1. 20 ? ? ? 27 10 21 ?

1.
Calculate the following:

Quantity

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Total Fixed Cost

Total Variable Cost

Total Cost

Average Cost

Marginal Cost

25

10

18

?

?

?

26

10

20

?

?

?

27

10

21

?

?

?

 

Analyse
the changes in the calculated costs as quantity produced increases.

Ans:

The
above scenario depicts the short run of production.

Short-Run Total Cost

The
total cost refers to the actual cost that is incurred by an organization to
produce a given level of output. The Short-Run Total Cost (SRTC) of an organization
consists of two main elements:

Total Fixed Cost (TFC):
These costs do not change with changes in the numbers of units produced or
sold. TFC remains constant even when the output is zero. TFC is represented by
a straight line horizontal to x-axis (output).

Total Variable Cost
(TVC): These vary directly with the changes in
the number of units produced or sold. These costs are directly proportional to
the output of a firm. This implies that when the output increases, total
variable cost also increases and when the output decreases, total variable cost
decreases as well.

In
Total Cost in Short-Run is obtained by adding the total fixed and the total
variable cost.

SRTC = TFC + TVC

Quantity

Total Fixed Cost

Total Variable Cost

Total Cost (TFC + TVC)

25

10

18

28

26

10

20

30

27

10

21

31

 

As
the TFC remains constant, the changes in SRTC are entirely due to variations in
TVC.

 

Short-Run
Cost of a firm

 

Short-Run Average Cost

The
average cost is calculated by dividing total cost by the number of units a firm
has produced. The average cost in short-run (SRAC) of a firm refers to per unit
cost of output as different levels of production.

To
calculate Average cost in short run, total cost is divided by the output. 

SRAC
= SRTC/Q = TFC + TVC /Q

=
TFC/Q + TVC/Q

Where,
TFC/Q = Average Fixed Cost (AFC) and TVC/Q = Average Variable Cost (AVC)

 

Therefore,
SRAC = AFC + AVC

Quantity

Total Fixed Cost

Total Variable Cost

AFC = TFC/Q

AVC = TVC/Q

Average Cost (AFC +
AVC)

25

10

18

10/25 = 0.40

18/25 = 0.72

1.12

26

10

20

10/26 = 0.38

20/26 = 0.77

1.15

27

10

21

10/27 = 0.37

21/27 = 0.78

1.15

 

The
Average Cost in Short-Run of a firm is U-shaped. It declined in the beginning,
reaches to a minimum and starts to rise. In the beginning, the fixed costs
remain the same while only the variable costs, such as cost of raw material,
labour, etc. changes. Later when the fixed cost get distributed over the
output, the average cost begins to fall. When a firm utilizes its capacities to
the full, the average cost reaches to a minimum. It is at this point that the
firm operates at its optimum capacity.

The
Average Cost in Short-Run represents the average cost in the short run for
producing a given quantity of output. The downward-slope of the SRAC curve
indicates that as the output increases, average costs decreases. However, the
SRAC curve begins to slope upwards, indicating that at output levels above Q1,
average costs start to increase.

 

                                                                                                           

                                                                                                    SRAC

 

                            Cost

 

 

                                                                        Q1
(Quantity)

 

U-Shaped
Average Cost in Short-Run

 

Short-Run Marginal Cost

Marginal
Cost (MC) is the extra cost a firm incurs when it produces one more units of a
product. Marginal Cost can be defined as the change in the total cost of a firm
divided by the changes in the total output. Marginal Cost is short run refers
to the change in short-run total cost due to a change in the firm’s output.

SRMC
= ØSRTC / ØQ

In
the marginal cost concept, ?Q = 1

Quantity

Total Cost

Marginal Cost

25

28

26

30

2

27

31

1

 

Marginal
Cost in short-run on a graph is the slope of the short-run total cost and
depicts the rate of change in the total cost as output changes. The marginal
coat of a firm is used to determine whether additional units need to be
produced or not. If a firm could sell the additional unit at a price greater
than the cost incurred to produce the additional unit (marginal cost), the firm
may decide to produce the additional unit.

Marginal
Cost in Short-Run

The
Marginal Cost in short-run (SRMC), Average cost in short-run (SRAC) and average
variable cost (AVC) is U-shaped due to increasing returns in the beginning
followed by diminishing returns. SRMC curve intersects SRAC curve and the AVC
curve at their lowest points.

Hence
the final figures are as below:

Quantity

Total Fixed Cost

Total Variable Cost

Total Cost

Average Cost

Marginal Cost

25

10

18

28

1.12

26

10

20

30

1.15

2

27

10

21

31

1.15

1

 

Conclusion:

A
Short-run period refers to a certain period of time where at least one input is
fixed while others are variable. In the short-run period, an organization
cannot change the fixed factors of production, such as capital, factory
building, plant and equipment, etc. However, the variable costs, such as raw
material, employee wages, etc, changes with the level of output. If a firm
intends to increase its output in the short run, it would need to hire more
workers and purchase more raw materials. The firm cannot expand its plant size
or increase the plant capacity in the short run. Similarly, when demand falls,
the firm would reduce the work hours or output, but cannot downsize its plant. Therefore,
in the short run only variable factors are changed, while the fixed factors
remain unchanged.

 

2.
Assume that a consumer consumes two commodities X and Y and makes five combinations
for the two commodities:

Combination

Units of X

Units of Y

A

25

3

B

20

5

C

16

10

D

13

18

E

11

28

 

Calculate
Marginal rate of Substitution and explain the answer.

Ans:

The
concept of marginal rate substitution (MRS) was introduced by Dr. J.R. Hicks and Prof. R.G.D. Allen to take the place of the concept of diminishing
marginal utility. Allen and Hicks are of the opinion that it is unnecessary to
measure the utility of a commodity. The necessity is to study the behavior of
the consumer as to how he prefers one commodity to another and maintains the
same level of satisfaction.

For
example, there are two goods X and Y which are not perfect substitute of each
other. The consumer is prepared to exchange goods X for Y. How many units of Y
should be given for one unit of X to the consumer so that his level of
satisfaction remains the same?

The
rate or ratio at which goods X and Y are to be exchanged is known as the
marginal rate of substitution (MRS). In the words of Hicks:

“The
marginal rate of substitution of X for Y measures the number of units of Y that
must be scarified for unit of X gained so as to maintain a constant level of satisfaction”.

Marginal
rate of substitution (MRS) can also be defined as:

“The
ratio of exchange between small units of two commodities, which are equally
valued or preferred by a consumer”.

Marginal
rate of substitution (MRS) refers to the rate at which one commodity can be substituted
for another commodity maintaining the same level of satisfaction. The marginal
rate of substitution is the amount of a good that a consumer is willing to give
up for another good, as long as the new good is equally satisfying. The MRS for
two substitute goods X and Y may be defined as the quantity of commodity X
required to replace one unit of commodity Y (or quantity of commodity Y
required to replace one unit of X) such that the utility derived from either
combinations remains the same. This implies that the utility of X 9or Y) is
equal to the utility of additional units of Y (or X) added to a combination. It’s
used in indifference theory to analyze consumer behavior. The marginal rate of
substitution (MRS) is calculated between two goods placed on an indifference
curve, displaying a frontier of equal utility for each combination of
“good X” and “good Y”. The marginal rate of substitution is
always changing for a given point on the curve, and mathematically represents
the slope of the curve at that point. MRS of X and Y is denoted as ?Y / ?X as
it continues to diminish as the consumer continues to substitute X for Y or
vice versa. According to the ordinal utility approach, MRS?,? (or MRS?,?)
decreases which means that the quantity of a commodity an individual is willing
to give up for an additional unit of the other commodity continues to decrease
with each substitute.

MRS?,?
is calculated using the following formula:

MRS?,?
= ?X / ?Y

Combination

Units of X

Units of Y

Changes in X (?X)

Changes in Y (?Y)

MRS?,?
= ?X/ ?Y

A

25

3

 

B

20

5

-5

2

-2.50

C

16

10

-4

5

-0.80

D

13

18

-3

8

-0.38

E

11

28

-2

10

-0.20

 

As
the consumer moves from combination A to B on Indifference Curve, he/she
sacrifices 5 units of commodity X and gets 2 units of commodity Y. Therefore MRS?,?
= -2.50

Similarly
when the consumer moves from combination B to C, he/she sacrifices 4 units of X
and gets 5 units of Y. Therefore MRS?,? = -0.80

Again
when the consumer moves from combination C to D, he/she sacrifices 3 units of X
and gets 8 units of Y. Therefore MRS?,? = -0.38

At
last when the consumer moves from combination D to E, he/she sacrifices 2 units
of X and gets 10 units of Y. Therefore MRS?,? = -0.20

The
concept of marginal rate of substitution is an important tool of indifference
curve analysis of demand. The rate at which the consumer is prepared to
exchange goods X and Y is known as marginal rate of substitution.

Conclusion:

The
marginal rate of substitution does not examine a combination of goods that a
consumer would prefer more or less than another combination, but examines which
combinations of goods the consumer would prefer just as much. It also does not
examine marginal utility – how much better or worse off a consumer would be
with one combination of goods rather than another – because all combinations of
goods along the indifference curve are valued the same by the consumer.

3.
a) Suppose the monthly income of an individual increases from Rs 20,000 to Rs 35,000
which increases his demand for clothes from 40 units to 50 units. Calculate the
income elasticity of demand and interpret the result.

Ans:

In
the words of Watson, “Income
elasticity of demand means the ratio of the percentage change in the quantity
demanded to the percentage in income.”

For
example, the demand for a product increases with increase in consumer s income
and vice versa, while keeping other factors of demand at constant. The degree
of responsiveness of demand with respect to change in consumer s income is
called income elasticity of demand. According to Watson, “Income elasticity of
demand means the ratio of the percentage change in the quantity demanded to the
percentage in income.”

According
to Richard G. Lipsey, “The
responsiveness of demand to change in income is termed as income elasticity of
demand.”

Mathematically,
the income elasticity of demand can be stated as:

 

            e ? =      Percentage change in quantity demanded

                               Percentage
change in income

Where,

Percentage
changes in quantity demanded =

 

      New quantity demanded – Original quantity
demanded (?Q)

                             Original quantity
demanded (Q)

 

Percentage
change in income =

 

            New income – Original income (?Y)

                        Original income (Y)

 

Thus,
the formula for calculating the income elasticity of demand is as follows:

e
? = ?Q/ ?Y x Y/Q

Where,

Q
is original quantity demanded

Q1
is new quantity demended

?Q
= Q1 – Q

Y
is original income

Y1
is new income

 ?Y = Y1 – Y

 

Given
that;

Y
= 20,000

Y1
= 35,000

?Y
= 35,000 – 20,000 = 15,000

Q
= 40 units

Q1
= 50 units

?Q
= 50 – 40 = 10

The
formula for calculating the income elasticity of demand is:

e
? = ?Q/ ?Y x Y/Q

Substituting
the values,

e
? = 10 / 15,000 x 20,000 / 40

=
0.333 ( 1)

Conclusion:

Positive cross
elasticity of demand: When an increase in the price of a related product
results in an increase in the demand for the main product and vice versa, the
cross elasticity of demand is said to be positive. Cross-elasticity of demand
is positive in case of substitute goods.