1. Choose and to maximize U(G,G) = ln ((c)ª¹ (¿)¹ ª³) for j=1,2 subject to: pie + ₂-pic-₂0. Let a¹ = .40, a² = .60, el = 8, e₂ = 6, e² = 14 and e² = 18. (a) Set up Lagrangian L = In ( (c)²¹ (2²₂) ¹ ª³ ) + x²][m²] + √₂ −mid – ½] for j = 1,2 (b) Take FOCs (c) Set X equal and find (pi) and (p₁) (d) Substitute (pi) and (f) Check MRS; (p1) into market clearing condition c + c = c + c² to find Pi (e) Using pi solve for optimal consumption DU (24) ad DU (22) 822 is the same for j = 1,2
1. Choose and to maximize U(G,G) = ln ((c)ª¹ (¿)¹ ª³) for j=1,2 subject to: pie + ₂-pic-₂0. Let a¹ = .40, a² = .60, el = 8, e₂ = 6, e² = 14 and e² = 18. (a) Set up Lagrangian L = In ( (c)²¹ (2²₂) ¹ ª³ ) + x²][m²] + √₂ −mid – ½] for j = 1,2 (b) Take FOCs (c) Set X equal and find (pi) and (p₁) (d) Substitute (pi) and (f) Check MRS; (p1) into market clearing condition c + c = c + c² to find Pi (e) Using pi solve for optimal consumption DU (24) ad DU (22) 822 is the same for j = 1,2
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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d, e and f please
![1. Choose and to maximize
U(G,G) = ln ((c)ª¹ (¿)¹ ª³) for j=1,2
subject to: pie + ₂-pic-₂0. Let a¹ = .40, a² = .60, el = 8, e₂ = 6, e² = 14 and
e² = 18.
(a) Set up Lagrangian L = In
( (c)²¹ (2²₂) ¹ ª³ ) + x²][m²] + √₂ −mid – ½] for j = 1,2
(b) Take FOCs
(c) Set X equal and find (pi) and (p₁)
(d) Substitute (pi) and
(f) Check MRS;
(p1) into market clearing condition c + c = c + c² to find
Pi
(e) Using pi solve for optimal consumption
DU (24)
ad
DU (22)
822
is the same for j = 1,2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2Fd1a4a34a-e20f-4b77-a3ba-18dd2a20c9c5%2Fwsgu90o_processed.png&w=3840&q=75)
Transcribed Image Text:1. Choose and to maximize
U(G,G) = ln ((c)ª¹ (¿)¹ ª³) for j=1,2
subject to: pie + ₂-pic-₂0. Let a¹ = .40, a² = .60, el = 8, e₂ = 6, e² = 14 and
e² = 18.
(a) Set up Lagrangian L = In
( (c)²¹ (2²₂) ¹ ª³ ) + x²][m²] + √₂ −mid – ½] for j = 1,2
(b) Take FOCs
(c) Set X equal and find (pi) and (p₁)
(d) Substitute (pi) and
(f) Check MRS;
(p1) into market clearing condition c + c = c + c² to find
Pi
(e) Using pi solve for optimal consumption
DU (24)
ad
DU (22)
822
is the same for j = 1,2
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