ADVANCED MACROECONOMICS Lecture 9 Investment 电子科大经管学院马捷
ADVANCED MACROECONOMICS Lecture 9 Investment 电子科大经管学院 马捷 1
Contents Baseline Model Model with Adjustment Cost ■Tobin'sq Implications ·Output movement Interest rate movement- ·Taxes Homework Empirical Application 电子科大经管学院马捷 2
Contents Baseline Model Model with Adjustment Cost Tobin’s q Implications • Output movement • Interest rate movement • Taxes Empirical Application 电子科大经管学院 马捷 Homework 2
Baseline Model A firm's profit function: P=a(K,X1X2,X32...,Xn)-Ikk πk>O,πK<o,rk is the capital rent. FOC: aP 6K =Ik(K,X1,X2,X33...,Xn)-Ik =0 元元元元元
Baseline Model A firm’s profit function: 0 , , is the capital rent. ( , , , , , ) 0 1 2 3 K KK K n K r P K X X X X r K FOC: ( , , , , , ) 0 1 2 3 K n K K X X X X r K P
→πk()=rg and K=f(rk,X's) →元x(K,X,X)k0XX)=1 Ork aK() → 1<0 OrK 兀KK →rk个→K↓ 一元 与元元元元元元元
r K r K r K r X X K X X r K f r X s K K KK K K n KK n K K K 0 ( ) 1 1 ( , , , ) ( , , , ) ( ) and ( , ) 1 1 '
The User Cost of Capital Most capital is not rented but is owned by firms that use it. rk(t)=r(t)pk(t)+pk(t)-Pk(t) =[r)+6-Ps]px() p<(t) =r+6-8号-回a.0 电子科大经管学院马捷 5
The User Cost of Capital Most capital is not rented but is owned by firms that use it. 电子科大经管学院 马捷 5 ]( 1 ) ( ) ( ) ( ) ( ) [ ( ) ] ( ) ( ) ( ) [ ( ) ( ) ( ) ( ) ( ) ( ) f p t p t p t r t r t p t p t p t r t r t r t p t p t p t K K K K K K K K K K K
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 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
Transversality Condition →4=π(K)+,4 1+r s2nuk+ A unit capital's contributes to the firm'sΠ： MB lim T→00 lim gr =0 or lim ArKT =0 T→00 1+r） T→0 (1+r) 电子科大经管学院马捷 10
Transversality Condition 电子科大经管学院 马捷 10 0 ( 1 ) 0 or lim ( 1 ) lim ( ) ( 1 ) 1 lim A unit capital' s contribute s to the firm' s : ( 1 ) ( ) ( 1 ) 1 lim 1 ( ) 1 0 1 0 1 0 0 T T T T T T T T t t t T T T T t t t T r q r q K r MB r q K r r q q K
