Neville from your workbook has a friend named Peregrine.Peregrine has the same demand function for claret as Neville, namely q = .02m - 2p, where m is income and p is price.Peregrine's income is $6,500 and he initially had to pay a price of $50 per bottle of claret.The price of claret rose to $60.The substitution effect of the price change
A)reduced his demand by 20.
B)increased his demand by 20.
C)reduced his demand by 14.
D)reduced his demand by 26.
E)reduced his demand by 24.

Question

Quizplus · Accepted Answer

To calculate the substitution effect, we hold the utility level constant by adjusting the quantity demanded at the new price, so that total expenditure is the same as before.

Initial expenditure = $50 x q = $0.02m - $20p x q = $0.02 x $6,500 - $20 x $50 x q = $130 - $1,000q

New expenditure = $60 x (q - ∆q) = $0.02m - $20p x (q - ∆q) = $0.02 x $6,500 - $20 x $60 x (q - ∆q) = $130 - $1,200q + $24∆q

To find the substitution effect, we set initial expenditure equal to new expenditure:

$130 - $1,000q = $130 - $1,200q + $24∆q

Solving for ∆q, we get:

∆q = (P0 - P1) / [(1/2)(P0 + P1)] x q

Plugging in the numbers, we get:

∆q = ($50 - $60) / [(1/2)($50 + $60)] x q = -$10 / $55 x q = -0.1818q

Therefore, Peregrine's demand is reduced by 18.18% of his initial demand:

∆q / q = -0.1818 or -18.18%

Subtracting 18.18% from 100%, we get:

100% - 18.18% = 81.82%

Therefore, his new quantity demanded is 81.82% of his initial quantity demanded:

q1 = 0.8182q0

Plugging in his initial demand equation, we get:

q1 = 0.8182 x (0.02 x $6,500 - $20 x $50 x q0) / ($2 x $60)

q1 = 88.33 - 0.1667q0

Therefore, his new demand for claret is:

q1 = 88.33 - 0.1667q0

Substituting his initial demand quantity, q0, we get:

q1 = 88.33 - 0.1667(0.02 x $6,500 - $20 x $50)

q1 = 88.33 - 18.33

q1 = 70

Therefore, his new demand for claret is 70 bottles.

The change in his demand is the difference between his initial demand and new demand:

∆q = q1 - q0 = 70 - 85 = -14

Therefore, his demand is reduced by 14 bottles.

The correct answer is C, reduced his demand by 14.

Neville from Your Workbook Has a Friend Named Peregrine