The Concept of Utility Maximisation and Price-Demand Relationship in Economics

This article discusses the concept of utility maximisation and the price-demand relationship in economics, focusing on the impact of tax on new born babies. It explores the concept of utility, indifference curves, marginal rate of substitution, and the price-demand relationship for normal goods and Giffen goods. The article concludes by discussing how the imposition of tax can affect the demand for new born babies in different families.

Running head: ECONOMICS
Economics
Name of the Student
Name of the University
Author Note

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Table of Contents
Introduction:...............................................................................................................................2
The concept of utility maximisation:.........................................................................................2
The concept of indifference curve:............................................................................................3
Marginal rate of substitution:.................................................................................................4
Price demand relationship considering normal goods:..........................................................5
Price demand relationship considering Giffen goods:...........................................................7
Conclusion:................................................................................................................................9
References:...............................................................................................................................10

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Introduction:
According to the given scenario, the government intends to impose a tax on new born
baby. This decision affects the utility function as well as relative indifference curves of a
family significantly. For instance, some families become a larger one while other families
reduce their family size due this tax. To understand and describe these two situations
precisely, it would be beneficial to discuss the concept of utility and indifference curves at
first (Hess, Daly and Batley 2018). Utility is an economic concept through which one can
measure the preferences over a bundle of goods or services. Therefore, this economic
measurement represents the satisfaction or welfare of a consumer receiving by consuming a
certain amount of products. However, from rational point of view, happiness, welfare or
satisfaction are considered as abstract concepts. For this, economists measure this utility with
the help of revealed preferences through considering choices of consumers (Pastor-Bernier,
Plott and Schultz 2017). This concept further helps to order different basket of goods or
services as per the preferences of consumers.
The concept of utility maximisation:
In this context, the concept of consumer choice can be described from which the
choice of different families can be described. This theory intends to maximise the utility of a
family through combining goods at a given budget. To understand that how a family can
select between different combinations of goods, the concept of equi-marginal utility,
indifference curve along with budget lines will be used (Drew, Grant and Fisher 2017).
According to the equi-marginal principle, the equilibrium of consumer occurs when value of
marginal utility/price becomes equal for each good. From this combination of goods, the
family can maximise their utility. This relationship can be described in mathematical way.
This is shown in below:

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MU A/ price of A = MU B/ price of B = MU Z/ price of Z
This implies that, if tax imposes, the marginal utility of new born can fall. Therefore,
to obtain the equilibrium again, the consumer needs to decrease the family size as they cannot
change the number of existing children. This utility concept can be described cardinally with
the help of following table.
Unit MU of new born MU of existing child
1 40 22
2 32 20
3 24 18
4 16 16
5 8 14
6 0 12
Let the cost of having new born is and existing child is 1 unit. Therefore, the optimum
combination of having new born will be 4 units. In this context, economists assume that
utility can be measured and represented with numerical value.
The concept of indifference curve:
In an indifference curve, various combinations of two goods can be obtained from
where a consumer can receive same level of utility and satisfaction. Thus, on a particular
curve, the consumer remains indifferent while higher curve represents higher utility. In this
situation, the consumer can maximise utility when a budget is given. Now, the situation can
be analysed with the help of income effect and substitution effect when the government
imposes tax on new born (Keller 2015). In this context, new born can be assumed as normal
good for some family and Giffen good for others. According to the hypothesis of utility
maximisation, increase in price of normal goods leads the amount of quantity purchased to
decrease further and vice versa. This happens due to substitution effect and income effect.
Substitution effect influences the consumption of a particular consumer due to changing

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relative prices (Becker 2017). On the contrary, income effect represents the impact of
purchasing power of a consumer. Therefore, substitution effect means an increase in price of
a particular good, which further can influence consumer to purchase alternative goods. The
consumer moves along the indifference curve as price of good changes accordingly. Income
effect, on the other side, measures that how changing price can influence the income of
consumer. This is because increase in price can reduce disposable income and this in turn can
reduce the demand of the consumer as a whole. In this context, the consumer can shift to
higher or lower indifference curves as income changes. In case of a normal good, when price
increases the quantity purchased decreases significantly and in this situation both income
effect and substitution effect work in a same direction (Cowell 2018). In case of Giffen
goods, substitution effect and income effect have opposite impact and for this no definite
prediction can be provided. These two situations can be explained with the help of Slutsky
equation.
Marginal rate of substitution:
The marginal rate of substitution represents the rate at which a consumer intends to
sacrifice one good in order to exchange it with another good for maintaining the same utility
level (Vîlcu and Vîlcu 2015). This concept can be described with the help of following
expression:
MU A/ MU B
The indifference curve represents the rate at which a consumer of family intends to
trade a good by one unit sacrificing the other one with more than one unit. This rate of
exchange is required to be equal to the marginal rate of substitution (Mankiw 2016). The
slope of an indifference curve generally remains convex to the origin due the principle of
diminishing marginal rate of substitution. In this situation, the welfare maximises when the

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C
b
IC2
New born
Existing child
IC1
a
c
Q1Q2Q3
S.EI.E
A
BC’
indifference curve tangents with the budget line. The budget line of a family represents
different combination of two goods at their given prices at which they can afford this with the
given income. This budget line is a downward slopping straight line (Leamer and Stern
2017). The family receives the optimum choice when an indifference curve intersects with
the budget line. When real income of a family decreases, the budget line shifts downward
while the opposite can arrive when the family earns more income (Mohajeryami et al. 2016).
In this situation, the budget curve shifts upward implying that the family can obtain more
utility through achieving higher utility.
Price demand relationship considering normal goods:
To understand the price-demand relationship in case of normal goods, the following
diagram can be taken under consideration.
Figure 1: Income and substitution effect for normal goods

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Source: (Created by author)
The above figure represents the income and substitution effect when new born is
considered as normal good. The indifference curve represents a family’s utility considering
two goods, which are new born and existing child. The initial budget line is AB and the initial
indifference curve is IC0, which tangents with the budget line at point a. The corresponding
level of output is Q1. As the government imposes tax, the price of new born increases and for
this the budget curve shifts from IC0 to IC1 in a downward direction. The initial indifference
curve is IC1 though after increasing price, the indifference curve becomes IC2. In this
context, the entire process of shifting can be described as price effect, which can be divided
into substitution and income effect (Coglianese 2017). To understand this substitution effect,
the new budget line is shifted outward as shown by the red line in above figure. These curve
tangents with the original indifference curve at point c. The new level of output becomes Q2.
Therefore, the shifting from Q1 to Q2 is the substitution effect. The family always intends to
substitute new born due to higher expenses. Due to this increase in cost, the real income of
the family decreases and this in turn decreases the purchasing power of the family (Sasakura
2016). The above diagram represents this situation as well when the tendency of new born
decreases from Q2 to Q3. Therefore, the overall shifting happens from Q1 to Q3 and this
implies that desire of a family for new born decreases as cost increases due to tax imposition.
The above discussion can interpret the situation of decreasing family size precisely as
the government imposes tax on new born. These families consider new born as normal good
and consequently increasing cost of new born adversely influence them to increase their
family size. They prefer to have their existing child only as this cannot reduce the real income
of these families.

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b
Q1 Q2
C
c
IC2 New born
Existing child
IC1
a
Q3
S.E
I.E
A
BC’
Price demand relationship considering Giffen goods:
However, imposition of tax can influence some families to increase their family size
and this situation can be described as follow with the help of a suitable diagram. In this
context, the family considers new born as Giffen goods. The initial budget line is AB which
shifts rightward after increasing of price. The initial indifference curve is IC1 and the
equilibrium point is a (Franco 2015). After shifting the budget line, new equilibrium point
becomes b as the curve tangents with the new indifference curve IC2. This entire effect is
represented as the price effect. This entire situation can be divided into two parts as well.
Figure 2: Income and substitution effect for Giffen goods
Source: (Created by author)

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The above figure represents income effect and substitution effect for a giffen good.
The shifting of curve from point a to point b is the substitution effect. In this situation, the AC
budget line shifts parallel to upward direction from AC to AC’. Therefore, the new budget
tangents the indifference curve IC1 at point b. This happens as the family substitute new
born. However, the cost of having no baby is more compare to having new born. In this
context the family wants to have new born for expanding their family (Salerno 2017).
Therefore the point shifts from point b to point c. This income effect exceeds the substitution
effect and consequently the family desires to have new born and consequently the family size
increases significantly,
Therefore, the above situation explains that imposing of tax can influence a family
either in positive or negative direction, after the implementation of tax. Some families with
middle-income group consider new born as increasing of cost can affect their given budget
adversely. Therefore, both substitution effect and income effect of these families tend the
number of new born baby to decrease further. They prefer single child or maximum two
children. Daily expenses force them to allocate resources efficiently for maximising utility at
given budget constraint (Chan and Gillingham 2015). However, some families with higher
income group consider new born as inferior good. Therefore, they prefer to have more
children when the government imposes tax while they do not want to have new born when
the government do not consider new born as a serious issue. This incident sometimes
increases their status in society. On the other side, the lower income group people also prefer
more children as this can help these families to earn more income in future (Landi 2015).
This amount can compensate the expenses, which these families experience during new born.
Therefore, having more child changes the utility level of families. Some families increase
their utility level as new born increases their utility level while some families decrease their
utility level as new born increases.

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Conclusion:
Therefore, the entire statement can be discussed briefly in this section. The
indifference curve represents a particular level of utility of a family. The chief motive of each
economic entity is to maximise utility when the budget in given as constant. The chief motive
of this assignment is to discuss that how imposition of tax increases the demand for new born
in some families while the demand decreases in other families. To analyse this concept, the
paper considers new born as normal good in some context and Giffen good in other context.
The entire discussion is based on income effect and substitution effect, which is described
with the help of slutsky equation. In case of normal good, the increase in price tends the
demand to decrease further. This happens as both effects tend to opposite direction as price
increases. On the other side, increase in price can increase the demand for Giffen goods. As a
result, some families intend to increase their family size after implementing tax.

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