Optimal Problem for Steel Mill and Fishery PDF

For Chapter 6.2, Optimal problem for the steel mill max πs (ls |p, w) = p𝜎(ls ) - wls ⏠⏣⏣ ⏡⏣⏣⏢ ls ∂πs (ls |p, w) FOC : =0 ⇒ ∂ls ∂𝜎(ls ) ⇒ p -w = 0...

For Chapter 6.2, Optimal problem for the steel mill max πs (ls |p, w) = p𝜎(ls ) - wls ⏠⏣⏣ ⏡⏣⏣⏢ ls ∂πs (ls |p, w) FOC : =0 ⇒ ∂ls ∂𝜎(ls ) ⇒ p -w = 0 ⇒ ∂ls ∂𝜎(ls ) ⇒ p =w ⇒ ∂ls ∂𝜎(ls ) ⇒ Choice of l's so that p |l =l' = w ∂ls s s Optimal problem for the fishery max 𝜋f (lf |q, w, ls ) = q𝜙(lf , 𝜌(σ(ls ))) - wlf ⏠⏣⏣ ⏡⏣⏣⏢ lf  ∂πf (lf |q, w, ls ) FOC : =0 ⇒ ∂lf ∂𝜙{ lf , 𝜌[𝜎(ls )]} ⇒ q -w = 0 ⇒ ∂lf ∂𝜙{ lf , 𝜌[𝜎(ls )]} q |lf =l'f - w = 0 ∂lf ∂𝜙(lf , 𝜌') ⇒ q |lf =l'f = w ⇒ ∂lf Because both are equal to w ⏦the equation right side of ls = l's lf = l'f the pair l's , l'f is the market allocation in an eocnomy with externalities. ∂𝜙{ lf , 𝜌[𝜎(ls )]} ∂𝜌[𝜎(ls )]} ∂𝜎(ls ) FOC : dπf |ls = q × × × dls > 0 ⇒ ∂𝜌 ∂𝜎 ∂ls ⏠⏣ ⏡⏣ ⏢ 0 ⏢ ⏠⏣⏣ ⏡⏣⏣ ⏢ 0 decrease in increase in increase in the quantity o fish the quant. of waste the quant. of steel when the quant. of when the quant. of when the labour effort ⏪⏪ 𝜌 ⏫ ⏪⏪𝜎 ⏫ steel increases ⏪⏪ ls ⏫ for prod steel increases waste increase max 𝜋s + 𝜋f ⏠⏣⏣ ⏡⏣⏣ ⏢ ls , lf 𝜋total = 𝜋s + 𝜋f max {[p𝜎(ls ) - wls ] + [q𝜙(lf , 𝜌(σ(ls ))) - wlf ]} ⏠⏣⏣ ⏡⏣⏣ ⏢ ls , lf d𝜋total d{[p𝜎(ls ) - wls ] + [q𝜙(lf , 𝜌(σ(ls ))) - wlf ]} = =0 ⇒ =0 ␦␥ dls dls = ∂𝜎(ls ) ∂𝜙{ lf , 𝜌[𝜎(ls )]} ∂𝜌[𝜎(ls )]} = ␦␥ p+q × -w = 0 ␦␥ ∂ls ∂𝜌 ∂𝜎 = ∂𝜎(ls ) ∂𝜙{ lf , 𝜌[𝜎(ls )]} ∂𝜌[𝜎(ls )]} ␦␥ p+q × =w ∂ls ∂𝜌 ∂𝜎 d𝜋total d{[p𝜎(ls ) - wls ] + [q𝜙(lf , 𝜌(σ(ls ))) - wlf ]} =0 ⇒ =0 dlf dlf Teoria eq general, cap bunuri si efecte externe la fel sa imi spuneti cu optim paretto cu microeconomie carte portocalie cap 12 Paul Sartre Fiinta si neant Michel Focault Un altfel de inchisoare