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practice2

# practice2 - Answer to practice problem from lecture 2 1...

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Answer to practice problem from lecture 2 1. Gordon will maximize his preferences U ( a; c ) = a 1 3 c 2 3 subject to the budget constraint M p a a + p c c . His Lagrangian will be L = a 1 3 c 2 3 + ( M ± p a a ± p c c ) @L @a : 1 3 a 2 3 c 2 3 ± a = 0 (1) @L @c : 2 3 a 1 3 c 1 3 ± c = 0 (2) @L : M ± p a a ± ± p c c ± = 0 (3) Gordon uses statements (1) and (2) to remove the Lagrange multiplier occur where the budget constraint holds with equality and 1 3 a 2 3 c 2 3 2 3 a 1 3 c 1 3 = c ± 2 a ± = p a p c c ± = 2 p a p c a ± He plugs this relationship into (3) M = p a a ± + p c c ± = p a a ± + p c 2 p a p c a ± ± = 3 p a a ± a ± ( p a ; p c ; M ) = M 3 p a c ± ( p a ; p c ; M ) = 2 p a p c M 3 p a ± = 2 M 3 p c Then, since the price of an album is \$10 while the price of a concert ticket is \$30, while Gordon±s monthly income is \$300, we know that he optimally

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practice2 - Answer to practice problem from lecture 2 1...

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