Problems Discrete change of capital stock and infinite rate of investment. -Expectation about demand and cost. The adjustment cost Internal adjustment cost External adjustment cost 电子科大经管学院马捷 6
Problems Discrete change of capital stock and infinite rate of investment . Expectation about demand and cost. The adjustment cost • Internal adjustment cost • External adjustment cost 电子科大经管学院 马捷 6
Model with Adjustment Cost Assumptions: ·Instantaneous profit:π(K)k-I-C(I) π()>0，π'()<0 A representative firm's problem: MarΠ=∫e"{π[K(]k(o)-I()-C[Itt where C()is the cost of adjusting K, C(0)=0,C'(0)=0andC"()>0 电子科大经管学院马捷
Model with Adjustment Cost Assumptions: • Instantaneous profit: • A representative firm’s problem: 电子科大经管学院 马捷 7 ( ) 0, '( ) 0 ( ) ( ), K I C I ( 0 ) 0, ( 0 ) 0 and ( ) 0 whereC( ) is the cost of adjusting , [ ( )] ( ) ( ) [ ( )] 0 C C C Max e K t t I t C I t dt t rt
Discrete Time 恤n-2ark4-cu 00 S.t.K,=K-1+I, =L-2a+lk&x-4-cu小 +∑(K+1,-K,) t=0 Let4=(1+r)y2,→ 0nlkK-1-Cu)-41-】 00 电子科大经管学院马捷 8
Discrete Time 电子科大经管学院 马捷 8 t t t t t t t t t s t I K I C I r Max 1 0 . . ( ) ( ) ( 1 ) 1 0 1 0 1 0 ( ) ( ) ( ) ( 1 ) 1 Let ( 1 ) ( ) ( ) ( ) ( 1 ) 1 t t t t t t t t t t t t t t t t t t t t t t t t K I C I q I r q r I K I C I r L' L
ocr01-(u+g小=0 →g,=1+C'(L) FOC for K, nyhKglhutw=0 三(1+r)π(K)=(1+r)9,-9+1 r9,-△q,) 0rq,=π(K,)+,9 1+r 电子科大经管学院马捷 9 元元元元
电子科大经管学院 马捷 9 1 1 1 1 1 1 or ( ) ( ) 1 1 ( ) (1 ) ( ) (1 ) 0 (1 ) 1 ( ) (1 ) 1 FOCfor : 1 '( ) 1 '( ) 0 (1 ) 1 FOCfor : t t t t t t t t t t t t t t t t t t t t t q r q K rq q r K r K r q q q r K q r q C I C I q r I