Question

An economy is described by the solow model, it has he following production function: Y= F(K,EL) K5 (EL) 0.5 E grows at rate g; L grows at rate n ; depreciation rate is ô. Savings rate is a constant s 1- We will fill in the model (in terms of Y, s) C= (in terms of Y, s Y = (in terms of C and I only) 2- This is the first year of our country's founding, the country is called NewNew England, NNE for short. it has a 100 people (L) and Capital (K). Every person in NNE saves 25% of their income. And existing capital depreciates at a rate of 7%. E= 1, both g and n equal zero. a 100 units of L T Y1 C. I 8 K Kta 0 3- We want to describe the economy per effective worker so, y=Y/EL ,k=K/EL ,c=C/EL ,i= 1/EL Derive the per capita production function y (hint, y will be expressed in terms of k) show your work SC y ? (in terms of y, s) (in terms of y, s) i = 4- Capital per person changes according to this law k+i-(6+n+ g) k kt+1 can you very briefly explain the intuition behind this equation? In the steady state, k= k+1 , derive the steady state k' equation in terms of s, 8, n,g the equations for i, y and the law of motion) (hint, use k' ?

Answer 1

yeFIKEL]-KaLEL. 1 를 - 눈= 8 A savings ale & dpuasin Cd) ate n It knoun that y=C+I& aloo (Z) Y-C+S y=C+ S y: ct69 opotion of y U-YC C-(1-3)y Pum 2 D we I- CI-I+)y y=11-6)Y+I Isy rom D, 2 (4 we y=C-S)YY 25%1 8-7% E-1, both 32 K 1002s 7 L 100 7end y-Ko.S1 0,5 L y=(lo0)Cloo) V2 K=L= 100 te o At l00 C = (1-6)Y 75 =75X1O0 =7 Ig- 25 =.25 X IOO = 25 SKo Ko -tx00 7 7 Ki = Ia -8 Koko K25-HIO0>| K1=18 At given L'not Ki = 118 (Faom 9 Y1-C1o0)as CI18) O. Taing Lt- 100 2 10x[lo.82= 108.62

(11 Ct C1 A) 1 = (1-.25) x 108.62= 81.465 C1= 81.47 1 2 I1: 1 27.15 13 ,25X108.62 SKI=.07 X 11g 8.26 SK1K2KI + T1-8 KI 11 K2-K1= K2 118+27.1S-8.26 K1+1= K2= 136.89 Ktt It Ct Lt KE T 118 75 25 100 100 100 g.26 13 6.29 27.15 gl.47 108.62 100 118 1 K Cu5 (EL) y = 93. (KEL)O.S EL EL EL ELIOS EL EL i = sks 17

(-s)Y-6) --4)k EL EL U-s)KOS 0.5 34 REtl =ke +it- C8tnt kE intuitiom- (Retl-kt) - Ak it-(8+nt9) RE eguation depiets the cnmgefk Jue investmentr inuaaos the sto ck of capital &it K . LE he above inereases the R. Jhe 8 is dupeaiation rate, the ate at wich peaus out. Thus it oleereases K. higher the Ihe'n' is population gnouoth ate, the ate of grosth f population capital pen epffeetive labore. lower s the Similosly highen teeunology oth na npovemnt of E', that a'. Ihe lower in govsth eapital fer effestive takor f R= nate -E =R Lt k L E

as Rt kG+1 Jue dtrady state is olafined te -(Stntg)ke i ke-keti (REHI-RE) 0 i6-(8tntg) ke it = (8tntz)kt L It =s YE EL EL Rt St nt Hene Rt F CRE)=RE S+nty FCRE) Rt RE &+nt 2 8+nt2