Please Answer the first part 2. A consumer has the utility functionu = (x₁c₁) ª (x₂-C₂), a+b=1U = (x1 - C1) (x2 - C2)b, a+b=1where the ci are interpreted as minimum subsistence levels of i, i = 1,2xi,i=1,2. Derive the consumer's Hicksian demand functions and expenditurefunction.3. The consumer has the utility function = x=x1ax21-a.(a) Find her indirect utility function.(b) Confirm Roy's identity by:i. Differentiating the indirect utility function with respect to the price ofgood 1;ii. Using the first-order conditions to obtain solutions for 1x1 and XX,and therefore an expression for -A1-Ax1;iii. Showing that (a) and (b) give the same result.

Since you have asked multiple questions and specifically mentioned to solve the first question, we…

2. A consumer has the utility function u = (x₁ − €₁)ª (x₂ − ₂)", a+b=1 U = (X1C1) (X2 C2), a+b=1 where the care interpreted as minimum subsistence levels of ,i = 1,2 xi,i=1,2. Derive the consumer's Hicksian demand functions and expenditure function.

2. A consumer has the utility function u = (x₁ − €₁)ª (x₂ − ₂)", a+b=1 U = (X1C1) (X2 C2), a+b=1 where the care interpreted as minimum subsistence levels of ,i = 1,2 xi,i=1,2. Derive the consumer's Hicksian demand functions and expenditure function.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

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Please Answer the first part

2. A consumer has the utility function
u = (x₁c₁) ª (x₂-C₂), a+b=1
U = (x1 - C1) (x2 - C2)b, a+b=1
where the ci are interpreted as minimum subsistence levels of i, i = 1,2
xi,i=1,2. Derive the consumer's Hicksian demand functions and expenditure
function.
3. The consumer has the utility function = x=x1ax21-a.
(a) Find her indirect utility function.
(b) Confirm Roy's identity by:
i. Differentiating the indirect utility function with respect to the price of
good 1;
ii. Using the first-order conditions to obtain solutions for 1x1 and XX,
and therefore an expression for -A1-Ax1;
iii. Showing that (a) and (b) give the same result.

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