Microeconomics Assignment: Consumer Choice and Price Effects Analysis

This microeconomics assignment analyzes consumer behavior through a series of questions. It begins by examining an individual's optimal commodity basket given income and prices, determining whether the basket fully utilizes income. The assignment then explores the concept of the marginal rate of substitution. The core of the assignment involves calculating the optimal commodity basket under different price scenarios, demonstrating the impact of price changes on consumer choices. It also delves into the concept of Giffen goods, explaining their characteristics and whether coffee, in this context, is one. Furthermore, the assignment decomposes the price effect into income and substitution effects using the Slutsky decomposition method. Finally, it concludes by analyzing the price elasticity of demand for coffee, determining whether it is a normal good and how its demand relates to changes in income.

Running head: MICROECONOMIC ASSIGNMENT
Microeconomic Assignment
Name of the Student
Name of the University
Author Note

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Table of Contents
Answer 1:.........................................................................................................................................2
Answer 2:.........................................................................................................................................2
Answer 3:.........................................................................................................................................3
Answer 4:.........................................................................................................................................3
Answer 5:.........................................................................................................................................4
Answer 6:.........................................................................................................................................4
Answer 7:.........................................................................................................................................7
References:......................................................................................................................................8

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Answer 1:
According to the problem, Sally’s income is I = $200 and the price of one cup of coffee is
$4 and that of one liter of milk is $1.
Therefore, if Sally buys a commodity basket consisting of 25 cups of coffee and 50 litres
of milk, then the amount of money spent on the commodity basket by Sally is:
M = 25*($4) + 50*($1) = $100 + $50 = $150
Therefore, the amount of money spent on this basket is $150, which is less than $200.
This implies that Sally is not spending the entire income on this commodity basket. A
commodity basket is considered to be optimal if it fully utilizes the income of the concerned
individual (Baumol and Blinder 2015).
This shows that the commodity basket is not optimal.
Answer 2:
The marginal rate of substitution of X for Y can be express as the amount of Y for which
one unit of X can be exchanged (Varian 2014):
MRSXY = MUX/MUY = 20/√x
Therefore, MRSXY = 20/√x.

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Answer 3:
The optimal commodity basket can be derived with the help of the equilibrium equation.
At equilibrium,
MUX/MUY= PX/PY (Wetzstein 2013).
This implies, 20/√x = 4
Therefore, √x = 5, which implies, X = 25
From the budget-line equation, we get that:
200 = 4*25 + 1*Y
Therefore, Y = 200 -100 = 100.
The optimal commodity basket of Sally is (X=25, Y= 100).
Answer 4:
If the price of coffee increases from $4 per cup to $5 per cup, then the optimality
condition for Sally can be written as follows:
MUX/MUY = PX/PY (Kreps 2012).
This shows that,
20/√x = 5 which implies, X = 16.

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Putting the value of X in the budget line equation of Sally, we get as follows:
200 = 5*16 + 1*Y, which implies, Y = 200 – 80 = 120.
The new optimal consumption basket for sally is therefore, (X = 16, Y =120).
Answer 5:
A Giffen good is defined as a special type of inferior product, whose income effect is so
strong that it offsets the substitution effect, in case of any change in the price levels of that good.
Giffen goods fall in the exceptions of law of demand as it shows a positively sloped demand
curve, which implies that with the increase in price, people tend to buy more of these
commodities (Biederman 2015).
In this problem, when the price of coffee is $4 per cup, Sally buys 25 cups of coffee and
when the price of coffee rises to $5 per cup, Sally buys 16 cups of coffee. Therefore, with an
increase in the price of coffee, the demand for coffee decreases, implying that coffee, in this
case, is not a Giffen good.
Answer 6:
With a change in the price of coffee from $4 to $5, the demand for coffee decreases from
25 units to 16 units. This price effect can be divided into income effect and substitution effect.
The income effect shows the change in the demand of a commodity due to increased or
decreased purchasing power as a result of purchasing power. On the other hand, substitution

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effect is that component of the price effect, which shows the change in demand of a commodity
due to sole change in the relative prices of the two commodities in a two-commodity economy.
According to Slutsky decomposition method, these two effects can be mathematically
derived as follows:
With an increase in price of coffee from $4 to $5, to keep the consumer at the same level
of utility, that is to maintain the same commodity basket as consumed Sally before, her new
income should be:
M1 = 5*25 + 1*100 = 125 + 100 = 225
This implies, ∆M = M1 – M0 = 225-200 = 25
Now, at the new price situation, given the same price of milk, if the income is
compensated, the consumption of both X and Y will change:
The substitution effect can be written as:
∆Xs = X(Px1, Py, M1) – X(Px0, Py, M0)
This can be diagrammatically shown as follows:

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Figure 3: Decomposition of Price effect into Income effect and Substitution effect
[Source: Created by author]
Thus, it can be seen that, with the increase in the price of coffee, the demand for coffee
decreases. This decrease in the quantity demanded can be attributed to two effects, namely the
income effect and the substitution effect (Sasakura 2016).
Income effect – Due to an increase in the price of coffee, the price of milk remaining the
same, the relative income decreases, as a result of fall in the purchasing power. This is an

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indirect effect of an increase in price of coffee. The demand decreases partially, from X0 to X0’,
due to this relative decrease in the real income of Sally. This is known as the Income effect.
Substitution effect- An increase in the price of coffee changes the relative price ratio,
thereby causing a negative substitute effect. This implies, the quantity demanded for coffee
decreases (from X0’ to X1), due to a change in the relative price ratio. This is known as the
Substitution effect (Phlips 2014).
Together, these two effects result to a price effect, which results in a decrease in quantity
demanded for coffee from X0 to X1.
Answer 7:
It can be seen from above calculations that with a one unit increase in price of coffee,
Sally’s demand for coffee decreases from 25 cups to 16 cups, that is, by 9 units. Again, it has
been already seen that coffee is not a Giffen good in this case. On the other hand, with one unit
increase in the price, the demand decreases by nine units, indicating that the demand for coffee in
case of Sally is highly price elastic. Therefore, it can be concluded from the above observations
that coffee is a normal good and with an increase in the income of Sally, the demand for coffee
will rise, that is, income of Sally and Sally’s demand for coffee are positively related (Gillespie
2014).

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References:
Baumol, W.J. and Blinder, A.S., 2015. Microeconomics: Principles and policy. Cengage
Learning.
Biederman, D.K., 2015. A strictly-concave, non-spliced, Giffen-compatible utility
function. Economics Letters, 131, pp.24-28.
Gillespie, A., 2014. Foundations of economics. Oxford University Press, USA.
Kreps, D.M., 2012. Microeconomic foundations I: choice and competitive markets (Vol. 1).
Princeton university press.
Phlips, L., 2014. Applied Consumption Analysis: Advanced Textbooks in Economics (Vol. 5).
Elsevier.
Sasakura, K., 2016. Slutsky Revisited: A New Decomposition of the Price Effect. Italian
Economic Journal, 2(2), pp.253-280.
Varian, H.R., 2014. Intermediate Microeconomics: A Modern Approach: Ninth International
Student Edition. WW Norton & Company.
Wetzstein, M.E., 2013. Microeconomic theory: concepts and connections. Routledge.