This document discusses how a consumer's utility is affected by changes in prices due to taxes. It analyzes the consumer theory concepts of utility maximization, budget constraints, indifference curves, and optimal consumption bundles. Specifically, it examines a person named Sally who faces a tax on petrol. It shows that the tax increases the price of petrol, lowers her optimal petrol consumption from 100 to 75 liters, and reduces her maximum utility from 122.47 to 106.06. Providing Sally with a $50 benefit would allow her to regain her original utility level by consuming an additional 25 liters of petrol.

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PRICE THEORY
No of Words: 867

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PRICE THEORY
ASSIGNMENT 1- CONSUMER THEORY

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Contents
QUERY 1: ....................................................................................................................................................... 4
QUERY 2: ....................................................................................................................................................... 6
QUERY 3: ....................................................................................................................................................... 7
QUERY 4: ....................................................................................................................................................... 9
QUERY 5: ..................................................................................................................................................... 10
QUERY 6: ..................................................................................................................................................... 10

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The utility function is of Sally acquainted by:
𝑈𝑈 = √𝑋𝑋𝑋𝑋
Here the level of utility is denoted by U.
Quantity of petrol in litres is denoted by X.
The quantity of composite good is denoted by Y.
Now the income of Sally per week is $300.
Also the price of petrol is 1.5 per litre which is denoted by PX.
Along with that the price of composite good is $1 per unit which is denoted by PY.
Sally’s budget restraintis acquainted by:
M= PXX + PYY
⇒ 300= 1.5X + 1Y
QUERY 1:
The utility of aperson is boosteddue to the budget restraint.
Here the utility function and the budget restraint are entrenched.
The accelerationposition is:
𝑀𝑀𝑀𝑀𝑋𝑋
𝑀𝑀𝑀𝑀𝑌𝑌
=
𝑃𝑃𝑋𝑋
𝑃𝑃𝑌𝑌
Also from the query MUX and MUY are acquainted:
𝑀𝑀𝑀𝑀𝑋𝑋 =
√𝑌𝑌
2√ 𝑋𝑋
and 𝑀𝑀𝑀𝑀𝑌𝑌 =
√ 𝑋𝑋
2√𝑌𝑌
Inputting the characters in the accelerationposition we get;

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⇒
√𝑌𝑌
2√ 𝑋𝑋
√ 𝑋𝑋
2√𝑌𝑌
=
1.5
1
⇒
2√𝑌𝑌√𝑌𝑌
2√ 𝑋𝑋√ 𝑋𝑋
=
15
10
⇒
𝑌𝑌
𝑋𝑋
=
3
2
⇒𝑌𝑌 =
3
2
𝑋𝑋 -------- (i)
Substituting equation (i) in the Budget Restraint, we get,
⇒300= 1.5X + 1 *
3
2
X
⇒300= 1.5X + 1.5X
⇒300= 3X
⇒ X= 100
Substituting the amount of X in the budget restraint, we get the amount of Y:
⇒ 300= 1.5*100 + 1*Y
⇒ 300= 150 + Y
⇒ Y= 150
Thus the suitable consumption batch for Sally is X*
=100 and Y*
=150
Achieving the maximum utility is done by substituting the suitableamount of X and Y which is
actually utility function of Sally:

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𝑈𝑈 = √𝑋𝑋𝑋𝑋
⇒𝑈𝑈 = √100 ∗ 150
⇒𝑈𝑈 = √15000
⇒𝑈𝑈 = 122.4745
Finally the level of utility that Sally achieves from the consumption batch is U= 122.4745
QUERY 2:
The suitable solution to the above problem is shown in the presentation below:
The budget line: 300= 1.5X + 1Y
Two points on the X-axis and Y-axis is acquainted by:
X=0; Y= 300, where Y=0; X= 200.
Here the budget line is adverselytilted.
Therefore the equation of the indifference curve is acquainted by utility function of Sally.
Here the indifference curve is also adverselytilted.
Y
300
*
Y*
=150
IC
BL
E

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The IC shows the indifference curve based on the consumption batch of Sally.
Therefore the suitable consumption batch (X*
, Y*
)is 100 and 150 units of petrol and composite
good is consumed by Sally.
This way the BL represent the budget line of Sally.
(Begg & Ward, 2003)
QUERY 3:
Application of tax on the price of petrol raises the price of petrol to $2 per litre. This change in
price alters Sally’s acceleration behavior.
The optimizing position is acquainted by:
𝑀𝑀𝑀𝑀𝑋𝑋
𝑀𝑀𝑀𝑀𝑌𝑌
=
𝑃𝑃𝑋𝑋
𝑃𝑃𝑌𝑌
⇒
√𝑌𝑌
2√ 𝑋𝑋
√ 𝑋𝑋
2√𝑌𝑌
=
2
1
This is due to Px after the tax is $2.
⇒
2√ 𝑌𝑌√𝑌𝑌
2√ 𝑋𝑋√ 𝑋𝑋
= 2

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⇒
𝑌𝑌
𝑋𝑋
= 2
⇒ 𝑌𝑌 = 2𝑋𝑋 --------- (ii)
This way the new budget line after the application of tax is:
300= 2X + 1Y
Now substituting in equation (ii) in the above equation of new budget line, we get;
⇒ 300= 2X + 1*(2X)
⇒ 300= 4X
⇒ X= 75
Now substituting the amount of X in the equation of the new Budget line we get the amount of
Y:
⇒ 300= 2*75 + 1*Y
⇒ 300= 150 + Y
⇒ Y= 150
Thus the suitable consumption batch changes and the new consumption batch is X*
=75 and
Y*
=150.
Thus we can conclude that due to taxation on petrol, the price of petrol rose which caused a
decline in the quantity demanded from 100 units to 75 units. On the other hand, the quantity of
the composite good remained unchanged to 150 units as there was no change in the price of
composite good.
Now the utility function of Sally is acquainted by:
𝑈𝑈 = √𝑋𝑋𝑋𝑋

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Now the new level of utility is obtained after taxation:
⇒𝑈𝑈 = √75 ∗ 150
⇒𝑈𝑈 = √11250
⇒𝑈𝑈 = 106.06
Thus the new level of utility is 106.06. This shows that as tax is imposed on the petrol, the price
of petrol goes up which decreases the quantity demanded of the petrol. All these affected the
utility level which declined from 122.47 to 106.06.
(Atkinson, Livesey, & Milward, Applied Economics, 1998)
QUERY 4:
The new suitable solution is depicted in the presentation below:
The new budget line is acquainted by:
300= 2X + Y
The points on the axes are;
When X=0; Y= 300 and when Y=0; X=150
Y
300
Y*
=150
EE’
IC
IC’

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QUESTION 5:
To achieve her real utility level, an extra 25 units of petrol must be consumed by Sally. So a
benefit of $50 must be paid to the Sally to regain her real utility.
Here the Benefit= PXX
Also the current price of X after tax is $2,
⇒Benefit= 2*25
= $50
If Sally got $50 as benefit then 25 litres of petrol will be consumed.
(Atkinson & Miller, Business Economics, 1998)
QUESTION 6:
Givingbenefit to Sally affects the adequacy of the corrective tax in a regressive way. The benefit
enables Sally to consume the same level of petrol before tax. The consumption of petrol
increases pollution leading to a declining externality in the climate. Thus, the corrective tax helps
to generate revenue which can be utilized to stop pollution.
Bibliography
Atkinson, B., & Miller, R. (1998). Business Economics. Harlow: Princeton Hall.
X200150100X*
=75
BLBL’

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Atkinson, B., Livesey, F., & Milward, B. (1998). Applied Economics. London: MacMillan. Retrieved 2014
Begg, D., & Ward, D. (2003). Economics for Business. New York: McGraw-Hill.
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