Asked by Toàn Tr?n Khánh on Jun 28, 2024
Verified
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.
Demand Function
A mathematical model that describes the quantity of a good or service demanded at various prices, holding other factors constant.
Substitution Effect
The substitution effect is a concept in economics that describes how consumers change their consumption patterns in response to changes in the prices of goods, opting for cheaper alternatives when prices increase.
Income
Money received, especially on a regular basis, for work, through investments, or from any other source.
- Perceive the consequences of changes in prices on the demand by consumers, with emphasis on income and substitution effects.
Verified Answer
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.
Learning Objectives
- Perceive the consequences of changes in prices on the demand by consumers, with emphasis on income and substitution effects.
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