Question

An 8-year old kid consumes 50 packs of Sour Patch Kids and 20 packs of Peach Rings per year. The price of a pack of Sour Patch Kids is $4 and the price of a pack of Peach Rings is $2.

a) Draw the budget line in the Sour Patch Kids - Peach Rings space.

b) Suppose the price of a pack of Sour Patch Kids stayed at $4, while the price of a pack of Peach Rings increased to $3. If the kid kept on eating the same number of packs of Sour Patch Kids and Peach rings as before, what would be his new budget line. Draw the new budget line using different color.

c) How much more the kid spends on 50 packs of Sour Patch Kids and 20 packs of Peach Rings with prices in part (b)?

Answer 1

First let us denote Sour Patch Kids as X variable and Peach Rings as Y variable

A) X costs $4 per pack and Y costs $2 per pack and it is given that the child consumes 50 packs of X and 20 packs of Y per year.

With this the total money spent by the child on X and Y are; 50*4 + 20*2 = 200 + 40 = $ 240 (M)

In a budget line the total amount is completely spent up by different combinations of X and Y

so, the equation is ; 4X + 2Y = M (240)

To get budget line:

let X=0, Y= 240/2

Y intercept is (0,120)

Let Y=0, X=240/4

X intercept is (60, 0)

Thus the points are (60,0) and ( 0,120)

B) As now the prices of Peach Rings have increased to $3 per pack and the child consumes the same quantity of Sour Pack Kids and Peach Rings, the total money spent by the kid is;

4(50) + 3(20) = 200 + 60 = 260 (M)

The equation of the budget line is; 4X + 3Y = $ 260

To get the budget line:

let X=0, Y= 260/3

Y=86.66 or 87

Y intercept is (0 , 87)

Let Y=0, X= 260/4

X= 65

X intercept is (65, 0 )

Therefore the points are ( 65,0) and (0,87)

Therefore the new Budget Line (2),  ( along with Budget Line 1 ) is ;

C) The kid spend an extra $ 20 on Sour Patch Kids and Peach Rings with the new price, as he consumes the same quantity of Sour Patch Kids and Peach Rings despite the change in price of Peach Rings

With the new spent money being $260 and the previously spent money being $240, extra money spent is;

260 - 240 = $20

Thus the child spends an extra $20 on Sour Patch Kids and Peach Rings after the change in price.