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.

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