Hi, I need some help with the attached question. It is taken from an optimisation problem set in my intermediate maths for economists course. Question 1*Consider a consumer who buys x, kilos of meat and x2 liters of petrol per month. Theconsumer's utility function is:u(x1, X2) = logx1+ logx2The domain of this function is the positive quadrant, R?.Suppose the price of petrol is $1.40 per liter and the price of meat is $28 per kilo. The totalamount that the consumer can spend on both goods is $560.a) Formulate the consumer's choice as a constrained optimization problem.b) What are the first order conditions for this problem?c) Show that the second order condition holdsd) How much petrol and meat will the consumer buy?e) Show that the maximum you have obtained is unique (global maximum).

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Answered: a) Formulate the consumer's choice as a…

a) Formulate the consumer's choice as a constrained optimization problem. b) What are the first order conditions for this problem? c) Show that the second order condition holds

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Hi, I need some help with the attached question. It is taken from an optimisation problem set in my intermediate maths for economists course.

Question 1*
Consider a consumer who buys x, kilos of meat and x2 liters of petrol per month. The
consumer's utility function is:
u(x1, X2) = logx1+ logx2
The domain of this function is the positive quadrant, R?.
Suppose the price of petrol is $1.40 per liter and the price of meat is $28 per kilo. The total
amount that the consumer can spend on both goods is $560.
a) Formulate the consumer's choice as a constrained optimization problem.
b) What are the first order conditions for this problem?
c) Show that the second order condition holds
d) How much petrol and meat will the consumer buy?
e) Show that the maximum you have obtained is unique (global maximum).

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