Question 1 Consider a consumer with a utility function of U(X1,X2,... , Xm) = ,az > 0, i = 1,2,3, .. ,n. P¿ is a price of 1 unit of the i-th good. Assuming that the consumer has the total budget of $M, derive his optimal consumption bundles in the following procedure. (a) Set up the consumer's utility maximization program with a Lagrangean multiplier. (b) What is an economic intuition of the Lagrangean multiplier? (c) Assuming an interior solution, get all the FOCS.

Micro Economics For Today
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Chapter6: Consumer Choice Theory
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Question 1 Consider a consumer with a utility function of U(X,,X2, ... , Xn) =
II-1 X , a; > 0, i = 1,2,3, ...,n. P; is a price of 1 unit of the i-th good. Assuming that
the consumer has the total budget of $M, derive his optimal consumption bundles in
the following procedure.
(a) Set up the consumer's utility maximization program with a Lagrangean multiplier.
(b) What is an economic intuition of the Lagrangean multiplier?
(c) Assuming an interior solution, get all the FOCS.
(d) Find an optimal consumption bundle while specifying each step required to get
the solution.
(e) Characterize the maximized utility as a function of $M and the parameters. What
does it look like?
(f) Find an exact value of the Lagrangean multiplier.
Transcribed Image Text:Question 1 Consider a consumer with a utility function of U(X,,X2, ... , Xn) = II-1 X , a; > 0, i = 1,2,3, ...,n. P; is a price of 1 unit of the i-th good. Assuming that the consumer has the total budget of $M, derive his optimal consumption bundles in the following procedure. (a) Set up the consumer's utility maximization program with a Lagrangean multiplier. (b) What is an economic intuition of the Lagrangean multiplier? (c) Assuming an interior solution, get all the FOCS. (d) Find an optimal consumption bundle while specifying each step required to get the solution. (e) Characterize the maximized utility as a function of $M and the parameters. What does it look like? (f) Find an exact value of the Lagrangean multiplier.
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