Compensation and the Twin Producer Gains from Production Quotas

doi:10.4236/tel.2011.13015

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Theoretical Economics Letters, 2011, 1, 70-72

doi:10.4236/tel.2011.13015 Published Online November 2011 (http://www.SciRP.org/journal/tel)

Compensation and the Twin Producer

Gains from Production Quotas

Troy G. Schmitz1, Andrew Schmitz2

1Morrison School of Agribusiness and Resource Man agement, Arizona State University, Mesa, Arizona

2Food and Resource Econom ics, IFAS, University of Florida, Gainesville, USA

E-mail: [email protected], [email protected]

Received June 21, 2011; revised August 12, 2011; accepted August 22, 2011

Abstract

The limited theory on production quotas focuses on the impact of introducing quotas when otherwise the

market would be competitive. We develop a model also on the effect of removing quotas, and then consider

the combined effects of both introducing and removing quotas. Under the value of quota approach, the

amount of money spent by the government for the buyout (i.e., value of quota) is equal to the sum of the net

gain to producers when the quota was introduced plus the net gain if it were removed. Compensation is the

key to a quota buyout, as producers have little interest in politically supporting a government compensated

buyout unless they gain by so doing.

Keywords: Compensation, Producer Gains, Production Quotas

1. Introduction

Theoretical studies on production quotas, such as those

by Wallace [1]; Johnson [2]; Rucker, Thurman, and Sum-

ner [3]; and Just, Hueth, and Schmitz [4], focus on the

impact of production quotas compared to a competetive

situation. In addition, Schmitz and Schmitz [5] ana-

lyzed the impacts of removing production quotas with an

empirical application to the removal of the U.S. produc-

tion quota for peanuts. They found that farmer compen-

sation for the buyout was based on the value of quota

approach. Farmers will lobby for the method of payment

that leads to their greatest benefit. Successful political

rent-seeking behavior by farmers will lead to an outcome

from a buyout that favors farmers relative to taxpayers

(Vercammen and Schmitz [6]; Schmitz, Furtan, and Bay-

lis [7]; Schmitz and Schmitz [5]). In this paper, we con-

sider the twin producer gains from both the introduction

and removal of quotas. Under one approach to compen-

sation, producers gain from both the implementation of a

quota and its removal. Under the value of quota approach,

for example, the value of quota at the time of removal

exactly equals the twin producer gains from the quota

(i.e., the gain from introducing the quota plus the gain

from removing it). Quotas when implemented can have a

much larger impact on the welfare of producers than

when they are removed, even though gains are present

when quotas are introduced and are present when they

are removed. In addition, consumers generally have

much more to gain from a production quota buyout than

do producers.

2. Theoretical Model

We present the theoretical discussion of the impact of

production quotas on 1) producer welfare when quotas

are introduced; 2) the effect of removing quotas; and 3)

the combined impact of both introducing and removing

quotas. In our analysis, we consider two periods where in

period 1 the quotas are introduced and in period 2 they

are removed.

2.1. Period 1

Consider Figure 1 where S is the supply schedule for

good x and D is the domestic demand. In the absence of a

quota, the competitive price is p0 and the corresponding

output is q0. Suppose we introduce a production quota

that restricts output to q1: price increases from p0 to p1.

As a result, producers gain (p1p0da – dcb)—a result often

ignored in the discussion of production quotas. Producer

welfare results are derived by comparing the competitive

equilibrium price p0 and quantity q0 with the quota price

p1 and quantity q1.

T. G. SCHMITZ ET AL.

Figure 1. Government quota buyout.

Under the quota, consumers pay a higher price for the

product which translates into a transfer to producers. The

cost to consumers from the quota is (p1p0ba) while the

net societal cost is (acb).

2.2. Period 2

Here the government terminates (through a govern-

ment-financed buyout compensation scheme) the quota

program to restore price p0 and quantity q0. W e examine

two extreme alternatives that the government might use

in making compensation payments: 1) the government

pays the value of quota (Vercammen and Schmitz [6];

Schmitz and Schmitz [5]), which is (p1p2ca), or 2) the

government pays the producers (p1p0da – dcb), which is

the gain from quota. Under 1), the net producer gain is

positive, (p0p2cd + dcb), and is equal to (p0p2cb). Under

2), the net producer gain is zero.

2.3. Combined Effects

There is no literature that analyzes the combined effect

of both introducing and removing quotas. This is not

surprising given that very little is written on th e theory of

quota buyouts. What is the combined effect on producers

from both the introduction of the quota and from its re-

moval? Under either approach to compensation dis-

cussed above, the net producer gain from the combined

introduction and removal of the quota is at least as great

as a gain from the introduction of the quota alone. The

results are as follows:

Proposition (1): If producers are paid the value of

quota, they gain from quota removal. However, they also

gained at the time that the quota was introduced (the

value of quota can be far greater than what produ cers can

gain from its removal). For a two-period analysis, given

a production quota and identical demand elasticities and

supply elasticities for the two periods, the producer gain

from introducing the quota plus the gain from removing

it is equal to the value of quota. This is the amount that

the government pays for the quota buyout. This can be

demonstrated as follows:

1) The gain to producers from the quota buyout is

(p0p2cd + dcb)

2) The net producer gain from introducing the quota is

(p1p0da – dcb)

3) The sum of items 1 and 2 above equals (p1p0da +

p0p2cd)

4) Item 3 above equals the value of quota (p1p2ca)

Proposition (2): If producers are paid the gains from

quota, the net producer gain is zero. However, they

gained at the time that the quota was introduced. For a

given production quota and identical demand elasticities

and supply elasticities, the producer gain from introduc-

ing the quota plus the gain from removing it is equal to

the gains from quota. This is the amount that the gov-

ernment pays for the quota buyout. This can be demon-

strated as follows:

1) The net producer gain from the quota buyout is

(p1p0da – dcb) + (–p1p0da + dcb)

2) The net gain to producers from quota implementa-

tion is (i1p0da – dcb)

3) The sum of items 1 and 2 above equals (p1p0da –

dcb)

4) Item 3 above equals the gains from quota (p1p0da –

dcb)

In the above, quotas when they are implemented gen-

erate producer gains that are paid for through higher

consumer prices. However, when they are removed (and

paid under the value of quota), the producer gains result

from treasury expenditures from the buyout.

In our model, given identical supply and demand con-

ditions, when the quota is implemented and when it is

removed, the value of quota reflects producer gains from

both the introduction and removal of the quota—not just

the value to producers when removing the quota. Gener-

ally, the gains from the introduction of quota are greater

than the gains from its removal.

3. Concluding Comments

It is common with quota buyouts that the payout be

based on the value of quota approach, where producers

gain from the buyout and also gain at the expense of

taxpayers. We emphasize that the producers gain from

both the removal of the quota and its introd uction. Under

certain conditions, the sum of these two gains is exactly

equal to the value of the production quota that exists

T. G. SCHMITZ ET AL.

when the quota is removed. Quota values are not a mea-

sure of the net gain to producers from a quota buyout

even though many policy analysts continue to believe so.

When assessing the magnitude of compensation, it is

important to consider both the introduction and removal

of quotas, otherwise one is left with the wrong impress-

sion of the size of the payout based on the value of the

quota. When considering both of the components, the

size of the compensation can be large. But, this result is

not surprising in view of the many packages that have

been put together to compensate losers from a change in

policy (Schmitz and Zerbe [8]).

4. References

[1] T. D. Wallace, “Measures of Social Costs of Agricultural

Programs,” Journal of Farm Economics, Vol. 44, No. 2,

1962, pp. 580-599. doi:10.2307/1235863

[2] P. R. Johnson, “The Social Cost of the Tobacco Pro-

gram,” Journal of Farm Economics, Vol. 47, No. 2, 1965,

pp. 242-255. doi:10.2307/1236572

[3] R. Rucker, W. Thurman and D. Sumner, “Restricting the

Market for Quota: An Analysis of Tobacco Production

Rights with Corroboration from Congressional Testimo-

ny,” Journal of Political Economy, Vol. 103, No. 1, 1995,

pp. 142-175. doi:10.1086/261979

[4] R. E. Just, D. L. Hueth and A. Schmitz, “The Welfare

Economics of Public Policy: A Practical Approach to

Project and Policy Evaluation,” Edward Elgar Publishing,

Cheltenham, 2004.

[5] A. Schmitz and T. G. Schmitz, “Benefit-Cost Analysis:

Distributional Considerations under Producer Quota Bu-

youts,” Journal of Benefit-Cost Analysis, Vol. 1, No. 1,

2010, Article 2.

[6] J. A. Vercammen and A. Schmitz, “Supply Management

and Import Concessions,” Canadian Journal of Econom-

ics, Vol. 25, No. 4, 1992, pp. 957-971.

doi:10.2307/135774

[7] A. Schmitz, H. Furtan and K. Baylis, “Agriculture Policy,

Agribusiness, and Rent-Seeking Behaviour,” University

of Toronto Press, Toronto, 2002.

[8] A. Schmitz and R. O. Zerbe Jr., “Applied Benefit-Cost

Analysis,” Edward Elgar Publishing, Cheltenham, 2008.