Question

PROBLEMS AND APPLICATIONS 1. Suppose that people consume only three goods, as shown in this table: Tennis Balls Tennis Racquets Coca-Cola a. What is the percentage change in the price of each of the three goods? What is the percentage change in the overall price level? b. Do tennis racquets become more or less expensive relative to Coca-Cola? Does the well-being of some people change relative to the well-being of others? Explain. 2. Suppose that the residents of Vegopia spend all of their income on cauliflower, broccoli, $2 $40 100 10 200 2010 price 2010 quantity 2011 price 2011 quantity $2 $60 $2 100 200

Please answer question 1 and show all your steps and workings.

Answer 1

1. (a)

Percentage change is price: [(P1 - P2)/{(P1 + P2)/2}] × 100

P1 = 2010 Price

P2 = 2011 Price

Therefore, Percentage change in price of;

Tennis Balls: [(2-2)/{(2+2)/2}]100

=〉 [0/{4/2}]100 =〉 0%

Tennis Rackets: [ (60 - 40) / {(60 + 40) / 2}]100

=〉 [ 20/{100/2}]100
=〉 [ 20/50] 100
=〉 40%

Coca-Cola:   [ (1 - 2) / {(1 + 2) / 2}]100
=〉 [ 1/{3/2}]100
=〉 [ -1/1.5] 100
=〉 |-66.67| ie. 66.67

Overall Price:

Average 2010 Price = 2010 Price of (Tennis balls + Tennis Rackets + Coca-Cola)/3

Ie. $(2 + 40 + 1)/3

=〉 $43/3 = $14.33 ≈ $14.

Average 2011 Price = 2011 Price of (Tennis balls + Tennis Rackets + Coca-Cola)/3

Ie. $( 2 + 60 +2)/3

=〉 $64/3 = $21.33 ≈ $21.

So, P1 = $14 (Average 2010 Price)

P2 = $21 ( Average 2011 Price)

Therefore, Overall Price = [ (P1 - P2) / {(P1 + P2) / 2}]100

Ie.

[ (14 - 21) / {(14 + 21) / 2}]100
=〉 [ -7/{ 35 /2}]100
=〉 [ -7/ 17.5] 100
=〉 | -40%| ie. 40%

H​​​​ence, Overall percentage change in price level is 40%.

1. (b).

Tennis Rackets will become less expensive relative to Coco Cola.

Reason: As per above calculation Proportion change in price of tennis racket is 40%.

While Proportion change in price of coco-cola is 66.67%

So Coco-cola is becoming more expensive compare to tennis racket.

The well-being of some people changes relative to the well-being of others, because those who bought lots Coco-cola become worse off relative to those who bought lots of Tennis rackets.