A consumer is maximising her utility function: U(x, y) = (x¹/3+y¹/3) ³, subject to the budget constraint x + 3y = 100. (a) Set up the Lagrangian function of this utility maximisation problem a first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate multiplier. (c) What are the utility maximising amounts of x and y if the budget const to x + 3y = 50? Also, calculate the Lagrange multiplier.
A consumer is maximising her utility function: U(x, y) = (x¹/3+y¹/3) ³, subject to the budget constraint x + 3y = 100. (a) Set up the Lagrangian function of this utility maximisation problem a first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate multiplier. (c) What are the utility maximising amounts of x and y if the budget const to x + 3y = 50? Also, calculate the Lagrange multiplier.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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Transcribed Image Text:A consumer is maximising her utility function:
U(x, y) = (x¹/³+y¹/³)³,
subject to the budget constraint x + 3y = 100.
(a) Set up the Lagrangian function of this utility maximisation problem and derive the
first-order conditions.
(b) What are the utility maximizing amounts of x and y? Also, calculate the Lagrange
multiplier.
(c) What are the utility maximising amounts of x and y if the budget constraint changes
to x + 3y = 50? Also, calculate the Lagrange multiplier.
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