Β c 2 ? 1 r 0 combining the last two fi rst order

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= β c 2 λ 1+ r = 0 Combining the last two fi rst order equations to eliminate λ gives us 1 /c 1 β /c 2 = c 2 β c 1 = λ λ 1+ r = 1 + r c 2 = β c 1 (1 + r ) and c 1 = c 2 β (1 + r ) sub into the Budget constraint y 1 + y 2 1 + r = c 1 + β c 1 (1 + r ) 1 + r = (1 + β ) c 1 c 1 = y 1 + y 2 1+ r (1 + β ) Similarly, solving for c 2 using the fi rst order conditions y 1 + y 2 1 + r = c 2 β (1 + r ) + c 2 1 + r (1 + r ) y 1 + y 2 = Ã 1 β + 1 ! c 2 c 2 = (1 + r ) y 1 + y 2 1 β + 1 5
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