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Welcome to the fifth lecture on Economics
Management and Entrepreneurship. If you recall,
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we had covered demand supply, market equilibrium
in the first 2 lectures and thereafter we
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covered demand elasticity, and in the last
lecture we covered demand forecasting. In
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a way, in the last few lectures, we have covered
more on the demand aspects of economics of
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a firm. Today, we shall discuss on production,
the supply aspects of the firm.
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In this lecture, we expect you to have the
concepts of production function, total, marginal,
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and average product, returns to factor, and
returns to scale, various curves such as iso-quant,
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iso-cost, iso-revenue, and product transformation
curves, and the effect of technological change
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on production. Each of these concepts we will
discuss hereafter.
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To start with we discussed about production
function. By production function, we mean
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the amount of production that is produced
amount of products that is produced because
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of certain factors, certain inputs, such as
material, labour, capital, and so on and so
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forth. Here, we defined production function
as the maximum possible output that can be
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produced using a given combination of inputs.
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It is also the minimum quantity of inputs
required to produce a given level of output
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basically it maps or it defines a relationship
between the inputs used and the outputs produced.
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A very popular production function is Cobb-Douglas
production function. It is basically a power
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function that defines the quantity produced
Q as a function of in this case I have given
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example of 2 input materials, 2 inputs X and
Y.
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The relationship that defines Q with X and
Y is a power function relationship Q equal
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to a into X to the power b into Y to the power
c and if I take a log transformation of both
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sides this becomes ln Q, natural logarithmic
of Q equal to ln a plus b ln X plus c ln Y.
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Cobb and Douglas 2 economist had suggested
that such a production function covers a very
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wide range of relationships between products
produced and the input materials inputs given
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to a firm.
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Then, we define 3 types of products: Total
product, marginal product, and average product.
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By total product, we mean the quantity Q produced
by a firm for a given set of inputs, naturally
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in a specific period of time that is called
total product. Marginal product on the other
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hand is the first differentiation of total
product with one of the factors. In this case,
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I have given an example of only one factor
let us say x is a factor. There can be many
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other factors. Then the marginal product is
given. I am sorry this would have been MPx
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rather than MRx.
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This should have been MPx equal to dQ by dX
is the amount by which the total product Q
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changes for a 1 unit change in a factor of
product of production X. So if it is for another
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factor of production Y then we write MPy equal
to dQ by dY. Basically, this says the amount
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by which the output Q changes for a unit change
in a particular factor of production X. Next
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is average product AP. This is simply the
ratio of the total amount produced by the
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value of A particular factor X employed and
this is called APx. Similarly if we have another
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input Y, then APy would be total product TP
by Y. So these are the 3 things that we shall
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be using hereafter.
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We next talk about returns to a factor are
also known as factor productivity. Returns
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to a factor or factor productivity is the
magnitude of percentage change in the output
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of a firm when a particular factor of production
undergoes a given percentage change.
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We show it in this case that as X increases
a particular factor x increases how the total
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product Q changes as x increases. Normally,
as x increases initially the rate of change
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of Q is high, but thereafter it shows a decline
and the rate of increase in Q so the decline
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becomes 0 and then it becomes negative again.
This rate of change is basically the marginal
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product. This would be MPx and not MRx. It
should be dQ by dX.
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So the slope of this line is positive and
is growing so the value is also growing marginal
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productive value is growing till a point of
inflection comes where the value decreases
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so hereafter the value decreases, but still
positive and somewhere here the slope can
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be negative meaning that the marginal product
becomes negative. So this shows that as a
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factor that is input to production increases
the amount of production may raise to certain
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extent becomes stagnant for sometime, and
then may actually decline.
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This is known as the law of diminishing return
or law of diminishing marginal returns. If
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the amount of an input factor is increased
while holding all other factors constant,
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then the marginal product of that factor will
eventually diminish. This is basically shown
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in this particular slide that keeping all
other factors at certain value. If one factor
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x increases then the amount of quantity produced
increases for sometime comes to a steady state
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value and thereafter it declines. This is
the law of diminishing returns.
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This we give the concept of production isoquant.
Basically, isoquantity produced that is same
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quantity produced for what combination of
the input materials. We have in this example
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considered labour and capital as the 2 input
materials for production and this particular
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1 curve for Q1 let say and this curve is for
Q2, it means to produce a quantity Q1 different
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combinations of labour and capital could be
used.
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We could use this labour, a low capital, but
high labour, or high capital requiring less
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labour we may also get the same quantity produced.
So this is the isoquantity or isoquant curve
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meaning that for different combinations of
Y and X are here Y and X we could get different,
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we could get the same value Q1 whereas this
is an example of another quantity produced
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which is Q2 and Q2 can be achieved for different
capital and labour, different capital.
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But these 2 curves are parallel to each other.
This is called production isoquant curves.
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This is a curve that represents combinations
of input factors. In this case, X and Y combined
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efficiently to produce the same quantity of
output. This production isoquant is a very
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useful technique graphical technique and we
shall be using it very frequently hereafter.
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As you can see if you consider any one isoquant
say for example this point on the isoquant
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Q1 indicates that you need high amount of
Y and low amount of X and point number 4 requires
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more labour X, but less capital Y. Now you
will see that suppose you move from 1 to 2
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it means you are using more labour, but less
capital. Now consider points 3 and 4 from
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3 to 4 you are also using more labour and
less capital, but we realize that the extent
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of labour force or labour are required to
move from 1 to 2 is much less than when you
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move from 3 to 4.
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The amount of labour required here is much
larger whereas the amount of labour required
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here is much less compared to the same reduction
in the value of capital that is 1 to 2 the
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level of capital requirement is reduced by
this amount and the level of capital requirement
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reduced by this amount, but correspondingly
the requirement of labour is much more. This
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is called substitutability of factors.
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The amount of additional labour required to
reduce capital requirement from point 1 to
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2 is much less than that required to reduce
capital from point 3 to 4. Such a diminishing
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substitutability is a feature of most production
systems. Firstly, that factors can be substituted
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that means you can use more labour and less
capital. This is substitution but as you move
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along you will see that the amount of substitution
required is much more than when it is operating
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at these points.
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Now we come to the concept of marginal rate
of technical substitution. Now here basically
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we say that it is the slope of the isoquant
dY by dX. Now just look at this isoquant,
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this is an isoquant. Now it is at any point
it has a slope defined by a tangent at any
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point so we would like to that is nothing
but dY by dX at that vertical point and this
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is the slope of the isoquant. It gives a major
of substitutability of 1 factor for another
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for producing the same quantity Q as you can
see it has a negative slope that is what we
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are writing, it is negative.
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Basically, dY by dX is the slope of the isoquant
curve and that is negative. dY by dX as you
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can see equal to can be written as equal to
dQ by dX by dQ by dY. So dQ, dQ cancels out,
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dY goes to the numerator. dX remains in the
denominator. So dY by dX can be written as
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dQ by dX by dQ by dY, but dQ by dX by definition
is the marginal product, the change in Q for
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a unit change in the value of X. So this is
MPx and this is MPy. So therefore, the rate
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of technical substitution is minus because
the slope is negative minus the marginal product
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of X by marginal product of Y.
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Now let us see whether substitutions how substitutions
happen in complements and in other cases.
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Now this is a case of perfect substitution.
An example that we have taken is electric
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power generation. In electric power generation
it can use either oil or it can use gas. Now
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here the isoquant curve is basically a straight
line and for a higher value of electricity
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(18:52) it is Q2, it is parallel to the Q1
isoquant line. So here we see that if I draw
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a line here like I did in the case of in this
case.
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This requirement is much less than this requirement
when it is a straight line it will be exactly
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the same. So
this is a case of perfect substitution by
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gas with oil or vice versa. But, if we consider
the case of complements, please recall that
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the complement is 1 which says that this is
a case of a car. In a car if we need 1 frame
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we will need 4 wheels. This is a perfect complement.
If we use 2 frames that is for 2 cars we need
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to have 8 wheels. The quantity produced is
1 car, here and the quantity produced is 2
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cars here. So this we see there is no substitution
here and here is a perfect substitution.
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Now we bring in the concept of isocost curve.
For that this will be required to know the
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least-cost combination of factors that means
we can find out at what price combination
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of factors the quantity produced is maximum.
Let the unit prices of the factors or production
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be Px and Py. Px is the unit price of input
X, Py the unit price of input Y therefore
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the total cost of the inputs will be unit
price Px multiplied by the amount of X used
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plus the unit price of unit of input Y into
the amount of input Y that is the total cost
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of input. Now, we can draw a isocost curve
and whose slope is actually it should be dY
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by dX which is nothing.
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But del TC by del X partial differentiation
of TC with respect to X and partial differentiation
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of TC with respect to Y and that is nothing
but if I take personal differentiation of
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TC with respect to X I get the unit price
Px and partial differentiation of TC with
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Y I get unit price Py therefore dY by dX is
nothing but the ratio of the unit price of
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x to unit price of y. Incidentally, at the
equilibrium dY by dX is nothing but dQ by
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dX by dQ by dY which is same as dY by dX and
this is the marginal product of X MPx and
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this is MPy. Therefore, the isocost curve
at the equilibrium will be equal to the marginal
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rate of technical substitution. This is shown
here.
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In this curve. As before we have the input
X here and the second input Y here. This is
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the iso-quant curve for quantity Q1. This
is iso-quant curve for quantity Q2 and we
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are assuming that Q2 is higher than Q1. Now
this is a particular iso-cost curve having
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a slope equal to unit price Px is basically
dY by dX and at this particular point the
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slope of the iso-quant curve is also dY by
dX therefore at this point the slope of the
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iso-quant curve and equals the slope of the
iso-cost curve.
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So this is the iso-cost curve and for higher
price, higher amount. Higher price this is
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another iso-cost curve and (25:10) they are
parallel. So this is Px by Py and basically
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dY by dX. So iso-cost curve is tangent to
iso-quant curve. This is the point of equilibrium.
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Now, movement from 1 iso-quant that is from
Q1 to another iso-quant Q2, so the change
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in the scale of operation. So when we increase
from 1 particular amount of production Q1
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to a higher level of production Q2 it means
that our scale of operation has increased
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or that the company has expanded. This is
also called expansion part. It has shown a
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different or any increased scale of operation.
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This is what we are now talking next, which
is returns to scale. Returns to scale is the
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magnitude of percentage change in the output
of a firm when each factor of production undergoes
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a given percentage change that means if both
X and Y are given equal percentage change
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then what is the change that happens in the
output of the firm. This is given by returns
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to scale.
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Returns to scale is also called expansion
path. Returns to scale of a production system
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describes the increase in output resulting
from a proportionate increase in all inputs
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just as I had told proportionate increase
in all inputs. Now if the percentage increase
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in output is greater than the percentage increase
in inputs, then it is a case of increasing
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returns to scale. That means let us say we
increase all inputs by 10% and we see that
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the output rises by 15%.
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This is a case of increasing returns to scale,
whereas if the percentage increase in output
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is equal to the percentage increase in inputs,
then it is a case of constant returns to scale
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if by giving a 10% rise in the value of all
inputs we see that there is a more or less
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10% rise in the output then we say it is a
case of constant returns to scale and lastly
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if we see that by giving a 10% increase in
all input factors the output reduces by less
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than 10% say for example 5% or 7% then it
is a case of decreasing returns to scale.
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Now this returns to scale can be described
from the (()(28:56) firstly graphically. Graphically
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this is our expansion path for a constant
returns to scale. That means if X and Y are
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given equal percent change then Q rises in
the same proportion. So this is a straight
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line. That is the constant returns to scale.
Increasing returns to scale for change in
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X and Y Q rises in a much bigger fashion whereas
here it is less.
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This is a case of decreasing returns to scale.
So, graphically one can depict returns to
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scale the 3 types constant, increasing, and
decreasing returns to scale in the front wheels.
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Of course it is possible that one can have
for a firm can experience what is known as
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variable returns to scale which means that.
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As X and Y changes Q may initially rise in
an increasing and thereafter decreasing and
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then may go down becomes like this, then we
say that it is a case of variable returns
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to scale or VRS. CRS for constant returns
to scale, IRS for increasing returns to scale,
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and DRS for decreasing returns to scale.
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Now this is explained here in another way.
It says that as before this is Y and this
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is X axis. These are isoquants for quantity
Q1 and Q2. We are assuming Q2 higher than
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Q1 and here we are saying suppose that the
firm is operating at this point giving an
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input X1 and the other input Y1 getting Q1
and suppose that X1 rises by a fraction f
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meaning X2 equal to 1 plus f into X1 and Y2
Y also increases by a fraction f meaning Y2
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equals 1 plus f into Y1 then the value of
production Q2 how it is related with Q1.
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Suppose we find that Q2 also rises by this
same fraction f that is Q2 equal to 1 plus
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f into Q1 that means the rise in Q2 is f of
Q1 by the same fraction f as the input. Each
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input was raised then we say that it is a
case of constant returns to scale. Whereas
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if we find that Q2 is higher than 1 plus f
into Q1 then it is a case of increasing returns
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to scale, whereas if we find that Q2 is less
than 1 plus f into Q1 then we say that it
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is a case of decreasing returns to scale.
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This we now illustrate with the help of Cobb-Douglas
production function. Recall that Cobb-Douglas
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production function is a power function Q
equal to a into X to the power b into Y to
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the power c taking natural logarithmic we
get ln Q equal to ln a plus b ln X plus c
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ln Y. We can write from here dQ by Q equal
to b dX by X plus c into dY by Y. Now this
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dQ by Q is the fractional change of dQ, dX
by X is the fractional change in X and dY
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by Y is the fractional change in Y.
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Now since all factors are increased by the
same proportion f the following will hold
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that is dX by X and dY by Y will be equal
to f. If it is so then what is dQ by Q? dQ
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by Q will be equal to b into f plus c into
f which is nothing but b plus c whole into
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f. So this also gives another way to define
whether the returns to scale is constant or
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increasing or decreasing by comparing b plus
c with 1. So from here we say that if b plus
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c equal to 1, then dQ by Q equal to f same
as the proportional change or fractional change
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that we are given to each of the inputs.
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Then it is a case of constant returns to scale.
Whereas if b plus c greater than 1 then this
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whole quantity is greater than f. It means
that for a change in f, change in X and Y
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by amount fractional change in X and Y by
an amount f leads to a higher than fractional
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higher value to the fractional change in Q
by more than f. So this is B plus C greater
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than 1, it is a case of increasing returns
to scale. b plus c less than 1 it is a case
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of decreasing returns to scale. Please note
that b and c are nothing but exponents in
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the production function therefore barely by
looking at or summing the values of b plus
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c.
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We can say whether the firm is operating in
an increasing returns to scale or a decreasing
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returns to scale. If we find that b plus c
is more than 1 then there is a chance, there
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is high probability thereby increasing the
amount of input we get more than proportionate
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increase in the value of Q. Whereas if we
find that b plus c less than 1 it means that
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if we increase X and Y by some equal amount
there will be less than proportionate increase
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in the value of Q. This information is very
important in deciding how much more input
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we should give to increase our production.
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Now we come to output elasticity and relative
to returns to scale. Output elasticity is
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epsilon Q is the percentage change in output
associated with a 1% increase in all inputs.
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We define this as epsilon Q as equal to del
Q by Q percentage change in output by del
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X by X, where X represents all inputs put
together or added together.
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So del Q equal to del Q by del X multiplication
X goes to the numerator X by Q. If epsilon
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Q is greater than 1 then also it is a case
of increasing returns to scale. If epsilon
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Q equal to 1 then it is a case of constant
returns to scale. If epsilon Q is less than
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1 it is a case of diminishing returns to scale.
This we say merely by understanding that we
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have defined epsilon Q the output elasticity
as the percentage change in or the fractional
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change in Q for a fractional change in X.
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Now we talk about product transformation curve.
Here this curve is relevant when the firm
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is producing 2 or more products. In this case,
we are considering of course only 2 product:
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Product 1 and product 2. We are considering
and the product transformation curve basically
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shows the locus of combinations of outputs
for a given input. Suppose that we are spending
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so much money in our input labour, capital,
material, and so on and so forth then we can
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produce different quantities of products 1
and product 2 for this same input.
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So this is using the same input different
combinations of product 1 and product 2 can
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be produced. For example, let us say by using
10 lakh rupees we could produce this amount
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of product 1 and this amount of product 2
or we could produce more product 2 and less
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product 1 and if we spend more on input instead
of 100 lakh suppose that we spend 200 lakh
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then we could produce more of product 1 or
more of product 2, but the curve will be a
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higher curve.
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So this is called a product transformation
curve for different inputs I have drawn 2
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curves. This is for lower amount of input.
This is for higher amount of input, but input
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is constant here. The curve shows the locus
of combinations of outputs for a given input.
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00:43:02,440 --> 00:43:12,109
The curve is downward sloping. The slope is
negative and becoming more and more because
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an increase in output of 1 product suppose
I increase an output from here to here then
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it decreases the output of the other so the
curve is negative. The slope is negative and
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therefore it is moving downward sloping for
higher input curves are like this. So this
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is the product transformation curve.
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Now we saw iso-revenue curve. Now if each
product has got the particular price then
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we can realize some revenue by selling different
amount of material that is if the price is
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P1 for product X1 or Q1 then P1Q1 plus P2Q2
that is the revenue. So this could be 1 revenue
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and for higher revenue can be realized if
we have more products manufacture product
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1 and 2.
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Now this diagram shows that we can decide
from a product transformation curve and the
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iso-revenue curve what should be our optimal
mix
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that means that if this is the iso-revenue
curve and this is the if our unit price for
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product 1 and product 2 are given then there
slope will decide the slope of this line and
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that slope and the slope of the product transformation
curve must be equal to decide the point at
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which the optimal product mix will be achieved.
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That means if I operate at this point that
means if I produce so much of product 1 and
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so much of product 2 and then I will realize
the maximum revenue out of producing and selling
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these goods. If however I produce this much
product 1 and this much product 2 then the
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revenue will be much less parallel to this
line going here. So this is an example of
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deciding how or how much of product X1 and
how of product 1 and how much of product 2
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should be produced given that unit selling
price.
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Now we talk about technological change and
its effect on production. As you know technology
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technological change is the order of the day
and production is getting affected as time
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progresses as new technology is coming. Now
technology can influence production in basically
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2 ways. One by a change in the process or
a change in the product when we talk about
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process change we are saying that we are able
to achieve the same output with less input.
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That means the productivity is high however
when we are bringing in a product change that
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means with the same input we were able to
produce more output. Now this is shown in
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the form of 2 figures. Now, here we are showing
this is a iso-quant for the input material
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X and input material Y and this let us assume
is the present operating condition of a firm
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using input X and input Y we are able to get
the same quantity for different combinations
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00:48:30,359 --> 00:48:32,470
of X and Y.
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Now if a superior technology is available,
then this curve will shift to its left meaning
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that we will be able to produce the same output,
but with less amount of X and less amount
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of Y. This curve will shift to the left, whereas
if it is a case of inferior technology another
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00:49:08,369 --> 00:49:17,960
firm using an inferior technology we will
experience an iso-quant curve which will be
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00:49:17,960 --> 00:49:24,240
on the right side of this meaning that it
will be somewhere here for the same quantity
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00:49:24,240 --> 00:49:35,250
Q it will require more X and more Y. This
is the case of process change.
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Now let us consider the case of product change.
Now this is a look at the axis. This is Q1
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the quantity of product 1 and this is Q2,
the quantity of product 2. So this is the
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00:49:55,410 --> 00:50:08,220
case of product transformation curve. Now
in the product transformation curve we for
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the same input we are saying that given the
same input we are able to produce different
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types of mix of product, different product
mix meaning, different values of Q1 and Q2
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00:50:25,049 --> 00:50:29,400
are produced for the same input.
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Now if we are using superior technology, then
with the same input the product transformation
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curve will move to its output indicating that
we are able to get more output for the same
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input, whereas a firm using inferior product
technology or product design will have a product
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transformation curve that will be moving to
its left meaning that for the same input,
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00:51:22,339 --> 00:51:31,829
output will be less. Now technological change
is a vast area and lot of studies have been
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made in this area and we have not discussed
them here.
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So if I summarize what we discussed today
to start with is that, the quantity produced
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in a company is a function of various input
factors and our interest was to decide or
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to find out if we increase a one factor how
much change is happening in our quantity produced.
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If we increase all factors by the same amount
how much change is happening to production
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and we are defining them as returns to a factor
or returns to scale.
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After that we considered the effect of technological
change on production. Well this 5 lectures
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we have devoted to general economics, microeconomics,
and the remaining lectures we shall spend
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on more operating decision making principals
of economics in particular costing, accounting,
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and similar such things that will be useful
in managerial decision making. Thank you.