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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] -

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
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,
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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