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Good morning. Welcome to the sixth lecture
on Economics, Management, and Entrepreneurship.
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In the last 5 lectures, we had covered basics
of microeconomics theory. Today, we shall
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discuss certain exercises on those theories
that we had developed in the last 5 classes
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and it will hopefully give you much more insights
into the real life applications of the basic
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microeconomic theory that we have discussed
in the last 5 lectures. I have covered 2 or
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3 exercises from relevant to each of the lectures
as you will see.
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The first exercise that I take is from the
demand supply and market equilibrium lecture.
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This is a problem on demand function for TV
sets is given as Q equal to minus 2000 P plus
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1000 Y plus 0.01 POP, where P is the prize
of a TV set, Y is the disposable income of
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a person in a year, and POP is population.
This expression is developed on the basis
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of data and it is assumed that this equation
defines the demand function for TV sets. Three
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questions are asked.
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Find the demand function and plot the demand
curve for TV in a year, if the disposable
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income Y is 16,000 per year per person, and
POP is 900 million persons. That means Y and
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POP values are given and we are required to
find out relationship containing Q with P.
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The second part of the question is if the
price of a TV set is 10,000 rupees per set
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find the quantity demanded. The third part
is population remaining same the disposable
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income is 11,000 rupees per year per person
instead of 16,000 which was given here.
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Suppose that it comes down to 11,000 then
plot the demand curve. So first thing is that
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we are starting with this particular equation
something like regression equation where a
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demand function for Q is a given as a function
of P, Y, and POP and we are required to find
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out relationship containing Q with P for Q
with P given the values of Y and POP.
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It is straight forward what we do to solve
the first part of the problem. Firstly, these
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are given this equation is given and these
are the initial values given. The first question
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is find the relationship between Q and P.
So if I put values of Y here and of POP here,
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then I get a constant which is 25 million.
So Q is equal to minus 2000 P plus 25 million
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and P thus equal to 12,500 minus 0.0005 Q.
So if I plot P against Q it will have a negative
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slope equal to minus 0.0005 that is what I
have shown here minus 0.0005 the intercept
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is 12,500 so this is 12,500 and the slope
is minus 0.0005.
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The second part of the question is (()
that if P equal to 10,000 then what is the
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value of Q. P we know the relationship between
Q and P Q equal to this so the value of P
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is given as equal to 10,000. The estimated
value of Q is 10,000 into minus 2000 that
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is minus 20,000 when we subtract that from
25,000 this becomes 20 million and we subtract
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that from 25 which gives us 5 million deficits
so that is the second part of the question.
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The third part of the question is if instead
of Y which is given as 16,000 rupees per year
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per person suppose that the disposable income
reduces from 16,000 to 11,000, population
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remaining same then, what is the demand function
and what is the demand plot the demand curve.
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So what we need to do is just put the value
of y as equal to 11,000 and not 16,000 and
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put POP equal to 900 million as it was so
that gives us a value Q equal to the coefficient
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of P does not change, only the constant changes.
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It was earlier 25 million now it has become
20 million. So intercept, so P equal to 10.000
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minus this. So, the coefficient of Q is minus
0.00005. Here also it remains the same. Only
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the intercepts change from 12,500 it has come
down to 10,000 which means that for this reduced
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disposable income the demand curve is a straight
line which is parallel to the original line.
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This is the original line for Y equal to 16,000,
POP equal to 900 million persons. So, this
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is shifted to the left, the slope of this
line remaining the same as, 0.00005 negative.
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This is the first question.
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Now we come to exercise 2. Now, this is an
example, where an earlier study has indicated
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that the supply function for TV sets is given
as a function of price of the TV set, price
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of a competing product such as a music set
then the labour cost that is price of labour
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and the input duty or Tariff on imported TV
set. So these are defined here PC, PL, and
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Tariff and this is the estimated regression
equation that relates Q with P, PC, PL, and
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T.
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Three parts of the question are given here.
The first part is find the supply function
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and plot the supply curve for TV in a year
when values of PC, PL, and T are given. If
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the price of TV set is 10,000 rupees, find
the quantity supply other values remaining
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same. If the value of T changes from the earlier
value of 2000 rupees to a new value 1,000
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rupees then how will this supply function
change? Now let us take out this particular
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exercise.
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So given the regression equation containing
Q. P, PC, PL, T values of PC, PL, and T are
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given and when I put these values here for
PC 8,000, for PL 80,000 for T 2,000 I get
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the relationship containing Q between Q and
P such as this from here I can find P which
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is 7500 plus 0.0005 Q. So the intercept is
7,500 and the slope of this line is 0.0005.
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So I plot this one here. This curve is the
supply curve having a positive slope whose
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value equal to 0.0005 and if P equal to 10,000
if P equal to 10,000 the value of Q is given
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as 10,000 into 2,000 that makes it 20 million
minus 15 million so that gives 5 million sets.
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Now the third part of the question is if other
values remain same, but only T changes from
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the given value of 2000 to 1000, then how
will the relationship between Q and P changes.
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The demand curve will have an equation. You
put the values here. T equal to 1000 so Q
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becomes 2000 P minus 13, 500,000 and from
here I can find P. The intercept is 6,750
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corresponding to the point here 6,750 and
the slope is exactly same positive and the
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value both are same so this line is parallel,
but the intercept being lower than the previous
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value it means that as T is reduced it shifts
to the right. So this is the exercise 2.
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Now we go to exercise 3. Here, we are trying
to find out the equilibrium value and there
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are 2 ways one is floating graphically. This
is our demand curve with a negative slope.
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This is our supply curve that has a positive
slope. The point of intersection gives the
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equilibrium value of price and output. In
this case, the value is obtained as 10,000
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rupees per set and this is 5 million TV sets
in a year. Analytically also one can find
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this value.
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Plot find the demand function that we have
already generated which is minus 2000 P plus
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25 million and supply function we have already
found out Q equal to 2000 P minus 15 million
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so equate them at the equilibrium point at
the equilibrium and we will get this equal
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to this and that will give us a value of Q
and P the equilibrium values of 10,000 for
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price and 5 million TV sets as the output
of the quantity. This is exercise 3.
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Now we come to exercise 4 in this example
this exercise we are given price and output
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for a particular product in these 2 columns
quantity and price and we are required to
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find out the total revenue, marginal revenue,
and average revenue. Now total revenue is
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nothing but
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Q into P is also known as sales or total sales
or sales revenue or total revenue. It is just
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the total amount obtained by selling this
amount of this quantity of goods. So nothing
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is sold, so the revenue is 0, total revenue
is 0. One at a price of 75 therefore the revenue
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is 75 into 1 75. Suppose the price is 70,
quantity is 2, so it is 140. If 3, it is 65
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these are given so just multiply. So product
of Q and P is basically equal to TR and is
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found out.
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This column gives the total revenue for this
quantity sold. Now marginal revenue is if
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quantity increases by 1 then what is the increment
of revenue. So from 0 to 1 the increment is
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75. 75 minus 0 is 75. From 1 to 2 total revenue
increases from 75 rupees to 140 rupees so
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the increment in total revenue is 140 minus
75 which is equal to 65. Similarly from quantity
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2 to 3, the total revenue increases from 140
to 195 giving an increment of 55 that is the
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marginal revenue.
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So the marginal revenue is calculated in this
manner and you will see that marginal revenue
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reduces and becomes negative and even more
negative as quantity increases and price reduces.
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Now average revenue is nothing but total revenue
by quantity and in this case, it is same as
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price. Of course, 75 by 1 is 75. This AR cannot
be found out. Sorry this should not have a
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0 there. It should be a hyphen here, because
0 by 0 is nothing. 75 by 1 is 75. 140 by 2
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is 70, 195 by 3 is 65, 240 by 4 is 60, 275
by 5 is 55, so basically this quantity, this
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average revenue is same as price excepting
for the first one. So this is how we find
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out total revenue, marginal revenue and average
revenue.
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Now, we come to our next exercise and this
says, assume that a company with the name
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ABC electronics has the following total revenue
and total cost functions. So total revenue
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function is given in this fashion and total
cost is given in this fashion and where Q
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is the quantity produced. Find the profit
function and hence find the optimum output
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that maximizes the profit.
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Now that we know total revenue and total cost
we can find a profit function and we can optimize
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the profit. We can find out the value of Q
that maximizes the profit that is what is
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the first part of the question? The second
part of the question is show that the profit
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is maximum when the marginal revenue equal
to marginal cost. So this is exercise 5. We
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go to the solution in this fashion.
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Define first of all that the profit function
pi is given by the difference between the
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total revenue and the total cost. So total
revenue minus total cost is the total profit
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made and then we find out profit function
and then we differentiate the profit function
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with respect to Q to find out the optimum
value of Q that maximizes profit. So what
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we do here. This is pi, the profit function
is total revenue minus total cost so you subtract.
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When we subtract the 2 we get this that is
minus 1500 plus 110 Q minus Q square. So this
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is a function of Q. So take the first derivative
d pi by dQ we get 110 minus 2 Q put that equal
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to 0. So this is the necessary condition for
a function to be maximum or minimum. The first
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derivative must be equal to 0 and that gives
the value of Q equal to 55. To find out whether
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this value of Q minimizes or maximizes pi,
we go to the second derivative.
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Second derivative is minus 2 which is less
than 0 it means that at this value of Q pi
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must be maximum. So the first part of the
question which is find the profit function
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it is subtracting TC from TR which is this
and the optimum value of Q that maximizes
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profit is 55. We have tested that it gives
the maximum value. The second part of the
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question was that show that at that optimum
point MR equal to MC.
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It is very straight forward. Pi equal to profit
equal to total revenue minus total cost which
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is written here. If I take the first derivative
with respect to Q which we have done here
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that is nothing but first derivative of TR
minus first derivative of TC. The first derivative
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of TR with respect to Q is nothing but MR
and the first derivative of TC with respect
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to Q is nothing but marginal cost and since
d pi by dQ has to be equal to 0 when it is
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maximum MR must to be equal to MC. So it is
very straight forward this is the second part
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of this exercise.
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To exercise 6, this exercise deals with arc
elasticity. Now, if you read this exercise
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during February, in an effort to reduce the
end-of-the-year inventory, an auto break assembly
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manufacturer offered rupees 6,000 discount
from the existing rupees 60,000 sticker price,
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on each break assembly. The monthly sale rose
from 15 to 23 on account of this price discount.
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Now you see that the change is something like
10% which is higher than 5%.
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And if you recall whenever there is a price
change of more than 5% we go for computing
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the arc elasticity of demand. The question
therefore is given. So the question therefore
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is given is to calculate the arc elasticity
for this break assembly and the second part
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is quite interesting it says calculate the
sticker price reduction necessary to eliminate
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the manufacturer's remaining inventory of
27 assemblies during the next month.
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Come to the solution part. This is the diagram
that shows the situation. Now, this is the
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demand function for the autobreak assembly.
Now, the operating point is here that initially
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the price was 60,000 and the quantity demanded
in the market were just 15 and the manufacturer
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reduced the price by giving a discount of
6,000 rupees bringing down the price from
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60,000 to 54,000 and that resulted in an increase
in the value of Q2.
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Now this reduction is as you can see is 10%
quite high therefore arc elasticity calculation
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is relevant here rather than point elasticity
calculation and according to our equation
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for arc elasticity it is the change in the
quantity by the average quantity by change
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in the price by the average price which results
in this expression Q2 minus Q1 by P2 minus
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P1 and P2 plus P1 by Q2 plus Q1. This division
by 2 cancels out.
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So we have price elasticity of demand that
is arc elasticity is given by this expression.
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Now put the values of Q2, Q1, P2, P1, etc
and we get a value of arc elasticity as equal
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to minus 4. Now the second part of the question
is at the end of the month there are 27 break
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assemblies available if the arc elasticity
is minus 4 then what should be the price at
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which it can be sold so that all the 27 can
be sold out that means if this Q3 is 27 what
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is the value of P3. So we use the same relationship
except in that instead of P2 we now write.
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We do not take the old value of P2, this actually
is P3. So instead of P2 it should be P3, P3
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and P3 and P3, therefore this changes should
be done. So I am just putting these values
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here so this expression gives a value of P3
equal to 52,000, P3 minus P1 equal to minus
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8000 that means a further discount of 8000
rupees per break assembly should be given
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and that will enable the manufacturer to sale
out its remaining 27 inventory break assemblies.
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So this is example 6 or exercise 6.
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Now we go to exercise 7. Exercise 7 is likewise
quite interesting. It says that video station
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sells video recordings of movies and also
sells blank cassettes for home recording.
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Now during Puja holidays, video station reduced
its prices as follows: For video recording
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it reduced its price from rupees 29.99 to
rupees 24.97 and for blank cassettes it reduced
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its price from rupees 19.99 to rupees 14.97.
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The trade association in a recent study has
estimated the point price elasticity to be
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as follows: For video recording it has found
out a value of minus 1.5 and for blank cassettes
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it found out a value of minus 4. Now in the
right of this trade associationâ€™s recommendations
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are estimated values of the point elasticities.
are the new prices justified meaning these
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prices that the video station is now charging
is it justified if the unit cost of manufacturing
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that is unit cost of preparing a video recording
and having a blank cassette are rupees 10
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and rupees 8 respectively. This is the question.
Is it justified?
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Now recall the relationship between the marginal
revenue, price, and
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point price elasticity epsilon P. Marginal
revenue equal to d by dQ of TR that is unit
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change in Q brings in how much change in the
total revenue. Total revenue is nothing but
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price into quantity PQ and as we know P is
a function of Q so if you take the derivative
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it is first function as it is into the derivative
of the second so, P into derivative of the
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second means, d by dQ which is 1 plus derivative
of the first function, which is dP by dQ into
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Q. So MR equal to this which is equal to P1
plus dP by dQ keep it like this.
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00:30:53,139 --> 00:31:04,950
And here it is Q by P is take P here and Q
here, so it becomes dP by P, dQ by Q and this
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is nothing but P taken outside 1 plus 1 by
dQ by Q by dP by P and this by definition
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is the point price elasticity of demand that
means a small change in P, a fractional change
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00:31:24,879 --> 00:31:31,659
in P gives rise to how much fractional change
in Q that is epsilon P. So, the relationship
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between marginal revenue, price and elasticity
are these things. Now, at the equilibrium
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as we already have seen marginal revenue equal
to marginal cost.
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Hence the equilibrium prices at which this
relationship will hold are the following:
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As you know marginal cost for video recording
is given as rupees 10 that will be equal to
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00:32:03,179 --> 00:32:16,159
price of video recording into 1 plus 1 by
epsilon P, so 1 plus 1 by minus 1.5, the value
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00:32:16,159 --> 00:32:25,039
that the trade association has estimated.
Now if I solve this equation I get the value
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of price of video recording which is 30 rupees
whereas the new prices that the company is
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00:32:37,049 --> 00:32:46,720
charging is only 24.97 that means this reduction
is not justified.
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Now we go for the blank cassettes. Blank cassettes
the marginal cost for the company for blank
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cassette is rupees 8. Using the same relationship
with the new value of epsilon P as estimated
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00:33:05,219 --> 00:33:11,489
by the trade association, which is equal to
minus 4. The value of the blank cassettes
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00:33:11,489 --> 00:33:26,480
would be the price should be set up 10.67
therefore setting rupees 8 is the setting
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00:33:26,480 --> 00:33:37,570
the price as rupees 14.97 is also not justified
it should be reduced to 10.67 whereas for
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00:33:37,570 --> 00:33:46,029
video recording it should be increased to
rupees 30. So the new prices that the company
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is charging are not justified. Now you can
see from this example that elasticity knowing
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the value of elasticity helps in fixing the
prices. Now we got to the next example.
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The next example, next exercise, this exercise
is on demand estimation and demand forecasting.
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00:34:14,669 --> 00:34:23,339
We start with a very simple example where
we show that the annual sales exercise is
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00:34:23,339 --> 00:34:33,930
like this. Annual sales of Babu restaurant
are as follows in thousand rupees: Starting
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00:34:33,930 --> 00:34:46,551
from annual sales so some year, let us say
2000, this is 2001, 2002 like that up to 2011
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00:34:46,551 --> 00:34:55,850
and 284 thousand rupees, 266 etc follows like
this and we are required to find out the annual
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00:34:55,850 --> 00:35:07,860
rate of growth assuming a constant growth
rate with annual compounding. Make a 5-year
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00:35:07,860 --> 00:35:09,770
forecast.
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00:35:09,770 --> 00:35:23,150
So basically we are assuming that here that
the growth of sale quantity sold at time t
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00:35:23,150 --> 00:35:35,930
follows a power function, follows a growth
such as this Q0 into 1 plus g to the power
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00:35:35,930 --> 00:35:47,970
t. Q0 is the sale in the year 2000 and g is
the annual growth rate and to the power t.
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00:35:47,970 --> 00:35:58,910
So this is the annual growth rate that means
in the starting from 2000, 2001 sale is expected
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00:35:58,910 --> 00:36:09,810
to be 2000 sale into 1 plus g. 2002 sale will
be 2000 sale into 1 plus g to the power 2
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00:36:09,810 --> 00:36:20,100
so on and so forth. So from here suppose that
we put the 2011 value as 568 and 2000 figure
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00:36:20,100 --> 00:36:29,650
as 284 and t is 10.
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00:36:29,650 --> 00:36:41,100
Then this is the relationship from here we
get 2 equal to 1 plus g to the power 10, therefore
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00:36:41,100 --> 00:36:57,650
ln 2 equal to 10 ln 1 plus g. There is a mistake
here there should be 10 ln 1 plus g and that
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00:36:57,650 --> 00:37:09,160
gives a value g equal to 0.0718. So, this
is the annual growth rate that is 7.18% and
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00:37:09,160 --> 00:37:18,240
suppose that we are asked to find out or estimate
5-year hence sale forecast of the annual sales
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00:37:18,240 --> 00:37:30,540
of Babu restaurant then it will be given as
Q15 as 284 into 1 plus g is 0.0718 to the
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00:37:30,540 --> 00:37:42,570
power 15 and that is 803.436 thousand rupees.
So this is a very simple example of sales
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00:37:42,570 --> 00:38:00,510
forecast that at any time the sale QT is defined
as a compounded annual growth function.
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00:38:00,510 --> 00:38:07,220
Now we take another exercise on demand forecasting
another simple example. The operations manager
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00:38:07,220 --> 00:38:17,090
of a TV set manufacturing company believes
that sales of its products in any month St
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00:38:17,090 --> 00:38:26,500
increase by the same percentage as income
It during the previous year. Write an equation
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00:38:26,500 --> 00:38:37,230
for sales forecast. This month, sales totaled
rupees 500 thousand while family disposable
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00:38:37,230 --> 00:38:46,630
income increased from rupees 25,000 to rupees
26,000 forecast the next year's sales.
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00:38:46,630 --> 00:38:54,500
So for the first part of the question is,
write an equation for sales forecast. The
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00:38:54,500 --> 00:39:02,530
problem statement says that the operation
manager believes that the sales of its product
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00:39:02,530 --> 00:39:12,270
in month, St increases by the same percentage
as income It. So we shall write St plus 1
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00:39:12,270 --> 00:39:23,870
as equal to St plus the change in S. The change
in S as mentioned here is some fraction of
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00:39:23,870 --> 00:39:31,510
St and that some fraction is nothing but as
income percentage change. The income percentage
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00:39:31,510 --> 00:39:36,750
change is It minus t minus 1 by It minus 1.
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00:39:36,750 --> 00:39:47,330
This is the fractional change which is same
for St. So, the expression U is the the random
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00:39:47,330 --> 00:39:59,150
error. So St plus 1 is St plus St into this
fraction which is same as now the next part
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00:39:59,150 --> 00:40:05,900
of the question is if the values are given
you just put the values here. We put 500,000
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00:40:05,900 --> 00:40:17,510
is the St which is taken outside so it is
1 plus 26,000 and it increased from 25 to
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00:40:17,510 --> 00:40:31,610
26 so 26 minus 25 by 25 and that resulted
in a value of 520,000 rupees that is the next
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00:40:31,610 --> 00:40:34,370
year's sales.
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00:40:34,370 --> 00:40:44,650
So today, we have seen some applications,
some exercises on basic microeconomic theory
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and also on demand forecasts. In the next
lecture, we shall take some more exercises
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00:40:55,520 --> 00:41:05,270
on production and then we switch over to cost
benefit analysis, break-even analysis, and
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00:41:05,270 --> 00:41:17,600
further in our forthcoming lectures next few
lectures we shall study various aspects of
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costing, accounting, and engineering economy.
Thank you very much.