# Lecture07 - Announcements Readings this week House ch 6 7 8...

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1 Announcements Readings this week • House, ch 6, 7, 8 • Mankiw, ch 3, 18 Problem sets • No PS this week – Instead, practice Midterm Ungraded , but strongly advised Alternative derivation: User cost () 11 1 1 1 1 2 22 2 2 2 2 Firm's objective: max ( , ) 1 (,) 1 1 1 K tt t t t t K t t t t K t t t t FK L wL pI w L p I r FK L r ++ + + + + -- +- - + æö ÷ ç - + ÷ ç ÷ ç èø + 1 subject to (1 ) t IK K d - =-- note change in timing convention ¬ Firm's objective is to maximize the PDV of profits 1 Capital accumulation identity ) t K d - ( , ) revenue (price of output is numeraire) = cost relative price of capital goods K K t wL p += =

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2 () 11 1 1 1 1 Optimal choice of capital stock max ( , ) 1 (,) 1 t K tt t t t t K t t t t K FK L wL pI w L p I r ++ + + -- +- - + + 1 subject to (1 ) ) t t IK K K d d - =-- =- - 1 1 ) 0 1 K K t MPK p p r d + - = + Substitute constraint and differentiate w/r/t t K 1 1 ) 1 KK t MPK p p r d + - + Special case: 1 K t p = 1 t MPK rr r dd - + + 1( 1 ) t MPK r r »- - + = + t MPK r d =+ return to capital = interest cost + depreciation = "rental rate" 1 1 ) 1 t MPK p p r d + - + General case: variable K t p 1 1 1 ) 1 K K t K
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Lecture07 - Announcements Readings this week House ch 6 7 8...

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