Suppose individuals consume two goods, baked beans 9₁ and apples 92. Total budget is y and prices are 0 ≤ p₁ < y/A and p2 ≥ 0. Preferences are represented by the indirect utility function v (y, p₁, p2) = ln (y – p₁ A) 1 5 ln [ap¹−³ + (1 − a)p²¯³] -
Suppose individuals consume two goods, baked beans 9₁ and apples 92. Total budget is y and prices are 0 ≤ p₁ < y/A and p2 ≥ 0. Preferences are represented by the indirect utility function v (y, p₁, p2) = ln (y – p₁ A) 1 5 ln [ap¹−³ + (1 − a)p²¯³] -
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Suppose individuals consume two goods, baked beans q1 and apples q2. Total budget is y and prices
are 0 < pi < y/A and p2 > 0. Preferences are represented by the indirect utility function
v (y, P1, P2)
In (y – p1 A)
+ (1– a)p]
In
ap
1- B
where
• A> 0 is a parameter reflecting baked bean needs,
• 0< a <1 is a parameter reflecting taste for baked beans and apples, and
• B2 0 is a parameter reflecting substitutability between baked beans and apples.
(a) Find the uncompensated demand functions for the two goods.
(b) Which, if either, good is a necessity?
Suppose that in a base period pi = P2 = 1 and in a later period pi =1+ 8 > 1 and p2 = 1.
(c) Explain what a true (or Konüs) cost of living index is and show that a true (or Konüs) cost of
living index at base-period utility can be expressed for an individual with total expenditure y as
[a(1 + 5)-9 + (1– a)
| 1/(1–B)
+
(1+6 - [a(1+6)-8 + (1 – a)])
| 1/(1–3)\ A
(d) Find an expression for the Laspeyres cost of living index as a function of preference parameters,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2db187f-4358-489b-9a78-422f426ca20c%2F86cd3a97-5a27-48fb-a5f7-ae02a2849538%2Fgamk8kj_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose individuals consume two goods, baked beans q1 and apples q2. Total budget is y and prices
are 0 < pi < y/A and p2 > 0. Preferences are represented by the indirect utility function
v (y, P1, P2)
In (y – p1 A)
+ (1– a)p]
In
ap
1- B
where
• A> 0 is a parameter reflecting baked bean needs,
• 0< a <1 is a parameter reflecting taste for baked beans and apples, and
• B2 0 is a parameter reflecting substitutability between baked beans and apples.
(a) Find the uncompensated demand functions for the two goods.
(b) Which, if either, good is a necessity?
Suppose that in a base period pi = P2 = 1 and in a later period pi =1+ 8 > 1 and p2 = 1.
(c) Explain what a true (or Konüs) cost of living index is and show that a true (or Konüs) cost of
living index at base-period utility can be expressed for an individual with total expenditure y as
[a(1 + 5)-9 + (1– a)
| 1/(1–B)
+
(1+6 - [a(1+6)-8 + (1 – a)])
| 1/(1–3)\ A
(d) Find an expression for the Laspeyres cost of living index as a function of preference parameters,
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