Question

In: Economics

Sophia is a student at university, every month she gets a scholarship of 500 €. Since...

Sophia is a student at university, every month she gets a scholarship of 500 €. Since she is currently living with her parents, she only spends her money on clothing and books. The price of books is 20 € and the price of clothing is 12,50 €.

(a) Draw a diagram of Sophia’s budget constraint. Calculate the slope and intercepts of this budget constraint.

(b) In a new diagram, show how Sophia’s budget constraint changes when the price of books rises to 25 €. Her scholarship and the price of clothing remain the same. Calculate the slope and the intercept of this budget constraint.

(c) The secretary of Education has just announced a decrease on scholarships all over the country. Sophia’s scholarship is now 400 €. The price of books is 20 € and the price of clothing is now 10 €. Draw a new diagram for Sophia’s budget constraint. Calculate the slope and the intercept of this budget constraint.

(d) Compare the budget constraints you found in parts b and c.

Expert Solution

a) Sophia currently receives a scholarship of 500 euros. Out of which she consumes cloths and books.
Price of cloths = 12.50 euros
Price of books = 20 euros.

Her equation budget line can be written as:
500 = 12.50C + 20B
or, 20B + 12.50C = 500

Slope of her budget line is -(price of cloths / price of books)
= - (12.50 / 20) = - 0.625

If her entire scolarship is spent on cloth, maximum cloth she would have bought = 500 /12.50 = 40 cloths (vertical intercept of budget line)
If her entire scolarship is spent on books, maximum books she would have bought = 500 /20 = 25 books (horizontal intercept of budget line)
The budget line can be drawn as follows :

b)Now given that price of books have increased to 25 euros.
scholarship is same as 500 euros
Price of cloths = 12.50 euros

Her equation budget line can be written as:
500 = 12.50C + 25B
or, 25B + 12.50C = 500

Slope of her budget line is -(price of cloths / price of books)
= - (12.50 / 25) = - 0.5

If her entire scolarship is spent on cloth, maximum cloth she would have bought = 500 /12.50 = 40 cloths (vertical intercept of budget line)
If her entire scolarship is spent on books, maximum books she would have bought = 500 /25 = 20 books (horizontal intercept of budget line)
The budget line can be drawn as follows :

c) Now as per announcement, scholrship reduces to 400 euros.
Price of books = 20 euros
Price of cloths = 10 euros.

Her equation budget line can be written as:
400 = 10C + 20B
or, 20B + 10C = 400

Slope of her budget line is -(price of cloths / price of books)
= - (10 / 20) = - 0.5

If her entire scolarship is spent on cloth, maximum cloth she would have bought = 400 /10 = 40 cloths (vertical intercept of budget line)
If her entire scolarship is spent on books, maximum books she would have bought = 400 /20 = 20 books (horizontal intercept of budget line)
The budget line can be drawn as follows :

d) Budget equation in part (b) : 25B + 12.50C = 500

Slope = -0.5
Vertical intercept = 40
Horizontal intercept = 20

Budget equation in part (c) : 20B + 10C = 400

Slope = -0.5
Vertical intercept = 40
Horizontal intercept = 20

All are same in both the cases thus the budget line turns out to be unchanged.

Rahul Sunny answered 1 year ago

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