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, we will solve the first question for you. If you want any…

2. A consumer has the utility function u = (x₁c₁) ª (x₂-C₂), a+b=1 U = (x1 - C1) (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 = (x₁c₁) ª (x₂-C₂), a+b=1 U = (x1 - C1) (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.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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

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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If u(X, Y) = X^(2/3) * Y^(1/3) and pX*X + pY*Y ≤ I, what is the compensation that keeps utility constant when ApX = -1 and (pX, pY, I) = (2, 1, 60) ?
Please solve from Part E to Part I. Kindly explain in detail, please. Thank you!
I JUST WANT THE DIAGRAM FOR EACH PART. PLEASE DRAW THE DIAGRAMS, DONT TYPE IT!!!!!! WRONG ANSWERS WILL BE REPORTED. Consider the representative consumer who decides consumption and leisure. The preference is given by U (C,L) = αln C + (1 −α) ln L. Assume h = 1, i.e., the time endowment is one day. Suppose the non-wage income π −T increases while the wage rate w falls at the same time. The size of the changes can be different. Determine the effects on consumption demand and labour supply (i.e., leisure demand). Use the indifference map to explain your results in terms of income and substitution effects for the following cases: (i) The increase in π −T exactly cancels out the drop in w, i.e., |∆ (π −T)|= |∆w|. (ii) The increase in π −T is greater than the drop in w, i.e., |∆ (π −T)|> |∆w|. (iii) The increase in π −T is smaller than the drop in w, i.e., |∆ (π −T)|< |∆w|.
Calculate the individual’s compensated variation.
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