hw3sol - 1. Firm maximizes max L = pA (L F) w (L + F ) 2....

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Unformatted text preview: 1. Firm maximizes max L = pA (L F) w (L + F ) 2. Cost function = w (L + F ) 3. MC = w . Constant marginal cost. w 4. AC = w(L+F ) . @AC = (L F1)2 . If w > 1 then economy of scale fails but L F @L if w < 1 then there is economy of scale. 5. max L = pA (L = B p p= " F) w (L + F ) s:t: Y Y B F )] 1 1 " max L = B " [A (L 1 " 1 1 " w (L + F ) FOC will give 1 which will be L=F + 6. =B 1 " AB " [A (L 1 w A AB 1 " 1 F )] " " 1 1 " =w " w AB " 1 " " 1 1 " 1 w w 2F + A AB 1 " " " 1 " +F ! 1. L= X t log ct + log (1 lt ) + t kt (1 + g) lt t 1 + (1 ) kt ct kt+1 FOC 1 ct 1 lt t = = = t (1 t+1 ) (1 + g) t t kt (1 + g) lt t+1 1 t kt+11 (1 + g) t 1 lt+1 ) kt + (1 ) ct + kt+1 = kt (1 + g) lt + (1 1 Three necessary conditions are 1 lt 1 ct = = (1 1 ct+1 ) (1 + g) t 1 k ct t (1 + g) lt t+1 1 t kt+11 (1 + g) t 1 lt+1 ) kt + (1 ) ct + kt+1 = kt (1 + g) lt + (1 Or stationary equilibrium can be by setting ct = ~ = (1 ) ct , (1+g)t ~ kt = kt (1+g)t 1 lt 1 ct ~ ~ ct + (1 + g) kt+1 ~ 2. BGP 1 l 1 ~ c + (1 + g) k ~ ~ k l c ~ l l 1 l 1 l l 1~ k l ct t t ~ h 1 1 ~ = kt+11 lt+1 + (1 ct+1 (1 + g) ~ ~ 1 + (1 ~ = kt lt ) kt i ) = = (1 1+g ~ l1 + (1 = k 1~ ) k l c ~ h ~ k 1 l1 + (1 ~ )k i ) = = = = = 1 ~ k l (1 ! 1+g 1 1 1+ ~ k =A l A (g + ) A B (g + ) )A B (1 )A + B (1 )A (1 )A (1 )A + B 3. Same as TA section 3 problem 2 ...
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This note was uploaded on 05/13/2010 for the course ECON 110D taught by Professor Schmitt-grohe during the Spring '08 term at Duke.

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hw3sol - 1. Firm maximizes max L = pA (L F) w (L + F ) 2....

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