Partial equilibrium study 20--8-15

PARTIAL EQUILIBRIUM COMPETITIVE
MARKET AND EMPIRICAL APPLICATION
(A micro-economic issue:-PhD seminar work)
BY
OGWUIKE PHILOMENA CHIOMA
LECTURER: DR OBAYELU A.E
August, 2015

INTRODUCTION
Microeconomic models are usually classified as partial and general equilibrium models. Léon
Walras first formalized the idea of a one-period economic equilibrium of the general economic
system, but Antoine Augustin Cournot and Alfred Marshall developed tractable models to
analyze an economic system.
This study is organized in two parts. Part one discusses theories, concepts and framework when
working with partial equilibrium. Part 2 discusses the empirical studies that used partial
equilibrium. Under the empirical review we seek to know if partial equilibrium model has been
used; who used it? And how has it been applied?
PART 1: THEORIES, CONCEPTS AND FRAMEWORK WHEN
WORKING WITH PARTIAL EQUILIBRIUM
This part is organized in 3 sections as follows: Section 1: Demonstrates an understanding of the
concepts of equilibrium, economic equilibrium and types of equilibrium; Section 2: Describe the
applications and limitations of partial equilibrium; Section 3: Differentiate between partial and
general equilibrium.
Section 1: Understanding the concepts of equilibrium, economic equilibrium and types of
equilibrium - Definitions and Concepts
Equilibrium: The word equilibrium is derived from the Latin word “aequilibrium” which means
equal balance. It is use in economics and was imported from physics. In physics it means a state
of even balance in which opposing forces or tendencies neutralize each other. Equilibrium can be

defined as: “A position from which there is no net tendency to move”. Net tendency emphasize
the fact that it is not necessarily a state at sudden inertia but may instead represent the
cancellation of power forces. In economics, equilibrium implies a position of rest characterized
by absence of change.
Economic equilibrium: Economic equilibrium is a state where economic forces (such as supply
and demand) are balanced and in the absence of external influences the (equilibrium) values of
economic variables will not change. For example, in perfect competition, equilibrium occurs at
the point at which quantity demanded and quantity supplied is equal.
General Equilibrium: General equilibrium theory studies supply and demand fundamentals in
an economy with multiple markets, with the objective of proving that all prices are at
equilibrium. The theory analyzes the mechanism by which the choices of economic agents are
coordinated across all markets.
Competitive Market:
What is a market? A market is one of the many varieties of systems, institutions, procedures,
social relations and infrastructures whereby parties engage in exchange. While parties may
exchange goods and services by barter, most markets rely on sellers offering their goods or
services (including labor) in exchange for money from buyers (Wikipedia).
When is a market said to be competitive? A competitive market is characterized by many
buyers and sellers. And buyers take the market price as given and determine their supply and
demand accordingly. The market price is determined so that market supply equals market

demand. A good is transferred if and only if the price is paid. Sellers and buyers have the same
information about goods.
Market Equilibrium: Market equilibrium refers to a condition where a market price is
established through competition such that the amount of goods or services sought by buyers is
equal to the amount of goods or services produced by sellers. This price is often called
the competitive price or market clearing price and will tend not to change unless demand or
supply changes and the quantity is called "competitive quantity" or market clearing quantity.
Market Equilibrium can be altered exogenously. Exogenous shift in supply or demand may be
through changes in technology or tastes or institutional policy conditional that there are
no endogenous forces leading to the changes in the price or the quantity. Perfect competition in
the goods market, and a perishable good imply that all output produced is sold.
Disequilibrium: Market Disequilibrium occurs where demand and supply are out of balance.
Such situations create shortages and oversupply. The regime price is disequilibrium price.
Partial Equilibrium: Partial equilibrium is a condition of economic equilibrium which takes
into consideration only a part of the market, ceteris paribus, to attain equilibrium. According to
George Stigler, "A partial equilibrium is one which is based on only a restricted range of data, a
standard example is price of a single product, the prices of all other products being held fixed
during the analysis. Partial equilibrium analysis uses supply and demand curves in a particular
market and ignores effects that occur beyond these markets. Economic analysis under partial
equilibrium focuses on policy effects within a single market and does not address effects external
to the market. A partial equilibrium analysis either ignores effects on other industries in the

economy or assumes that the sector in question is very, very small and therefore has little if any
impact on other sectors of the economy.
Examples of partial equilibrium
a. Consumer’s Equilibrium: With the application of partial equilibrium analysis, consumer’s
equilibrium is indicated when he is getting maximum aggregate satisfaction from a given
expenditure and in a given set of conditions relating to price and supply of the
commodity.
The conditions are: 1) the marginal utility of each good is equal to its price (P), i.e.
And (2) the consumer must spend his entire income (Y) on the purchase of goods, i.e.
It is assumed that his tastes, preferences, money income and the prices of the goods he wants to
buy are given and constant.
Factors of production, i.e., land, labor, capital, and entrepreneurs are in equilibrium when they
are paid the maximum possible so as maximize the income. Here the Price = Marginal Revenue
Product. At this price it does not have any enticement to look for employment anywhere else.
Producers’ equilibrium occurs when they maximize their net profit subject to a given set of
economic situations.

A firm's equilibrium point is when it has no inclination in changing its production neither more
nor less.
Equilibrium for an industry happens when there is normal profit made by an industry. It is such
a situation when no new firm wants to enter into it and the existing firm does not want to exit. In
the short run: Marginal Revenue = Marginal Cost i.e. MR=MC
In long run: Marginal Cost = Marginal Revenue = Average Revenue = Long run Average Cost
i.e. LMC=MR=AR=LAC at its minimum are the conditions of equilibrium. It means that a firm
is earning only a "normal profit" and has no intension to leave the industry.
In all these cases; those who have incentive to change it have no opportunity and those who have
the opportunity have no incentive.
Characteristics of partial Equilibrium in a competitive market
Only one price prevails in the market for a single product where the quantity of goods purchased
by a buyer = total quantity produced by different firms. All the firms produce till that level
where Marginal Cost=Marginal Revenue, and sells the product at market price ruling at that
point of time.
ii. The quantity of factors which its owners want to sell should be equal to the quantity which
the entrepreneurs are ready to hire.

Assumptions
The perfectly competitive market holds under the following assumptions:
Commodity price is given and constant for the consumers.
Consumers' taste and preferences, habits, incomes are also considered to be constant.
Prices of prolific resources of a commodity and that of other related goods (substitute or
complimentary) are known as well as constant.
Industry is easily availed with factors of production at a known and constant price compliant
with the methods of production in use.
Prices of the products that the factor of production helps in producing and the price and quantity
of other factors are known and constant.
There is perfect mobility of factors of production between occupation and places.
Partial Equilibrium Analysis
Partial or particular equilibrium analysis, also known as micro economic analysis, is the study of
the equilibrium position of an individual, a firm, an industry or a group of industries viewed in
isolation. In other words, this method considers the changes in one or two variables keeping all
others constant, i.e., ceteris paribus (others remaining the same). The ceteris paribus is the crux
of partial equilibrium analysis. Partial equilibrium analysis is the analysis of an equilibrium
position for a sector of the economy or for one or several partial groups of the economic unit
corresponding to a particular set of data. Partial equilibrium implies that the analysis only
considers the effects of a given policy action in the market(s) that are directly affected. That is

the analysis does not account for the economic interactions between the various markets in a
given economy. This is as opposed to a general equilibrium setup where all markets are
simultaneously modeled and interact with each other.
The advantages of partial equilibrium modeling
i.) The main advantage of the partial equilibrium approach to Market Access Analysis is its
minimal data requirement. In fact, they only required data for the trade flows, the trade policy
(tariff), and a couple of behavioral parameters (elasticity).
ii. Another advantage is that it permits an analysis at a fairly disaggregated (or detailed) level.
For example, it allows the study of the effects of the liberalization (for instance) of “Wheat flour
imports by Nigeria, a level of aggregation that is neither convenient nor possible in the
framework of a general equilibrium model. This also resolves a number of “aggregation biases.
Illustrating the aggregation bias
The graphics above illustrates an aggregation bias by considering 2 products (Apples and
Oranges) falling into the same product category (Fruits). Apples face a tariff tA but demand for
apples (DA) is perfectly inelastic. Consequently, tA does not entail welfare cost on the Apples

market since it does not affect the level of imports. On the Oranges market, demand is somehow
elastic but imports face no tariff. Again, there is no welfare cost. Therefore, the protection on the
Fruits market is clearly not associated with welfare cost when analyzing its component level,
while analysis implemented at the Fruits (aggregated) level would conclude that there is welfare
cost the blue stripe triangle because of the aggregation bias.
By the same logic, the partial equilibrium may allow the analysis of the likely impact of trade
agreements more accurately, as the negotiations are conducted at a very disaggregated level.
iii. In general, by virtue of their simplicity, partial equilibrium models tend to be more
transparent and easy to implement. Modeling is straightforward and results can be easily
explained.
The disadvantages of partial equilibrium modeling
1. Since partial equilibrium is only a “partial” model of the economy, the analysis is only
done on a pre-determined number of economic variables. This makes it very sensitive to
a few (badly estimated) behavioral elasticities.
2. Due to their simplicity, partial equilibrium models may miss important interactions and
feedbacks between various markets. In particular, the partial equilibrium approach tends
to neglect the important inter-sectoral input/output (or upstream/downstream) linkages
that are the basis of general equilibrium analyses. It also misses the existing constraints
that apply to the various factors of production (e.g., labor, capital, land…) and their
movement across sectors.
3. It is restricted to one particular portion of the economy. It lacks the ability to study the
interrelations of all the parts of the economy. Partial equilibrium analysis will fail if the

improbable assumptions, which disconnect the study of specific market from the rest of
the economy are not taken into consideration. Partial equilibrium analysis has been
unsuccessful in explaining the outcome of economic disturbance in the market that leads
to demand and supply changes, moving from one market to another and thus instigating
second- and third-order waves of change in the whole economy.
SECTION 2: APPLICATIONS AND LIMITATIONS OF PARTIAL
EQUILIBRIUM
Applications: (a.) In general, if you want to analyze whole economies, interaction between
markets or anything in which you think that the variable (e.g. labor) that you want to analyze is
so important, that it may have serious effects on other markets, one usually uses general
equilibrium models. Therefore, most applications of general equilibrium techniques are currently
in Macroeconomics or Finance.
b.) If you want to analyze a single market (and if you think the effect on other markets is not that
important) or if you want to introduce assumptions that would lead to problems in general
equilibrium models (e.g. oligopoly models), then you probably should use a partial equilibrium
model. Applications of partial equilibrium discusses, when does an individual, a firm,
an industry, factors of production attain their equilibrium points. In partial equilibrium, the
dynamic process is that prices adjust until supply equals demand. It is a powerfully simple
technique that allows one to study equilibrium, efficiency and comparative statics.

c.) In partial equilibrium analysis, the effects of policy actions are examined only in the markets
that are directly affected. Supply and demand curves are used to depict the price effects of
policies. Producer and consumer surplus is used to measure the welfare effects on participants in
the market.
Illustration
If the country is a “large country” in international markets, then the country’s imports or exports
are a significant share in the world market for the product. Whenever a country is large in an
international market, domestic trade policies can affect the world price of the good. This occurs
if the domestic trade policy affects supply or demand on the world market sufficiently to change
the world price of the product. If the country is a “small country” in international markets, then
the policy-setting country has a very small share in the world market for the product—so small
that domestic policies are unable to affect the world price of the good. The small country
assumption is analogous to the assumption of perfect competition in a domestic goods market.
Domestic firms and consumers must take international prices as given because they are too small
for their actions to affect the price.

Differences between partial and general equilibrium
General equilibrium theory is distinguished from partial equilibrium theory by the fact that it
attempts to look at several markets simultaneously rather than a single market in isolation.
Partial Equilibrium General Equilibrium
• Developed by Alfred Marshall • Developed by Léon Walras .
• Related to single variable
• More than one variable or economy as
a whole is taken into consideration
• Based on two assumptions:
Ceteris paribus
Other sectors are not affected due to change in one
sector.
• Based on the assumption that various
sectors are mutually interdependent.
There is an effect on other sectors due to
change in one.
• Other things remaining constant, price of a good is
determined
•Prices of goods are determined
simultaneously and mutually.
Hence all product and factor markets are
simultaneously in equilibrium.

THEORIES WHEN WORKING WITH PARTIAL EQUILIBRIUM
Price theory
Price theory is an economic theory that contends that the price for any specific good/service is
the relationship between the forces of supply and demand. The theory of price says that the point
at which the benefit gained from those who demand the entity meets the seller's marginal costs is
the most optimal market price for the good/service. This is a static analysis which explains the
determination of equilibrium prices of the products and factors in different market categories.
The values of the various variables such as demand, supply, and price were taken to be relating
to the same point or period of time.
Example: The competitive equilibrium
Price of market balance:
P – Price; Q – Quantity demanded and supplied; S – Supply curve; D – Demand curve; P0 –
equilibrium price

A – Excess demand – when P<P0; B – Excess supply – when P>P0
Three basic properties of equilibrium in general have been proposed: Equilibrium property P1:
The behavior of agents is consistent; Equilibrium property P2: No agent has an incentive to
change its behavior.
Equilibrium Property P3: Equilibrium is the outcome of some dynamic process (stability).
In a competitive equilibrium, supply equals demand. Property P1 is satisfied, because at the
equilibrium price the amount supplied is equal to the amount demanded. Property P2 is also
satisfied. Demand is chosen to maximize utility given the market price: no one on the demand
side has any incentive to demand more or less at the prevailing price. Likewise supply is
determined by firms maximizing their profits at the market price: no firm will want to supply any
more or less at the equilibrium price. Hence, agents on neither the demand side nor the supply
side will have any incentive to alter their actions.
To see whether Property P3 is satisfied, consider what happens when the price is above the
equilibrium. In this case there is an excess supply, with the quantity supplied exceeding that
demanded. This will tend to put downward pressure on the price to make it return to equilibrium.
Likewise where the price is below the equilibrium point there is a shortage in supply leading to
an increase in prices back to equilibrium. Not all equilibria are "stable" in the sense of
Equilibrium property P3. It is possible to have competitive equilibria that are unstable. However,
if equilibrium is unstable, it raises the question of how you might get there. Even if it satisfies
properties P1 and P2, the absence of P3 means that the market can only be in the unstable
equilibrium if it starts off there.

In most simple microeconomic stories of supply and demand a static equilibrium is observed in a
market; however, economic equilibrium can be also dynamic. Equilibrium may also be
economy-wide or general, as opposed to the partial equilibrium of a single market. Equilibrium
can change if there is a change in demand or supply conditions. For example, an increase in
supply will disrupt the equilibrium, leading to lower prices. Eventually, a new equilibrium will
be attained in most markets. Then, there will be no change in price or the amount of output
bought and sold — until there is an exogenous shift in supply or demand (such as changes
in technology or tastes). That is, there are no endogenous forces leading to the price or the
quantity.
Concept of economic surplus or total welfare or Marshallian surplus
Consumer surplus or consumers' surplus is the monetary gain obtained by consumers because
they are able to purchase a product for a price that is less than the highest price that they would
be willing to pay. Producer surplus or producers' surplus is the amount that producers benefit by
selling at a market price that is higher than the least that they would be willing to sell for; this is
roughly equal to profit (since producers are not normally willing to sell at a loss, and are
normally indifferent to selling at a breakeven price).

Graphical illustration of Producer’s and consumers’ Surplus in the market
In partial equilibrium the welfare effects on consumers who purchase and the producers who produce in the
market is distinguished by consumer surplus and producer surplus. In Figures 1&2, P= Price; Q = Quantity; D-
Demand Curve and S-Supply Curve
Figure 1: Consumer Surplus
Figure 2: Producer surplus
Consumer surplus
This is the amount that a consumer is willing to pay for a particular good minus the amount that
he actually pays. The amount he is willing to pay should be greater. In Figure 1, P1 is the price
that a consumer is willing to pay for a particular product. But the producer may reduce the price
to P2 expecting either increased buyers or increased purchase by willing buyers. For this same
reason, the producer may further reduce the price to P3, again.

The price keeps on falling until the equilibrium point P’, where the demand and the supply
curves intersect. Hence the consumer surplus for first consumer is P1 - P’, decreasing for the
second consumer to P2 - P’, and so on. Thus the total consumer surplus in the market can be
obtained by summing up the three rectangles. The triangle with the purple outline to the left
indicates that area.
Producer surplus
The producer surplus is the amount that a producer finally receives by selling a particular
product minus the amount he is ready to accept for that good. The amount that the producer
receives should be greater.
If only one unit of the commodity was demanded at the price P1, this becomes the price which
the producer expects to receive. But if two units are demanded, the minimum price at which the
producer would be ready to increase the supply shifts to P2.That means that the price increases
with demand. This continues until the ultimate prevailing market price, P’ obtained by the
intersection of the demand and supply curve in the market. The producer's surplus here would be
initial price minus the final price. And total consumer surplus in the market will be summation of
the three rectangles.
Game theory
This is a kind of welfare theory where Pareto optimality is applied as a measure of efficiency. An
outcome of a game is Pareto optimal if there is no other outcome that makes every player at least
as well off and at least one player strictly better off. That is, a Pareto Optimal outcome cannot be
improved upon without hurting at least one player. This theory is the first fundamental theorem
of welfare economics in the partial equilibrium case. Under economic terms, it states that if the

price p∗ and the allocation (x∗, q∗) constitute a competitive equilibrium, then this allocation is
Pareto optimal. Where p∗ is the equilibrium price received by firms, and x* and q* are the
production inputs and output respectively. This theorem is just a formal expression of Adam
Smith’s invisible hand — the market acts to allocate commodities in a Pareto optimal manner.
Cob-web model or Theorem
The cob-web model or Theorem analyzes the movements of prices and outputs when supply is
wholly determined by prices in the previous period. As prices move up and down in cycles,
quantities produced and demanded also seem to move up and down in a counter-cyclical manner
(e.g. prices of perishable commodities like vegetables). This is a theory under dynamic
equilibrium otherwise called micro dynamics. In order to find out the conditions for the cycles:
one has to look at the slope of the demand curve and then of the supply curve.
Assumption of Cobweb theorem
The cob-web Model is based on the following assumption: The current year’s (t) supply depends
on the last year’s (t-1) decisions regarding output level. Hence current output is influenced by
last year’s price. i.e. P (t-1)
The current period or year is divided into sub-periods of a week or fortnight. The parameters
determining the supply function have constant values over a series of periods. Current demand
(Dt) for the commodity is a function of current price (Pt). The price expected to rule I the current
period is the actual price in the last year.

The commodity under consideration is perishable and can be stored only for one year. Both
supply and demand functions are linear .i.e. both are straight line curves which increases or
decreases at a constant proportion.
Example of a Cob-web Model
Under the cobweb model below, the assumption holds that supply is a function of previous year
i.e. S= f (t-1) (‘t’ is the current period and‘t-1’ is a previous period) and the demand is the
function of price i.e. Dt =f (P). The equality between the quantity supplied and quantity demand
is the Market equilibrium i.e. St=Dt. Equilibrium is established through adjustment in price
changes during the last year which will take place over a several consecutive periods.

Supposing the price of onion last year was P1. The onion growers supply Q1 this year basing on
last year price giving the market demand and supply curves for onions by DD and SS curves
respectively in diagram.
Suppose there is drought which decreases output and hence supply to OQ2 > OQ1. Price goes up
to OP2 in the current period., The onion growers will produce OQ3 in response to the higher
price OP2 which exceeds the equilibrium quantity OQ1, the actual need of the market. The
excess supply then lowers the price to OP3 which invariably discourage production and reduce
supply to OQ4 in the third period. But this quantity is less than the equilibrium quantity OQ1.
This will lead to again rise in price to OP4, which in turn will encourage the producers to produce
OQ1 quantity. The equilibrium will be established at point g where DD and SS curves intersect.
This series of adjustments from point a,b,c,d, and e to f is traced out as a cobweb pattern which
converge towards the point of market equilibrium g. This is also termed as the dynamic
equilibrium with lagged adjustment.

As the supply will be more due to high price in the market. On the other hand the demand will be
less as compared to the supply OQ2 and the demand will reduced to OQ2. The fall in demand
will force the producer to decrease price to OP2 in next period. But at this price OP2 the demand
will be OQ2 which is more than the supply OQ1 which reduced. This way the prices and
quantities will circulate constantly around the equilibrium.
General equilibrium theory attempts to explain the behavior of supply, demand, and prices in a
whole economy with several or many interacting markets, by seeking to prove that a set of prices
exists that will result in an overall (or "general") equilibrium. General equilibrium theory both
studies economies using the model of equilibrium pricing and seeks to determine in which
circumstances the assumptions of general equilibrium will hold.
PART 2: THE EMPIRICAL STUDIES THAT USED PARTIAL
EQUILIBRIUM
Partial equilibrium models have been used in many economic analyses over decades. Most
recently Phan Sy Hieu, Steve Harrison and Dominic Smith (2015) used partial equilibrium
approach to Calculate
Regional and Total Economic Surpluses. The paper used numerical examples to demonstrate
different formulae to calculate the regional and total economic surpluses of commodities. The
study tackled the objective to illustrate the spatial equilibrium model for 2 products and 3 regions
with original linear supply and demand functions. It shows how an inverse matrix of coefficients
of original supply and demand functions should be used to solve coefficients of inverse supply

and demand functions. The study recommends that original and inverse supply and demand
functions are appropriate for calculating the regional and total economic surpluses of
commodities.
A social time preference (STP) assigns current values to future consumption based on society’s
evaluation of its desirability. STP is a kind of public interventions and its analysis requires the
use of different discount rates. The World Bank (2008) estimated the Social Discount Rate for
Nine Latin American Countries which was inputted in the estimation of STP. The elasticity of
marginal utility ε of consumption was the third ingredient estimated among others for the
estimation of STP. The marginal utility of income elasticity was estimate on the basis of two
elements: (i) the effective marginal tax rate; and (ii) the average tax rate. Further, ε was
estimated at different points of the income distribution before proceeding to average these
values.
Result shows calibrated ε and average of its estimates for each and across the countries. The
cross country average of each of the ε was 1.6. This offers information regarding the constancy
of ε along the income distribution.
Meta-analysis is a comparatively recent inductive empirical method that seeks to find similarities
and explain differences between scientific findings on similar research questions across
publications. A study of a meta-analysis of partial and general equilibrium results has been done
by Sebastian Hess and Stephan von Cramon-Taubadel (2005). The aim of this analysis is to
identify model characteristics (e.g. partial vs. general equilibrium, level of disaggregation) and
other factors (e.g. the database employed) that influence simulation results in a systematic

manner, and to derive quantitative estimates of these influences. Meta-analysis has three
objectives:
Evaluating methods (Stanley 2001; Florax, de Groot and de Mooij 2002): This approach has
evolved especially in economics and related disciplines in which reproducible measurements are
often hard to obtain and quantitative results are known to depend heavily on the methods that
have been applied. Meta-analysis can quantify the share of variance within a given set of
estimates that is due to different methodologies and a priori assumptions. Partial equilibrium
models was found to produce significantly larger estimates of welfare gains than general
equilibrium models, ceteris paribus.
References
Alarudeen A., 2011. Government Wage Review Policy and Public-Private Sector Wage
Differential in Nigeria. AERC Research Paper 223 African Economic Research
Consortium, Nairobi January 2011 The African Economic Research Consortium ISBN:
9966-778-95-0.
Albouy D. Supply and Demand: Partial Equilibrium and Comparative Statics. Economics 101A
Hess, S. and Von Cramon-Taubadel, S. 2007., Meta-analysis of general and partial equilibrium
simulations of Doha Round outcomes. Agricultural Economics, 37: 281–286.
doi: 10.1111/j.1574-0862.2007.00252.x
Hieu Sy, P., Harrison, S. and Smith, D. 2015. Recommended Methods to Re-Calculate Regional
and

Total Economic Surpluses after Solving Spatial Equilibrium Models by the Non-Linear
Programming Method. Modern Economy, 6, 520-534.
http://dx.doi.org/10.4236/me.2015.65051
Lattaa G. S., Sjølie K. H. and Solberg B. 2013 A review of recent developments and
applications of partial equilibrium models of the forest sector Journal of Forest
Economics 19 (2013) 350–360
Miller N 2006 Competitive Markets and Partial Equilibrium Analysis. Notes on Micro-economic
Theory: Chapter 7 Vers: August 2006
Parappurathu S. Partial Equilibrium Models for Agricultural Policy Analysis. National Center for
Agricultural economics and Policy Research, New Delhi-110012
http://en.wikkipaedia,org

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