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V DETERMINANTS OF EP
Price Elasticity of demand is influenced by:
192
9.1.6 Elasticity
1. Availability of substitutes
Generally, the more substitutes that are available, the more elastic
the demand for a good. The demand for a class of goods (soft
drinks) is usually more inelastic than the demand for a specific
brand of the good (Pepsi or Coca-Cola). A Firm may try to
differentiate their product to make the demand relatively more
inelastic.
2. Proportion of item in budget
When the expenditures on a product are a relatively small portion
of a budget, the demand is relatively more elastic.
3. Time available to adapt
The longer that consumers or buyers have to make adjustments in
their behavior, the more elastic the demand is likely to be. The
absolute value of the short run price elasticity of demand for
gasoline would be smaller than the absolute value of the long
run price elasticity of demand. The longer time allows
consumers more opportunity to adjust to price changes.
VI INTERPRETATION OF EP
Some examples of price elasticities of demand reported in M
icroeconomics for
Today, [Tucker, p 123, South-Western College Publishing, 1999. Sources Archibald and Gillingham, Houthakker and
Taylor, Voith] are presented in Table IV.5. Note that the demand is relatively more
elastic for longer periods. Some goods, like movies, are inelastic in the short
run and elastic in the long run.
The coefficient or price elasticity can be used to estimate the percentage
change in the quantity that consumers are willing and able to buy given a
percentage change in the price. It is important to understand that this
measure does not apply to the equilibrium conditions in the market.
193
9.1.6 Elasticity
Table IV.5
Selected Price Elasticities
Item
Short Run EP
Long Run EP
Automobiles
-1.87
-2.24
Movies
-.087
-3.67
Medical Care
-.31
-.92
Gasoline
-.20
-.70
In Table IV.5 the short run EP for gasoline is -.2. This suggests that a 1%
increase in price will reduce the quantity demanded by .2%. A 10% decrease
in price would increase the quantity demanded by 2%. In the case of movies,
a 1% increase in the price would change the quantity demanded by 3.67% in
the long run.
(B) INCOME ELASTICITY OF DEMAND
The responsiveness of buyers to changes in their incomes is measured by
income elasticity. While EP measures a movement along a demand function as
the price changes, income elasticity (EM) measure a shift of the demand
function caused by a change in income.
Δ Q
Income elasticity (EM) is defined:
[ E ≡
M
]
Δ Income
In Figure IV.A.12 the original demand function is represented as D. D1
represents a decrease in demand (at each price a smaller quantity is
purchased. When a larger quantity is purchased at each price, this will
represent an increase of demand to D2.
194
9.1.6 Elasticity
$ 10
(D) Q = 10 – 1P
Given the original
9
(D1) Q1 = 7 - 1P
(D2) Q2 = 13 – 1P
8
demand function (D),
rice P 7
consumers are willing and
6
A
B
C
able to purchase 5 units of
5
4
the good. If income
3
increased by 50% and
2
D1
D
D2
“caused” the demand to
1
shift to D
1 2 3 4 5 6 7 8 9 10
Q/ut
2, where 8 units
Figure IV.A.12
are purchased at $5. This is
a 60% increase in demand. Income elasticity (EM) is calculated:
E
%ΔQ
+60
=
=
= +1 . 2
M
%ΔM
+50
In this case, an increase in income resulted in an increase in demand. A
decrease in income might decrease the demand (to D1). In this case income
%ΔQ
− 60
E
=
=
= +1 . 2
M
%ΔM
− 50
elasticity would be
When EM is positive, the good is called a normal good. If an
increase in income reduces demand (or a decrease in income increases
demand), EM will be negative and the good is categorized as an inferior good.
a. EM < 0 means the good is inferior, i.e. for an increase in income the
quantity purchased will decline or for a decrease in income the quantity
purchased will increase
195
9.1.6 Elasticity
b. 1 > ΕM> 0 means the good is a normal good, for an increase in income
the quantity purchased will increase but by a smaller percentage than the
percentage change in income.
c. For EM > 1 the good is considered a superior good.
CROSS ELASTICITY
Cross elasticity (EXY) is used as a measure of the relationship between two
goods. EXY is defined as:
% Δ Q
E
≡
x
XY
% Δ P y
Consider two goods that are substitutes: butter and margarine. Cross
elasticity cam be used to measure the relationship between the price of butter
and the demand for margarine (EMargarine- butter) or the relationship between the
demand for butter and the price of margarine (Ebutter-margarine). The value of EXY is
not the same as or equal to EYX. In Figure IV.A.13 the concept of EXY is shown.
PM
PMH
DBH
PM
DM
DB
Q
Q
QBH
Q /ut
MH
M Q /ut
M
B
Panel
Panel
Figure
A
B
IV.A.13
196
9.1.6 Elasticity
In panel A, the demand for margarine (DM) is shown. At a price of PM, the
quantity demanded is QM. In Panel B, the demand for butter (DB) is shown. At
a price of PB, the quantity demanded is QB. If the price of margarine increased
to PMH (in Panel A), the quantity of margarine demanded decreases to QMH.
Since less margarine is purchased, the demand for butter increases to DBH (in
Panel B). Given the higher demand for butter the butter demanded (given the
higher price of margarine) has increased. A decrease in the price of margarine
would shift the demand for butter to the left (decrease). The coefficient of
cross elasticity would be positive.
In the case of complimentary goods, an increase (decrease) in the price of
tennis balls would reduce (increase) the demand for tennis rackets. The
coefficient of cross elasticity would be negative. If EXY is close to zero, that
would be evidence that the two goods were not related. If EXY were positive or
negative and significantly different from zero, it could be used as evidence that
the two goods are related. It is possible that EXY might be positive or negative
and the two goods are not related. The price of gasoline has gone up and the
demand for PC’s has also increased. This does not mean that gasoline and
PC’s are substitutes.
197
9.1.6 Elasticity
•
When Εxy > 0, [a positive number] this suggests that the two goods are substitutes
•
When Εxy < 0, [a negative number] this suggests that the two goods are
compliments
9.1.6.1 ELASTICITY AND BUYER RESPONSE
E lasticity is a convenient tool to describe how buyers respond to changes
in relevant variables. Price elasticity (EP) measures how buyers respond to
changes in the price of the good. It measures a movement along a demand
function. It is used to describe how much more of less the quantity demanded
is as the price falls or rises.
Income elasticity (EM) is a measure of how much the demand function
shifts as the income(s) of the buyer(s) changes. Cross elasticity (EXY)
measures how much changes in the price of a related good will shift the
demand function.
Elasticity can be calculated to estimate the relationship between any two
related variables.
198
10 Production and Cost
10 PRODUCTION AND COST
D ecisions about production require individual agents to make decisions
about the allocation and use of physical inputs. Objectives of agents,
technology, availability and quality of inputs determine the nature of these
decisions. Since the objectives are often pecuniary, it is often necessary to
relate the decisions about the physical units of inputs and outputs to the costs
of production.
If the prices of the inputs and the production relationships are known (or
understood), it is possible to calculate or estimate all the cost relationships for
each level of output. In practice however, the decision maker will probably
have partial information about some of the costs and will need to estimate
production relationships in order to make decisions about the relative amounts
of the different inputs to be used.
10.1 PRODUCTION
P roduction is the process of altering resources or inputs so they satisfy
more wants. Before goods can be distributed or sold, they must be produced.
Production, more specifically, the technology used in the production of a good
(or service) and the prices of the inputs determine the cost of production.
Within the market model, production and costs of production are reflected in
the supply function.
Production processes increase the ability of inputs (or resources) to satisfy
wants by:
• a change in physical characteristics
• a change in location
• a change in time
• a change in ownership
199
10.1 Production
At its most simplistic level, the economy is a social process that allocates
relatively scarce resources to satisfy relatively unlimited wants. To achieve this
objective, inputs or resources must be allocated to those uses that have the
greatest value. In a market setting, this is achieved by buyers (consumers)
and sellers (producers) interacting. Consumers or buyers wish to maximize
their utility or satisfaction given (or constrained by) their incomes, preferences
and the prices of the goods they may buy. The behavior of the buyers or
consumers is expressed in the demand function. The producers and/or sellers
have other objectives. Profits may be either an objective or constraint. As an
objective, a producer may seek to maximize profits or minimize cost per unit.
As a constraint the agent may desire to maximize “efficiency,” market share,
rate of growth or some other objective constrained by some “acceptable level
of profits. In the long run, a private producer will probably find it necessary to
produce an output that can be sold for more than it costs to produce. The
costs of production (Total Cost, TC) must be less than the revenues (Total
Revenue, TR).
Given a production relationship (Q = f (labor, land, capital, technology, …))
and the prices of the inputs, all the cost relationships can be calculated. Often,
in the decision making process, information embedded in cost data must be
interpreted to answer questions such as:
• “How many units of a good should be produced (to achieve the
objective)?”
• “How big should may plant be?’ or How many acres of land should I
plant in potatoes?”
Once the question of plant size is answered, there are questions,
• “How many units of each variable input should be used (to best achieve
the objective)?”
• “To what degree can one input be substituted for another in the
production process?”
200
10.1 Production
The question about plant size involves long run analysis. The questions
about the use of variable inputs relate to short-run analysis. In both cases, the
production relationships and prices of the inputs determine the cost functions
and the answers to the questions.
Often decision-makers rely on cost data to choose among production
alternatives. In order to use cost data as a “map” or guide to achieve
production and/or financial objectives, the data must be interpreted. The
ability to make decisions about the allocation and use of physical inputs to
produce physical units of output (Q or TP) requires an understanding of the
production and cost relationships.
The production relationships and prices of inputs determine costs. Here the
production relationships will be used to construct the cost functions. In the
decision making process, incomplete cost data is often used to make
production decisions. The theory of production and costs provides the road
map to the achievement of the objectives.
10.1.1 (1) PRODUCTION UNIT
I n the circular flow diagram found in most principles of economics texts,
production takes place in a “firm” or “business.” When considering the
production-cost relationships it is important to distinguish between firms and
plants. A plant is a physical unit of production. The plant is characterized by
physical units of inputs, such as land ® or capital (K). This includes acres of
land, deposits of minerals, buildings, machinery, roads, wells, and the like.
The firm is an organization that may or may not have physical facilities and
engage in production of economic goods. In some cases the firm may
manage a single plant. In other instances, a firm may have many plants or no
plant at all.
201
10.1.1 (1) Production Unit
The cost functions that are associated with a single plant are significantly
different from those that are associated with a firm. A single plant may
experience economies in one range of output and diseconomies of scale in
another. Alternatively, a firm may build a series of plants to achieve constant
or even increasing returns. General Motors Corp. is often used as an example
of an early firm that used decentralization to avoid rising costs per unit of
output in a single plant.
Diversification is another strategy to influence production and associated
costs. A firm or plant may produce several products. Alfred Marshall (one of
the early Neoclassical economists in the last decade of the 19th century)
considered the problem of “joint costs. “ A firm that produces two outputs
(beef and hides) will find it necessary to “allocate” costs to the outputs.
Unless specifically identified, the production and cost relationships will
represent a single plant with a single product.
10.1.2 (2) PRODUCTION FUNCTION
A production function is a model (usually mathematical) that relates
possible levels of physical outputs to various sets of inputs, eg.
Q = f (Labor,
Kapital, Land, technology, . . . ).
To simplify the world, we will use two inputs Labor (L) and Kapital (K) so,
Q = f (L, K, technology, ...).
Here we will use a Cobb-Douglas production function that usually takes the
form: Q = ALaKb. In this simplified version, each production function or
process is limited to increasing, constant or decreasing returns to scale over
the range of production. In more complex production processes, “economies
of scale” (increasing returns) may initially occur. As the plant becomes larger
(a larger fixed input in each successive short-run period), constant returns
202
10.1.2 (2) Production Function
may be expected. Eventually, decreasing returns or “diseconomies of scale”
may be expected when the plant size (fixed input) becomes “too large.” This
more complex production function is characterized by a long run average cost
(cost per unit of output) that at first declines (increasing returns), then is
horizontal (constant returns) and then rises (decreasing returns).
10.1.3 (3) TIME AND PRODUCTION
A s the period of time is changed, producers have more opportunities to
alter inputs and technology. Generally, four time periods are used in the
analysis of production:
“market period” -
A period of time in which the producer cannot change any inputs nor
technology can be altered. Even output (Q) is fixed.
“Short-run”-
A period in which technology is constant, at least one input is fixed
and at least one input is variable.
“Long-run” -
A period in which all inputs are variable but technology is constant.
“The very Long-run” -
During the very long-run, all inputs and technology change.
Most analysis in accounting, finance and economics is either long run or
short-run.
203
10.1.4 (4) Production in the Short-Run
10.1.4 (4) PRODUCTION IN THE SHORT-RUN
I n the short-run, at least one input is fixed and technology is unchanged
during the period. The fixed input(s) may be used to refer to the “size of a
plant.” Here K is used to represent capital as the fixed input. Depending on the
production process, other inputs might be fixed. For heuristic purposes, we will
vary one input. As the variable input is altered, the output (Q) changes. The
relationship between the variable input (here L is used for “labor”) and the
output (Q) can be viewed from several perspectives.
The short-run production function will take the form
Q = f (L), K and technology are fixed or held constant
A change in any of the fixed inputs or technology will alter the short-run
production function.
Q
Or
In the short run, the TP
B
relationship between the
TP
physical inputs and output can
be describes from several
A
perspectives. The relationship
can be described as the total
product, the output per unit of
input (the average product, AP)
O
L
Input (L)
A
LB
or the change in output that is
Figure V.1
attributable to a change in the
variable input (the marginal product, MP).
204
10.1.4 (4) Production in the Short-Run
Total product (TP or Q) is the total output. Q or TP = f(L) given a fixed
size of plant and technology.
Average product (APL) is the output per unit of input. AP = TP/L (in this
case the output per worker). APL is the average product of labor.
AP
output
TP
Q
=
=
=
L
Input
L
L
Marginal Product (MPL) is the change in output “caused” by a change in
the variable input (L),
ΔT P
ΔQ
MP =
=
L
ΔL
ΔL
(A) TOTAL AND MARGINAL PRODUCT
Over the range of inputs there are four possible relationships between Q and L
(1) TP or Q can increase at an increasing rate. MP will increase, (In Figure V.1
this range is from O to LA.)
(2) TP may pass through an inflection point, in which case MP will be a
maximum. (In Figure V.1, this is point A at LA amount of input.) TP or Q may
increase at a constant rate over some range of output. In this case, MP will
remain constant in this range.
(3) TP might increase at a decreasing rate. This will cause MP to fall. This is
referred to as “diminishing MP.” In Figure V.1, this is shown in the range from
LA to LB.
(4) If “too many” units of the variable input are added to the fixed input, TP
can decrease, in which case MP will be negative. Any addition of L beyond LB
will reduce output: the MP of the input will be negative. It would be foolish to
continue adding an input (even if it were “free”) when the MP is negative.
The relationship between the total product (TP) and the marginal product (MP)
can be shown. In Figure V.2, note that the inflection point in the TP function is
at the same level of input (LA) as the maximum of the MP. It is also important
205
10.1.4 (4) Production in the Short-Run
to understand that the maximum of the TP occurs when the MP of the input is
zero at LB.