) that such analyses impose undue restrictions on

key longrun price relationships. ERS could point to the theoretical and empirical results presented in this

and previous studies (for example, Wohlgenant and Haidacher, 1989) as it gives more serious

consideration to a more general, variable-proportions price analysis.

Fixed-proportions production models have become part of the fabric of food and farm price analyses.

Although the approach suggests some simple and intuitive price relationships, it is important to remember

that food and farm price data have repeatedly failed to support such relationships (Wohlgenant, 1994,

1989; Wohlgenant and Haidacher, 1989; George and King, 1971). Some empirical results associated with

the fixed-proportions model presented in this report are questionable. While one cannot rule out the

possibility that rising nonfarm input prices or expanding consumer demand leads to narrowing retail-tofarm price spreads, it may be at least as likely that such predictions stem from the restrictions associated

with fixed-proportions production as they do from a refutation of efficient food markets.

A serious error would be to infer that because the competitive, fixed-proportions estimates reported in this

study deviate from patterns observed in the data, food markets are inefficient. Such inference might be

reinforced with information on widening retail-to-farm price spreads, the industrialization of the food

sector, and measures of systematic positive profits earned by the food sector. The competitive, variableproportions estimates appear to conform with observations because it explains why, in competitive

markets, increases in consumer prices are not fully passed through to farmers, why nonfarm input price

increases lead to widening retail to farm price spreads, why an expanding farm supply results in farm

prices falling by more than retail prices, and how firms in a competitive industry could earn positive

longrun rents. Furthermore, the variable-proportions estimates are based on the observed price series that

policymakers, analysts, and the public are interested in predicting rather than on the underlying fixed ratios

of input and output quantities.

17
References

Elitzak, H. Food Cost Review, 1995. Food and Consumer Economics Division, U.S. Dept. Agr.,

Economic Research Service. Agricultural Economic Report No. 729 (April 1996).

Friedman, M. Price Theory. Hawthorne, NY: Aldine Publishing Co., 1976.

George, P.S., and G.A. King. Consumer Demandfor Food Commodities in the United States with

Projectionsfor 1980. Giannini Foundation Monograph No. 26. University of California, Berkeley, 1971.

Hanson, K., S. Robinson, and G. Schlüter. "Sectoral Effects of a World Oil Price Shock: Economywide

Linkages to the Agricultural Sector," Journal ofAgricultural and Resource Economics. 18(1), (1993):

666-673.

Lee, C, and G. Schlüter. "Growth and Structural Change in U.S. Food and Fiber Industries: An

Input-Output Perspective," American Journal ofAgricultural Economics. 75 (1993): 666-673.

O'Brien, P.M. Implicationsfor Public Policy, Food and Agricultural Markets: The Quiet Revolution.

Lyle P. Schertz and Lynn M. Daft (eds.). Washington, DC: National Planning Association Report No. 270,

1994.

Panzar, J.C., and R.D. Willig. "On the Comparative Statics of a Competitive Industry with Inframarginal

Firms," American Economic Review. 68 (June 1978): 474-478.

Putnam, J.J., and J.E. Allshouse. Food Consumption, Prices, and Expenditures, 1996. U.S. Dept. Agr.,

Economic Research Service. Statistical Bulletin No. 928 (April 1995).

Schroeter, J.R. "Estimating the Degree of Market Power in the Beef Packing Industry," Review of

Economics and Statistics. 70(1988): 158-62.

Silberberg, E. The Structure ofEconomics: A Mathematical Analysis. New York: McGraw-Hill, 1978.

Tomek, W.G., and K.L. Robinson. Agricultural Product Prices. Chapter 6. Ithaca, NY: Cornell

University Press, 1981.

Wohlgenant, M.K. "Retail to Farm Price Linkages to a Complete System of Demand Functions: Extension

to Disaggregated Marketing Costs and Tests for Market Power." An unpublished report in cooperation

with the Economic Research Service (1997).

. "Impact of Changes in Consumer Demand on Farm-Level Demand for Food," Policy

Implicationsfor U.S. Agriculture ofChanges in Demandfor Food. H. Jensen and J. Chalfant (eds.). Iowa

State University Press, CARD (1994).

. "Demand for Farm Output in a Complete System of Demand Functions," American Journal of

Agricultural Economics. 71(2), (December 1989): 241-252.

, and R.C. Haidacher. Retail to Farm Linkage for a Complete Demand System ofFood Commodities. U.S. Dept. Agr., Economic Research Service. Technical Bulletin Number 1775, December 1989.
Appendix

This appendix reports the formulas used to construct the fixed- and variable-proportions estimates of the

percentage change in the retail-to-farm price ratio reported in table 1. Both sets of estimates assume that

output markets and all input markets are perfectly competitive. Both sets of estimates incorporate

information on farm shares and own-consumer demand elasticities. The farm share values used in the

computations are beef (0.65), pork (0.55), poultry (0.52), eggs (0.62), dairy (0.47), processed fruits and

vegetables (0.20), fresh fruit (0.32), and fresh vegetables (0.33). The own-consumer demand elasticities

used are beef (-0.7765), pork (-0.6464), poultry (-0.7274), eggs (-0.0933), dairy (-0.2108), processed fruits

and vegetables (-0.3115), fresh fruit (-0.1177), and fresh vegetables (-0.2226). The own-consumer

demand elasticities are diagonal elements of the system of demand equations reported in Wohlgenant and

Haidacher(1989).

In addition, the variable-proportions results reported in table 1 are based on the same econometric

estimates of the quasi-reduced form retail- and farm-price equations used by Wohlgenant (1994). Letting

Pffj* denote the percentage change in the retail price of the jth industry, p^/, the percentage change in the

farm price of theyth industry, F*, the percentage change in theyth industry's farm supply, w*, the

percentage change in the Food Marketing Cost Index, Z*, thejth industry's consumer demand shifter

(expressed as a sum of percentage changes) as defined in Wohlgenant (1989) and Wohlgenant and

Haidacher (1989), the estimated quasi-reduced form for retail prices is:

Beef and veal p¡,* = -0.850 F* + 0.340 w* + 0.850 Z^*

Pork PJ,2 = -L078 F/ + 0.303 w* + 1.078 Z^""

Poultry PJ,; = -7.226 F/ + 0.108 w + 7.226 Z^*

Eggs PJ,; = -3.982 F; + 0.628 w + 3.982 Z/

Dairy pj,* = -0.760 F¡ + 0.840 w* + 0.760 Z^*

Processed fruits and vegetables p^^* = -0.488 F¡ + 0.997 w* + 0.770 Z/

Fresh fruit p^/ = -0.823 F/ + 7.002 w* - 0.760 Zy^

Fresh vegetables p¡,* = -0.789 F/ + 0.824 w* + 0.789 Z/

and for farm prices is:

Beef and veal p^* = -1.308 F/ - 0.076 w* + 1.308 Z;*

Pork p,; = -L960 F/ - 0.267 w* + 7.960 Z/

Poultry PP¡ = -2.358 F/ - 0.775 w* + 2.358 Z^*

Eggs p^; = -6.423 F; + 0.401 w* + 6.423 Z/

Dairy p^; = -7.67S F/ + 0.659 w* + 7.67S Z5*

Processed fruits and vegetables p^^* = -0.161 F/ + 0.934 w* + 0.273 Z^*

Fresh fruit Pf./ = -0.169 Fj* + 7.020 w* -0.170 Zy*

Fresh vegetables p^/ = -2.397 F/ + 0.468 w* + 2.397 Z/

The fully-reduced-form estimates are obtained by combining the above estimates with the estimated system

of consumer demand equations reported in Wohlgenant and Haidacher (1989) according to equations 30a

and 30b in Wohlgenant and Haidacher (1989), or (19a) and (19b) in Wohlgenant (1989). Estimates of the

variable-proportions effects reported in table 1 are fully reduced-form estimates combined according to the

simulations described in the next three sections.

In the following discussion, the percentage change in the retail price is denoted as p^*, and the percentage

19
change in the retail-to-farm price ratio is denoted as O?^ I PpY = p^ - /?/. The particular computations

associated with the three simulations are described in the following sections.

Effects of Shift in Consumer Demand

In this simulation, consumer demand in each market expands so that the retail price in each market rises by

1 percent. The simulation assumes no consumer substitution associated with the exogenous increase in

demand across the eight markets. Since p^ = 1 exogenously, the following discussion focuses on the

computation of percentage change in farm prices used in the computation of the retail-to-farm price

spread, 1 - /?/.

Under the fixed-proportions assumption of one farm and one nonfarm input, equation 6 in the text

simplifies to p^ = s^ pp + {\ -Sp)w * in which w* denotes the percentage increase in nonfarm input prices,

and 5;r denotes the cost share of farm commodities. Since w* = 0and/7^* = 1, /?/ = \lsp. The fixed

proportions estimates of the effect of a shift in consumer demand reported in table 1 are then 1 - {\lsp).

The variable proportions computation is the same computation reported by Wohlgenant (1994), and it is as

follows. Under the variable-proportions model, it is necessary to solve for the shift in consumer demand in

each industry that will result in an exogenous 1-percent increase in retail price. In the variable proportions

model, the industry's quantity-dependent demand functions take the form Q* = '"^PR + Z*where

71 represents the magnitude of the own price elasticity, and Z * represents the demand shifter associated

with the quantity-dependent formulation. The vertical shift in demand, then, is found by setting p^ = 1

(in the demand equation) and solving 0 = -n + Z\or Z* = n. Hence, the 8-by-l vector of (magnitudes)

of own-consumer-demand price elasticities (n) are the estimated total shifts in demand. According to

equations 30b in Wohlgenant and Haidacher (1989) or equations 19b in Wohlgenant (1989)

Pf = ^(el(I^ - A^y^A^ + IJn, and p* - p* = Ig - A^(eli[^ - A^Y^A^ + [JlL, whereIgis an 8-by1 vector of ones.

Effects of Shift in Farm Supply

In the fixed-proportions analysis of an exogenous 1-percent increase in farm supply, once an estimate of

Pp is obtained, the percentage change in the retail price is p^ = SpPp and the percentage change in the

retail-to-farm price ratio is/7^* - Pp = {Sp - \)pp. In the fixed-proportions analysis, the estimate of pp is

computed from the relationship E^ = SpC^ or £^ = F Ip* in which E^ is the price elasticity of farm

demand, F *is the percentage change in the farm supply, ^^ = Ô *IPR is the own-retail price elasticity, and

ß *is the percentage change in consumer food demand. Under the assumption of fixed proportions, a 1-

percent increase in farm supply implies p/ = (5*^^) ^ and/7^* -/?/ = {Sp - \){Spep)~\

In the variable-proportions model, a 1-percent increase in the farm supply of any market affects prices in

all markets. This is reflected in equations 30a and 30b in Wohlgenant and Haidacher (1989) and

Wohlgenant (1989) which imply/7^* = {{^ - A^y^A^ and

PR - PF = (L ~ â^y^A^ - (á^(L ~ ^^i^'^^^^-

Effects of Shift in Nonfarm Input Price

Under the fixed-proportions assumption of one farm and one nonfarm input, equation 6 simplifies to

PR '^ ^FPF ^ (1 ~Sp)y^ * in which w* denotes the percentage increase in nonfarm input prices and Sp denotes

the cost share of farm commodities. Hence, when w* - \ p* = {\ - Sp). Then, given the relationship

20
ED = SpCj) (see the "Effects of Shift in Farm Supply" section for definitions), and given the restriction that

the percentage change in food consumption is equal to the percentage change in farm demand, it follows

PF " ^F^PR' The corresponding estimates of P;J* - pp under fixed proportions are then

(1 - Sp) (1 - 1/^^).

Under the variable proportions assumption, estimates of the percentage change in retail price and the

difference in the percentage change in the retail and farm price caused by a 1-percent exogenous increase

in the price of the single nonfarm input are computed according to equations 30a and 30b in Wohlgenant

and Haidacher (1989) or equations 19a and 19b of Wohlgenant (1989). In particular, the percentage

change in the retail price is computed as

p; = (/, - A^r'A^ and p^ - p; = (7^ - A^y'A^ - {A^(I_^ - A^Y'A^^A^).

21