Production:factor prices Intensive-form production function: y:=YIAL =F(k,1)=f(k);k=KIAL markets are assumed to be perfect,i.e.every input earns its marginal product and firms make zero profits. real interest rate equals the marginal product of capital:MPK=f(k)=r. wage per unit of effective labor (w) w=f(k)-f(k)k 2021/4/17 11
2021/4/17 11 Production: factor prices Intensive-form production function: yt = Y/AL = F(k, 1)=f(kt); k=K/AL • markets are assumed to be perfect, i.e. every input earns its marginal product and firms make zero profits. • real interest rate equals the marginal product of capital: MPK= f’(kt) = rt. • wage per unit of effective labor (wt ) w fk f kk t t tt
Production:factor prices F(KAL)=ALF(K/AL1=ALf(k 1.MPK= F(K,AL）=AL, OK af (k)ak=f"(k) ak,OK →片='(k) 2.π=0 F(K,AL)= F(KALK F(K AL AL aK, a(AL) F(K AL)F(KAL)K OF(K2AL) AL OK AL (AL) f(k)=f'(k)k,+w, 2021/4/17 三w,=f(飞)-f'(k,)k 12
2021/4/17 12 Production: factor prices ( , ) ,1 (, ) 1. 2. 0 (, ) (, ) (, ) (, ) (, ) (, ) t tt tt t tt tt t t tt t t tt t t tt t t t tt t tt t tt t tt t tt t tt t tt t t tt tt t tt tt t tt F K AL ALF K AL AL f k F K AL k f k MPK A L f k K kK r fk F K AL F K AL F K AL K AL K AL F K AL F K AL K F K AL AL K AL AL fk f kk t t t tt w w fk f kk
Firms Initial capital stock Ko,owned equally by all old individuals. No depreciation,8-0. In period 0,the capital owned by the old and the labor supplied by the young combine to produce output that is distributed according to marginal products. 2021/4/17 13
2021/4/17 13 Firms Initial capital stock K0 , owned equally by all old individuals. No depreciation, =0. In period 0, the capital owned by the old and the labor supplied by the young combine to produce output that is distributed according to marginal products
Households budget constraint Young choose how much to consume of labor income w,A4,and how much to save. S,=(w,A-C) →C241=(1+54)S, →C,+C21/1+r4）)=w,A Lifetime budget constraint in the form of present value of lifetime consumption constrained to be equal to present value of human capital (for someone working one period,pretty simple) 202114/17 14
2021/4/17 14 Households budget constraint Young choose how much to consume of labor income wt At and how much to save. Lifetime budget constraint in the form of present value of lifetime consumption constrained to be equal to present value of human capital (for someone working one period, pretty simple). 1 21 1 1 21 1 1 1 t tt t t tt t t t tt S wA C C rS C C r wA