Question

5) lan views playing Wartcraft and drinking soda as perfect complements (one soda with one hour of playing Wartcraft). Currently, sodas are $1 each and Wartcraft costs $1 per hour. Ian has $12 of income. a. Compute lan's Compensating Variation if the price of Wartcraft rises to $2. b. Compute lan's Equivalent Variation if the price of Wartcraft rises to $2. c. Compute lan's change in Consumer Surplus if the price of Wartcraft rises to $2

Answer 1

5)

a) in Initially,

price of watercraft = $1

price of drinking soda = $1

Ians income = $12

therefore, the total number of units where Ian can purchase = 6 units f both ....in ordered pairs (6,6)

when the price of the watercraft is increased to $2,

the total cost needed for purchasing (6,6) same units of previous = $18

therefore, compensating Variation (CV) = $12 - $18

CV = -$6

b) Total number of units Ian purchased when the price of watercraft is $1 = (6,6)

Total number of units Ian purchased when the price of watercraft is $2 = (4,4)

when the price is again $1, then total income used for purchase (4,4) units = $8

Therefore, The Equivalent Variation(EV) = $8 - $12

EV = -$4

c) The quantity of soda is represented as Qs and The quantity of watercraft is represented as Qw

Price of soda is represented as Ps and price of watercraft is represented as Pw

Total income = (Ps * Qs) + (Pw * Qw) = 12 =====> Ps is always 1 in this question and Qs and Qw is always same

Therefore, Qw(1+Pw) = 12

Qw = 12/(1+p)

Consumer Surplus(CS) when the price of watercraft changes to $1 to $2 = integral of 12/(1+p) with upper-limit 2 and lower limit 1

CS = 12(ln(3)−ln(2))

CS ≈  $4.865581297297973