Question

Consider an economy such that Capital per effective worker: kt Output per effective worker: yt = 2k0:5 Depreciation rate: 8 = 0.16 Saving rate: s= 0.3 Workforce growth rate: &N = 0.2 Technology growth rate: gA = 0.2 Evolution of capital per effective worker : kt+1 - kt = >> 1 _ syt-(6+8N+gA+SNSA)kt 1+gN+SA+SNSA In the steady state, capital per effective worker does not change over time. Let k* denote the steady state level of capital per effective worker. • In the steady state, capital per efficient worker is b) 4 d) 1 • Which one of the following statements is correct? a) In the steady state, capital per efficient worker is higher when technology grows at a faster rate. b) In the steady state capital per worker grows at a faster rate when technology grows at a faster rate. c) Both a and b. d) None of the above. • In the steady state, a) Capital per effective worker does not change over time b) Capital per worker does not change over time c) Capital does not change over time d) All of the above

Answer 1

o.. Given, Page 1 Ktt K = 54 - (Stqut 9A + INAKE lt gut GAT INGA K* = Steady state level of capital per llective worken. Therefore, Ktti = K+ k* - putting the values given, in egn- 0 = 0:3 (@ktº) - (-0.16+ 0.2+0.2+0.04 kt 1+ 0.2+0 2 + 0.04 0 2 0-3427 pon- (0.6%)** 144 0.6K = 0.6 k*- ✓ KA = K* VK = I K = 1 In the steady state, capital pen efficient I worker ů 1 Ed).

-2 s. Technology growth rate : 9A0-2 let ustake, 9A = 0.4 Jaster rate than 0.2) Then we have In the steady state: - Ktt K+ = kt. therefore making the substitutions: KA-K4 = 0.3 (QK05)-(0.16+ 0.2+0.4 +0.08 K* 1+ 0.2+04+0.08 = 0.6JK* -0.84 KK 1.68 06 UK4 = 0.84K* 0.6 = 0.84 KA J K = 0.60 0184 Squaring both sides, * = 0.51 In the steady state capital -per efficient worker is lower when technology groues at a faster rate (0.4) than 0.2 ... argument ta) is false In the steady state, Capetal per worker does not grow but remains constant

(hage-3) Page is the argument (b) is fabe. (d) None of the above 4 answer. - In the steady state, (d) All of the above