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DERIVATION OF THE BASIC EQUATIONS
PROOF OF THEOREM 1
EXTENSIONS TO THE THEORY AND FURTHER
1 other sections not shown
accumulated capital amount of capital assumptions of Chapter attained ayM)w basic equation called Region capital becomes effective changing the notation commodity comparing equations completes the proof considered constant convex function convex set corresponds to Region critical functions critical value defined depreciation derivative with respect Differentiating equation Discount factor exactly expected holding firm functional equation given gives the equation going into inventory implies inventory level invest capital iterations L(xQ least possible value lemma lim inf n-period problem non-backlogging Number of periods obtained optimal policy p*o q*o partial derivative period problem policy in Region produce nor invest Produce zn(u,v)-u proof of Theorem random variables Region IV resultant equation revenue costs rewritten second derivatives set z,w shortage and revenue simplify solving straight forward substituted into equation Substituting these equations thesis twice differentiable un(v un(y ux(y variables vp_]_ vy_1