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Extra info for CFA-Level 1-Curriculum-Volume.2-2011

Example text

Clearly these identities are contradictory to Assumption As 4,3),4) and 5). 6), Assumption As 4 will be omitted. For the objective function of the production sector we assume the following ASSUMPTION As 5. The objeative function of the v: JR! x JR++ -+- :R V(t,r,q;w) =- wt + r + Q{q) (t,r,q;w) The value of the objective function is equal - wt + r p~oduation seato~ satisfies the equaUty to E JR! x JR++ • the sum of cash flow and the valuation of stock Q{q). Equivalently, the objective function could be assumed to have the following form - wt + r - Q{y) + Q{q) , so that it represents the sum of real profits and the valuation of stock.

The :rest:riated objective jUnction of the p:roduation seato:r is the funation := v: JR! + -+- R+ defined by eLsewhere. 3). 3 is the following. 5. Under Assumptions As 3-6~ the fUnction Vis twiae aon- tinuousZy differentiabZe in x on JR~ and in (1,r) on int DP (x) 3 • -. (x e:lR++). Furtherrnore~ the Hess'Lan of V b1'Lth respeat to (1,r) on int oP (x) (x e: JR~) is negative definite. 7). + the sectors choose a trade (1,r) in a feasible set. 5). 6. It has already been noticed that the notional labour demand 1 r P* p* (x) is finite.

39 Let the inequality £(x) > 0 hold for all x F O. It can be observed that £i{x) > 0 corresponds with anti-clockwise motions of trajectories. Hence the ray generated by qi is crossed by a trajectory, coming from the tangent cone co{Si) and going into co{Si_l)' Therefore, the function £ is non-increasing on the common boundary of co(Si) and co(Si_l)' Furthermore, £(x) is positive for x F O. If, analogously, £(x) < 0 for all x F 0, then trajectories have a clockwise motion. ) 1. and Co(S. 5). If there is an i £i(X) = 0, then i E {1,2, ••• ,n} and an X E int co(Si) such that is an element of co (Si) and also an eigenvector of Ai (cf.

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