Download influence of isocost and isoquant on firm out subject to

PART 1:
PART 2:
1) Substitution effect and income effect of an increase in the price of rice on households demand.
Substitution effect refers to the idea that as prices rise or income decreases, consumers will
replace more expensive items with less costly alternatives. Let say an individual eats Rice Kripsies
tariffs but if the price should rise, the alternative to this is ofada rice which is much cheaper.
Although beneficial to some (discount retailers). In general, the substitution effect is very negative in
nature as it limits choice. This is true not only for products but also for services. Examples of
substitution effect in action can sometimes be observed in Nigeria when the price of rice increases
because of the on importation, during this time less expensive food such as Garri or beans will
consumed.
Income effect on the other hand is the impact or the increase or decrease of income on the
demand of a commodity. It is the change in an individual or economy income and how that change
will impact the quantity demanded of a good or service. The relationship between income and the
quantity demanded is a positive one as income increases so does the quantity of goods and services
demanded. Example, when a person’s income increases other things remaining the same, that
person will demand more goods and services; thus increasing their consumption. The degree to
which a person or economy will spend will spend more of their income on consumption is called the
marginal propensity to consume (MPC).the MPC depends on the individual or company saving
characteristics. Rice is a normal good especially since it is a staple food. No matter the increase in
price of rice, a portion of one income is spent on rice but the portion greatly depends on the income
of the individual. Rice consumption in Nigeria, as the country’s economy decreased due to the out
flux of capital to other countries that export rice. People are less likely to add a little meat to their
diet and rely heavily on rice. To survive, at low levels of income, it is necessary to spend all available
funds on rice meat being too expensive. At a higher income one can purchase much more rice than
would be necessary for sustainance.it is then worthwhile to substitute a little meat for some of that
rice and have a more enjoyable diet. In this instance rice is an inferior good. When income increases
however, the demand curve for normal goods shifts to the right and and the demand curves for the
inferior goods to the left.
2) Engel curve and its behavior in the case of a) normal good b) inferior good
Engel law is an observation in economics stating that as income rises, the proportion of
income spent on food falls, even if actual expenditure on food rises. In other words, the income
elasticity of demand of food is between 0 and 1.
Engel curve is the graphical representation of an households expenditure on a particular
good or service variation with household income. There are variations of Engel curves. It
describes how the proportion of household income spent on a good varies with income.
Alternatively, Engel curves can also describe how real expenditure varies with household
income. These curves are named after a German statistician Ernest Engel. The shape of the
curve depends on a lot of many demographic variables and other consumer characteristics. A
good Engel curve reflects its income elasticity and indicates if the good is an inferior, normal or
luxury good.
For normal goods, the Engel curve has a positive gradient. This is as income rises the quantity
demanded increases. Amongst normal goods there are two possibilities. Although the engel
curve remains upward sloping in both cases, it bends towards the y axis for necessities and
towards the x axis for luxury goods.
For inferior goods however, the Engel curve has a negative gradient. That means that as the
consumer has more income, they buy less of the inferior commodity as they are able to
purchase better commodities.
3) The law of diminishing returns is at its best in a short run phenomenon.
The law of diminishing returns is a concept in economics which states that as more and more
variable factors are added to a fixed factor, a point in time will present itself in which there is less
and less satisfaction (returns) derived i.e. as more and more of a commodity is consumed,
satisfaction decreases.
In the short run is a time period where at least one factor of production is in fixed supply. A
business has chosen its scale and most stick to this in the short run. In the short run , the law of
diminishing returns states that as we add more and more units of a variable input to fixed amounts
of land and capital ,the change in total output will at first rise and then fall.
Diminishing returns to labor also occurs when marginal product of labor starts to fall. This means
that the total output will be increasing at a decreasing rate. This is because as new workers will not
have as much capital equipment to work with so it becomes diluted among a large workforce.
4) Isocost: a) derivation b) show how the tools of isoquant and isocost influence the firm’s output
maximization subject to a cost constraint.
Isoquant is also called as equal product curve or production indifference curve or constant product
curve. Isoquant indicates various combinations of two factors of production which give the same level of
output per unit of time. The significance of factors of productive resources is that, any two factors are
substitutable e.g. labour is substitutable for capital and vice versa. No two factors are perfect
substitutes. This indicates that one factor can be used a little more and other factor a little less, without
changing the level of output.
It is a graphical representation of various combinations of inputs say Labour(L) and capital (K) which give
an equal level of output per unit of time. Output produced by different combinations of L and K is say, Q,
then Q=f (L, K). Just as we demonstrate the MRSxy in respect of indifference curves through hypothetical
data, we demonstrate the Marginal Rate of Technical Substitution of factor L for K (MRTS L,K )
Assumptions
There are two factor inputs labour and capital
The proportions of factor are variable.
Physical production conditions are given
The Scale of operation is variable
The state of technology remains constant
The shape of Isoquant
In this section we examine the characteristics of isoquants, define the economic region of production
and consider the special cases where the commodities can only be produced with least cost factor
combination.
We can see that the shape of isoquant plays an important a role in the production theory as the shape
of indifference curve in the consumption theory. Iso quant map shows all the possible combinations of
labour and capital that can produce different levels of output. The iso quant closer to the origin
indicates a lower level of output. The slope of iso quant is indicated as $ $=MRSLk=$ $In economics an
isocost line shows all combinations of inputs which cost the same total amount. Although similar to the
budget constraint in consumer theory, the use of the isocost line pertains to cost-minimization in
production, as opposed to utility-maximization. For the two production inputs labour and capital, with
fixed unit costs of the inputs, the equation of the isocost line is where w represents the wage rate of
labour, r represents the rental rate of capital, K is the amount of capital used, L is the amount of labour
used, and C is the total cost of acquiring those quantities of the two inputs.
The absolute value of the slope of the isocost line, with capital plotted vertically and labour plotted
horizontally, equals the ratio of unit costs of labour and capital. The slope is:
The isocost line is combined with the isoquant map to determine the optimal production point at any
given level of output. Specifically, the point of tangency between any isoquant and an isocost line gives
the lowest-cost combination of inputs that can produce the level of output associated with that
isoquant. Equivalently, it gives the maximum level of output that can be produced for a given total cost
of inputs. A line joining tangency points of isoquants and isocosts (with input prices held constant) is
called the expansion path.
The cost-minimization problem
Main article: Conditional factor demands
The cost-minimization problem of the firm is to choose an input bundle (K,L) feasible for the output level
y that costs as little as possible. A cost-minimizing input bundle is a point on the isoquant for the given y
that is on the lowest possible isocost line. Put differently, a cost-minimizing input bundle must satisfy
two conditions:
it is on the y-isoquant
no other point on the y-isoquant is on a lower isocost line.
The case of smooth isoquants convex to the origin
If the y-isoquant is smooth and convex to the origin and the cost-minimizing bundle involves a positive
amount of each input, then at a cost-minimizing input bundle an isocost line is tangent to the yisoquant. Now since the absolute value of the slope of the isocost line is the input cost ratio , and the
absolute value of the slope of an isoquant is the marginal rate of technical substitution (MRTS), we reach
the following conclusion: If the isoquants are smooth and convex to the origin and the cost-minimizing
input bundle involves a positive amount of each input, then this bundle satisfies the following two
conditions:
It is on the y-isoquant (i.e. F(K, L) = y where F is the production function), and
the MRTS at (K, L) equals w/r.
The condition that the MRTS be equal to w/r can be given the following intuitive interpretation. We
know that the MRTS is equal to the ratio of the marginal products of the two inputs. So the condition
that the MRTS be equal to the input cost ratio is equivalent to the condition that the marginal product
per dollar is equal for the two inputs. This condition makes sense: at a particular input combination, if an
extra dollar spent on input 1 yields more output than an extra dollar spent on input 2, then more of
input 1 should be used and less of input 2, and so that input combination cannot be optimal. Only if a
dollar spent on each input is equally productive is the input bundle optimal.
influence of isocost and isoquant on firm out subject to constraint:
Isoquant is also called as equal product curve or production indifference curve or constant product
curve. Isoquant indicates various combinations of two factors of production which give the same level of
output per unit of time. The significance of factors of productive resources is that, any two factors are
substitutable e.g. labour is substitutable for capital and vice versa. No two factors are perfect
substitutes. This indicates that one factor can be used a little more and other factor a little less, without
changing the level of output.
It is a graphical representation of various combinations of inputs say Labour(L) and capital (K) which give
an equal level of output per unit of time. Output produced by different combinations of L and K is say, Q,
then Q=f (L, K). Just as we demonstrate the MRSxy in respect of indifference curves through hypothetical
data, we demonstrate the Marginal Rate of Technical Substitution of factor L for K (MRTS L,K )
Assumptions
There are two factor inputs labor and capital
The proportions of factor are variable.
Physical production conditions are given
The Scale of operation is variable
The state of technology remains constant
The shape of Isoquant
In this section we examine the characteristics of isoquants, define the economic region of production
and consider the special cases where the commodities can only be produced with least cost factor
combination.
We can see that the shape of isoquant plays an important a role in the production theory as the shape
of indifference curve in the consumption theory. Isoquant map shows all the possible combinations of
labor and capital that can produce different levels of output. The isoquant closer to the origin indicates a
lower level of output. The slope of isoquant is indicated as $ $=MRSLk=$ $
Shows all the possible combinations of labor and capital that can produce different levels of output.
The isoquant closer to the origin indicates a lower level of output. The slope of isoquant is indicated as $
$=MRSLk=$ $
Properties/Characteristics of Isoquants
Isoquants, abbreviated as IQs, possess the same properties as those of the indifference curves. For the
convenience of the students, we can state them as follows.
Two isoquants do not intersect each other:
No isoquant can touch either axis
Isoquant is oval in shape
A higher IQ implies a higher level of output
IQs are never parallel to each other. Interspacing between them is least at the ends and maximum in the
middle.
IQs are convex to the origin: convex isoquants possess continuous substitutability of K and L over a
stretch. Beyond this stretch, K and L are not substitutable foe each other.
IQs may be linear when labour and capital are perfect substitute. A linear isoquant implies that either
factor can be used in proportion. If isoquant has several linear segments separated by kinks, the
isoquant is called kinked isoquant or activity analysis isoquant or linear programming isoquant. Such
isoquants are used in linear programming.
If Land K are prefect complements to each other, the IQ is L-shaped. Such isoquant is known a inputoutput isoquant or Leontief isoquant. There is only one combination of L and K available for production.
It is the corner point of L-shaped isoquant.
If marginal product of one of the two factors is zero, IQ is parallel to the axis on which the factor with
zero marginal products is represented.
If one of the two factors has negative marginal product the IQ slopes upwards from left to right.
If both the factors have negative marginal products, the IQ is concave to the origin.
If the producer has a preference for a factor of production, the IQ is quasi linear.
If the factors to be employed in whole numbers units only. The IQ is discontinuous.
Isocost curves:
Isocost curve is the locus traced out by various combinations of L and K, each of which costs the
producer the same amount of money (C ) Differentiating equation with respect to L, we have dK/dL = w/r This gives the slope of the producer’s budget line (isocost curve). Isocost line shows various
combinations of labor and capital that the firm can buy for a given factor prices. The slope of isocost line
= PL/Pk. In this equation, PL is the price of labor and Pk is the price of capital. The slope of isocost line
indicates the ratio of the factor prices. A set of isocost lines can be drawn for different levels of factor
prices, or different sums of money. The isocost line will shift to the right when money spent on factors
increases or firm could buy more as the factor prices are given.
Slope of iso cost line
With the change in the factor prices the slope of iso cost lien will change. If the price of labour falls the
firm could buy more of labour and the line will shift away from the origin. The slope depends on the
prices of factors of production and the amount of money which the firm spends on the factors. When
the amount of money spent by the firm changes, the isocost line may shift but its slope remains the
same. A change in factor price makes changes in the slope of isocost lines.
Least Cost Factor Combination or Producer’s Equilibrium or Optimal Combination of Inputs:
The firm can achieve maximum profits by choosing that combination of factors which will cost it the
least. The choice is based on the prices of factors of production at a particular time. The firm can
maximize its profits either by maximizing the level of output for a given cost or by minimizing the cost of
producing a given output. In both cases the factors will have to be employed in optimal combination at
which the cost of production will be minimum. The least cost factor combination can be determined by
imposing the isoquant map on isocost line. The point of tangency between the isocost and an isoquant is
an important but not a necessary condition for producer’s equilibrium. The essential condition is that
the slope of the isocost line must equal the slope of the isoquant. Thus at a point of equilibrium
marginal physical productivities of the two factors must be equal the ratio of their prices. The marginal
physical product per rupee of one factor must be equal to tht of the other factor. And isoquant must be
convex to the origin. The marginal rate of technical substitution of labour for capital must be diminishing
at the point of equilibrium.
The Economic region of production
The firm would not operate on the positively sloped portion of an isoquant because it could produce the
same level of quantity with less capital and labour. Economic region of Production:
Ridge lines: separate the relevant (i.e. negatively sloped) from the irrelevant (or the positively sloped)
portion of the isoquant.
Ridge lines joins points on the various isoquants where the isoquants have zero slope (and thus zero
MRTSlk) .