325_Lecture14_March16

325_Lecture14_March16 - FIRMS IN THE TWO-PERIOD FRAMEWORK...

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1 F IRMS IN THE T WO- P ERIOD F RAMEWORK (CONTINUED) M ARCH 16, 2011 March 16, 2011 2 B ASICS Model Structure ± Timeline of events ± Notation ± k 1 :c a p i t a l u s e d f o r p r o d u c t i o n i n p e r i od 1 (decided upon in “period 0”) ± n 1 :l a b o r u s e d f o r p r o d u c t i o n i n p e r i o d 1 ± w 1 :r e a l w a g e r a t e f o r l a b o r i n p e r i o d 1 ( w 1 = W 1 / P 1 ) ± i :n o m i n a l i n t e r e s t r a t e ± P 1 o m i n a l p r i c e o f o u t p u t p r o d u c e d a n d s o l d b y f i r m i n p e r i o d 1 AND nominal price of one unit of capital bought by the firm in period 1 for use in period 2 (recall time to build…) Underlying assumption/view of world: capital goods are not necessarily “distinct” from consumption goods (i.e., computers purchased by both firms and individual consumers) Start of economic planning horizon End of economic planning horizon
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2 March 16, 2011 3 F IRM P ROFIT M AXIMIZATION Model Structure ± A dynamic profit maximization problem ± Because firm exists for both periods ± All analysis conducted from the perspective of the very beginning of period 1 ± Æ Must consider present-discounted-value (PDV) of lifetime (i.e., two- period) profits ± Dynamic profit function ± (specified in nominal terms – could specify in real terms…) ± Two-period model: k 3 = 0 (no machines needed in “period 3”) 23 22 2 2 2 2 11 1 1 1 2 (,) 1 1 Pk Pf k n Pwn ii i i ±² ²± ± ² ² ± ±±± Period-1 profits Total revenue in period 1 (price x output) Value of pre- existing capital (an asset for firms) Total labor cost in period 1 Total cost of buying capital for period 2 (time to build Æ must purchase period-2 capital in period 1) (PDV of) period-2 profits Total revenue in period 2 (price x output) Value of pre- existing capital (an asset for firms) Total labor cost in period 2 Total cost of buying capital for period 3 (time to build Æ must purchase period-3 capital in period 2) = 0 March 16, 2011 4 F IRM P ROFIT M AXIMIZATION ± FOCs with respect to n 1 , n 2 , k 2 with respect to n 1 : with respect to n 2 : with respect to k 2 : 2 2 2 2 1 1 1 2 1 1 P k i i ± ² ² ± = 0 1 (, ) 0 n Pw ² 2 0 n ² ±± 2 2 1 0 k P P ² Identical except for time subscripts Equation 1 Equation 2 Equation 3
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3 March 16, 2011 5 F IRM P ROFIT M AXIMIZATION Model Structure ± FOCs with respect to n 1 , n 2 , k 2
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325_Lecture14_March16 - FIRMS IN THE TWO-PERIOD FRAMEWORK...

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