Question

Problem 3: Solow Model with No Technological Change Assume that we live in an imaginary world where there are two countries: Cocoloco and Sambapati. These two countries have the same population size, population growth, depreciation rate and production function. But Sambapati has a larger capital stock than Cocoloco. Output in both countries is produced according to the following constant-returns-to-scale production function that lies at the heart of the standard Solow growth model: Y(t) = 25[K(0°SILOJOS where Y (t) is the aggregate output in year t, Kt) is the capital in year t, and Lt) is the labor in yeart. Assume that the savings rate is 27% (s = 0.27), the population grows at a rate of 1.8% per year (n = 0.018), and capital depreciates at a rate of 2.5% per year (d = 0.025).

please solve these 4 parts. will leave good review thanks!

Answer 1

(e), (h); c subscript for Cocoloco and s for Sambapati. G= Growth

y = income per capita

k capital per capita(worker)

time	k	yc	ks	ys	Gc	Gs
0	200	353.55	600	612.37
1	286.86	423.42	739.54	679.86	19.76	11.02
2	388.85	492.98	891.30	746.37	16.43	9.78
3	505.23	561.93	1054.50	811.83	13.99	8.77
4	635.23	630.09	1228.35	876.19	12.13	7.93
5	778.04	697.33	1412.10	939.45	10.67	7.22
6	932.87	763.57	1605.03	1001.57	9.50	6.61
7	1098.92	828.75	1806.44	1062.56	8.54	6.09
8	1275.43	892.83	2015.65	1122.40	7.73	5.63
9	1461.65	955.79	2232.03	1181.11	7.05	5.23
10	1656.86	1017.61	2454.95	1238.69	6.47	4.87
11	1860.37	1078.30	2683.83	1295.14	5.96	4.56
12	2071.51	1137.85	2918.11	1350.49	5.52	4.27
13	2289.66	1196.26	3157.27	1404.74	5.13	4.02
14	2514.19	1253.54	3400.78	1457.91	4.79	3.78
15	2744.54	1309.71	3648.19	1510.01	4.48	3.57
16	2980.14	1364.77	3899.01	1561.05	4.20	3.38
17	3220.48	1418.73	4152.84	1611.06	3.95	3.20
18	3465.06	1471.62	4409.26	1660.06	3.73	3.04
19	3713.40	1523.44	4667.87	1708.05	3.52	2.89
20	3965.05	1574.22	4928.33	1755.05	3.33	2.75
21	4219.60	1623.96	5190.27	1801.09	3.16	2.62
22	4476.62	1672.69	5453.39	1846.18	3.00	2.50
23	4735.75	1720.42	5717.36	1890.33	2.85	2.39
24	4996.63	1767.17	5981.90	1933.57	2.72	2.29
25	5258.91	1812.96	6246.74	1975.91	2.59	2.19
26	5522.28	1857.80	6511.63	2017.37	2.47	2.10
27	5786.42	1901.71	6776.32	2057.96	2.36	2.01
28	6051.07	1944.72	7040.58	2097.70	2.26	1.93
29	6315.95	1986.82	7304.22	2136.62	2.17	1.86
30	6580.80	2028.05	7567.02	2174.72	2.08	1.78
31	6845.40	2068.42	7828.82	2212.01	1.99	1.72
32	7109.53	2107.95	8089.42	2248.53	1.91	1.65
33	7372.96	2146.65	8348.68	2284.28	1.84	1.59
34	7635.52	2184.54	8606.44	2319.27	1.76	1.53
35	7897.02	2221.63	8862.57	2353.53	1.70	1.48
36	8157.29	2257.94	9116.93	2387.07	1.63	1.42
37	8416.17	2293.49	9369.41	2419.89	1.57	1.38
38	8673.52	2328.29	9619.90	2452.03	1.52	1.33
39	8929.19	2362.36	9868.29	2483.48	1.46	1.28
40	9183.08	2395.71	10114.49	2514.27	1.41	1.24
41	9435.04	2428.35	10358.42	2544.41	1.36	1.20
42	9684.99	2460.31	10600.00	2573.91	1.32	1.16
43	9932.82	2491.59	10839.15	2602.78	1.27	1.12
44	10178.44	2522.21	11075.82	2631.04	1.23	1.09
45	10421.76	2552.18	11309.94	2658.71	1.19	1.05
46	10662.71	2581.51	11541.47	2685.78	1.15	1.02
47	10901.23	2610.22	11770.34	2712.28	1.11	0.99
48	11137.23	2638.33	11996.53	2738.22	1.08	0.96
49	11370.68	2665.83	12220.00	2763.60	1.04	0.93
50	11601.52	2692.76	12440.71	2788.45	1.01	0.90
51	11829.70	2719.11	12658.65	2812.77	0.98	0.87
52	12055.18	2744.90	12873.77	2836.57	0.95	0.85
53	12277.93	2770.15	13086.07	2859.86	0.92	0.82
54	12497.92	2794.85	13295.53	2882.66	0.89	0.80
55	12715.12	2819.03	13502.14	2904.97	0.87	0.77
56	12929.51	2842.70	13705.89	2926.80	0.84	0.75
57	13141.07	2865.86	13906.77	2948.17	0.81	0.73
58	13349.78	2888.53	14104.79	2969.09	0.79	0.71
59	13555.65	2910.72	14299.94	2989.56	0.77	0.69
60	13758.65	2932.43	14492.22	3009.59	0.75	0.67
61	13958.78	2953.68	14681.65	3029.20	0.72	0.65
62	14156.05	2974.48	14868.22	3048.38	0.70	0.63
63	14350.45	2994.83	15051.95	3067.16	0.68	0.62
64	14541.98	3014.75	15232.85	3085.54	0.67	0.60
65	14730.66	3034.25	15410.93	3103.52	0.65	0.58
66	14916.49	3053.33	15586.21	3121.12	0.63	0.57
67	15099.48	3072.00	15758.70	3138.34	0.61	0.55
68	15279.64	3090.27	15928.43	3155.20	0.59	0.54
69	15456.99	3108.15	16095.41	3171.69	0.58	0.52
70	15631.54	3125.65	16259.67	3187.84	0.56	0.51
71	15803.31	3142.78	16421.22	3203.63	0.55	0.50
72	15972.32	3159.54	16580.09	3219.09	0.53	0.48
73	16138.59	3175.94	16736.30	3234.22	0.52	0.47
74	16302.13	3192.00	16889.88	3249.03	0.51	0.46
75	16462.98	3207.70	17040.85	3263.52	0.49	0.45
76	16621.15	3223.08	17189.24	3277.69	0.48	0.43
77	16776.67	3238.12	17335.08	3291.57	0.47	0.42
78	16929.57	3252.84	17478.40	3305.15	0.45	0.41
79	17079.86	3267.25	17619.21	3318.43	0.44	0.40
80	17227.59	3281.35	17757.57	3331.44	0.43	0.39
81	17372.76	3295.14	17893.48	3344.16	0.42	0.38
82	17515.42	3308.65	18026.98	3356.62	0.41	0.37
83	17655.60	3321.86	18158.11	3368.80	0.40	0.36
84	17793.31	3334.79	18286.89	3380.73	0.39	0.35
85	17928.59	3347.44	18413.35	3392.39	0.38	0.35
86	18061.47	3359.82	18537.52	3403.81	0.37	0.34
87	18191.98	3371.94	18659.44	3414.99	0.36	0.33
88	18320.15	3383.80	18779.13	3425.92	0.35	0.32
89	18446.01	3395.40	18896.62	3436.62	0.34	0.31
90	18569.59	3406.76	19011.96	3447.10	0.33	0.30
91	18690.92	3417.87	19125.16	3457.34	0.33	0.30
92	18810.03	3428.74	19236.26	3467.37	0.32	0.29
93	18926.96	3439.38	19345.29	3477.18	0.31	0.28
94	19041.74	3449.79	19452.28	3486.79	0.30	0.28
95	19154.39	3459.98	19557.27	3496.18	0.30	0.27
96	19264.94	3469.96	19660.27	3505.38	0.29	0.26
97	19373.44	3479.71	19761.33	3514.38	0.28	0.26
98	19479.90	3489.26	19860.48	3523.18	0.27	0.25
99	19584.37	3498.60	19957.74	3531.80	0.27	0.24
100	19686.86	3507.75	20053.14	3540.23	0.26	0.24

Representative DATA UNTIL T= 100. Space on portal restricting more than this. You may use the formula to generate the data for rest of years. Do ask for further help on this.

(e) Figire 3C:

Use kt = k(t-1)+sy(t-1)-(n+$\delta$)k(t-1)

then yt = 25(kt)^0.5

4500.00 4000.00 3500.00 3000.00 2500.00 income per capitaly(t)) 2000.00 1500.00 1000.00 500.00 0.00 5000 10000 20000 25000 30000 15000 capital per worker(k(t)) ys yc —

(h) gt = (yt-yt-1)/yt*100

FIGURE 3D

Growth rates Growth rate (G) 0 10 20 30 40 50 60 70 80 90 100110120130140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 —G — Gs

(g). The model reaches steady state where k(t+1) = k(t). The model doesn't reach steady state in t=300.

(h) Rule of 70 says the country will double income in t = 70/growth rate = 70/3.5 = 20 years.