Question

Mr. Y is BBA graduate student and consumes 2 goods: textbooks and cup of Tea. Mr. Y also earns
a typical grad student income, Rs. 40 a month. He can either spend it all on textbooks and get 5,
or he can spend it all on Tea and get 20 cups.
a. Construct the budget line.
b. Given this information, construct the equation for Mr. Y budget line (put Textbooks on
the x-axis and Tea on the y-axis).
c. Mr. Y gets a research grant and his income increase to Rs. 80 a month. What is the new
equation of his budget lie? Assume that prices are the same as used in part a. If the
marginal utility of a textbook is 20, what is the marginal utility of Tea if he is maximizing
his utility?
d. Now assume that textbooks and Tea are complements for Mr. Y. For him to consume one
textbook, he needs 1 cup of Tea. How many textbooks does he consume given his income
of Rs. 40, and the prices used in part a? What if course (subject) is so boring that Mr. Y
needs 2 cups of Tea for every book that he consume

Answer 1

a.

b. General budget line:

$X \times P_x+Y \times P_y= M$

X = quantity of textbooks

$P_x$ = Price of a textbook

Y = quantity of tea cups

$P_y$ = Price of a tea cup

If Mr. Y spends all on textbooks then:

$X= 5 \\ 5P_x= 40 \\ P_x= 8$

If Mr. Y spends all on tea cup:

$Y= 20 \\ 20P_y= 40 \\ P_y= 2$

Equation of budget line:

8X+2Y= 40

c. New M= M'= 80

Equation of budget line:

8X+2Y= 40

MU of textbook= 20

Utility maximizing condition:

MU of textbook/MU of tea cup= $\frac{P_x}{P_y}$

20/Mu of tea cup= $\frac{8}{2}$

MU of tea cup=$\frac{20}{4}= 5$

d. Now assume that textbooks and Tea are complements for Mr. Y. For him to consume one textbook, he needs 1 cup of Tea:

X= Y Condition 1

8X+2Y= 40

8X+2X= 40 (Use condition 1)

10X= 40

X= 4= Y Quantity of textbooks consume

Mr. Y needs 2 cups of Tea for every book that he consumes:

2X= Y

New budget line:

$10X+2Y= 40 \\ 10X+2 \times 2X= 40 \\ 14X= 40 \\ X= 2.85$

Quantity of textbooks consume is 3.