In a 2-good model, where the goods are denoted X, and x2, the consumer's utility 1 1 function is as follows: U = x Money income available is denoted m. All of this income is spent on the two goods. The prices of the two goods are p1 and p2 respectively. By minimising expenditure, subject to the utility function, find the compensated (Hicksian) demand functions; that is, demand for each good expressed in terms of U, p, and pɔ. Do not check the second order conditions.
In a 2-good model, where the goods are denoted X, and x2, the consumer's utility 1 1 function is as follows: U = x Money income available is denoted m. All of this income is spent on the two goods. The prices of the two goods are p1 and p2 respectively. By minimising expenditure, subject to the utility function, find the compensated (Hicksian) demand functions; that is, demand for each good expressed in terms of U, p, and pɔ. Do not check the second order conditions.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Can you please help solve question 8 I have added a similar question AWNSERED so it is easier to understand the logic behind it, please show full working so I can compare it to my own work I am having trouble with the algebra
Thank you
Transcribed Image Text:10.
In a 2 good (8, and x) model, the consumer's utility is given by:
U= +
where U is utility. P, is the price of good 1. p, is the price of good 2 and m is
income.
Find the hicksian (compensated) demand functions, x, - x, (U.p.) for each
good by minimising the expenditure required to attain a given level of utility.
Assume the second order conditions hold.
(a)
1-pX, +P,X, + 2U -x - x)
1.-2.--0
1, -U ---0
Dividing first equation by the second gets:
Now substitute this into the third equation:
P +P
x -U*
pi + p
Similarly for the other one to get: x -U
Transcribed Image Text:8.
In a 2-good model, where the goods are denoted X, and x2, the consumer's utility
1
function is as follows: U = x,x.
Money income available is denoted m. All of this income is spent on the two goods.
The prices of the two goods are p, and
P2 respectively.
(a)
By minimising expenditure, subject to the utility function, find the compensated
(Hicksian) demand functions; that is, demand for each good expressed in terms of U,
P1 and p2. Do not check the second order conditions.
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