Egwald Economics: Microeconomics
Production Functions
by
Elmer G. Wiens
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Cobb-Douglas
| CES
| Generalized CES
| Translog
| Diewert
| Translog vs Diewert
| Diewert vs Translog
| Estimate Translog
| Estimate Diewert
| References and Links
Cost Functions:
Cobb-Douglas Cost
| Normalized Quadratic Cost
| Translog Cost
| Diewert Cost
| Generalized CES-Translog Cost
| Generalized CES-Diewert Cost
| References and Links
Duality: Production / Cost Functions:
Cobb-Douglas Duality
| CES Duality
| Theory of Duality
| Translog Duality - CES
| Translog Duality - Generalized CES
G. Generate CES Data and Estimate a Translog Production Function
1. The three factor CES production function is:
q = A * [alpha * (L^-rho) + beta * (K^-rho) + gamma *(M^-rho)]^(-nu/rho) = f(L,K,M).
where L = labour, K = capital, M = materials and supplies, and q = product. The parameter nu is a measure of the returns to scale, while the parameter rho yields the elasticity of substitution sigma = 1/(1 + rho).
2. The three factor Translog production function is:
ln(q) = ln(A) + aL*ln(L) + aK*ln(K) + aM*ln(M) + bLL*ln(L)*ln(L)+ bKK*ln(K)*ln(K) + bMM*ln(M)*ln(M) + bLK*ln(L)*ln(K) + bLM*ln(L)*ln(M) + bKM*ln(K)*ln(M) = f(L,K,M).
where L = labour, K = capital, M = materials and supplies, and q = product.
3. The coefficients of the translog production function vary with sigma and nu.
The program will generate a set of 208 observations, and use ordinary least squares to estimate the Translog coefficients.
The observations are the CES function's cost-minimizing combinations of L, K, and M at the factor prices, wL, wK, wM for values of q from 15 to 40.
The factor prices are distributed about the base factor prices by adding a random number distributed uniformly in the domain [-2, 2]. The program generates the CES cost-minimizing values of L, K, and M for each combination of base prices for each value of q in the [15, 45] domain.
Base Factor Prices |
wL | wK | wM |
8 | 8 | 8 |
7 | 13 | 6 |
6 | 7 | 13 |
13 | 6 | 7 |
9 | 15 | 11 |
11 | 9 | 15 |
15 | 11 | 9 |
| | |
12 | 12 | 12 |
Set the parameters below to re-run with your own CES parameters.
Restrictions: .5 < nu < 2; .2 < sigma < 5; .1 < alpha, beta, gamma < .9
sigma = 1 → nu = alpha + beta + gamma (Cobb-Douglas)
sigma < 1 → inputs complements; sigma > 1 → inputs substitutes
Coefficient Estimates
|
Variable
| Coefficient
|
std error
| t-ratio
|
lnA | -0.000163 | 0 | -0.456 | lnL | 0.350031 | 0 | 2905.669 | lnK | 0.400138 | 0 | 3142.321 | lnM | 0.249929 | 0 | 2365.024 | lnLlnL | -0.020202 | 0 | -953.21 | lnKlnK | -0.021175 | 0 | -976.741 | lnMlnM | -0.017252 | 0 | -906.31 | lnLlnK | 0.024163 | 0 | 687.158 | lnLlnM | 0.016283 | 0 | 484.651 | lnKlnM | 0.018168 | 0 | 591.562 |
R2 = 1 |
R2b = 1 |
# obs = 208 |
The table below displays the CES function's cost-minimizing combinations of L, K, and M at the factor prices, wL, wK, wM for values of q from 15 to 40.
The column est q = f(L, K, M) (using the translog function as estimated), where L, K, and M are the CES function's cost-minimizing combinations.
CES Production Function Data |
obs # | q | est q | L | K | M | wL | wK | wM |
1 | 15 | 15 | 15.22 | 19.25 | 10.09 | 7.96 | 6.9 | 9.22 |
2 | 16 | 16 | 19.88 | 15.02 | 13.19 | 6.22 | 9.88 | 7.2 |
3 | 17 | 17 | 16.88 | 21.26 | 12.21 | 8.7 | 7.58 | 9.1 |
4 | 18 | 18 | 20.13 | 18.03 | 15.4 | 6.58 | 8.56 | 6.44 |
5 | 19 | 19 | 20.18 | 22.5 | 13.52 | 7.66 | 7.7 | 8.76 |
6 | 20 | 20 | 16.92 | 23.98 | 19.06 | 9.76 | 7.4 | 6.06 |
7 | 21 | 21 | 22.46 | 22.4 | 17.32 | 8.72 | 10 | 8.46 |
8 | 22 | 22 | 21.81 | 25.4 | 17.81 | 8.98 | 8.58 | 8.14 |
9 | 23 | 23 | 26.18 | 26.27 | 15.78 | 7.1 | 8.08 | 9.2 |
10 | 24 | 24 | 24.55 | 26.43 | 20.01 | 9.22 | 9.66 | 8.38 |
11 | 25 | 25 | 27.52 | 28.55 | 17.92 | 7.42 | 8.12 | 8.78 |
12 | 26 | 26 | 23.33 | 34.38 | 19.73 | 10 | 7.24 | 8.7 |
13 | 27 | 27 | 26.11 | 31.67 | 22.08 | 8.3 | 7.56 | 7.22 |
14 | 28 | 28 | 24.16 | 36.47 | 22.91 | 9.26 | 6.52 | 7.04 |
15 | 29 | 29 | 33.4 | 35.57 | 17.7 | 6.18 | 6.56 | 9.32 |
16 | 30 | 30 | 32.44 | 33.34 | 22.91 | 6.36 | 7.04 | 6.84 |
17 | 31 | 31 | 30.13 | 38.05 | 23.54 | 9.28 | 8.06 | 8.86 |
18 | 32 | 32 | 36.92 | 32.27 | 26 | 6.84 | 9.16 | 7.38 |
19 | 33 | 33 | 28.33 | 44.43 | 25.91 | 9.3 | 6.26 | 7.38 |
20 | 34 | 34 | 35.1 | 41.39 | 24.12 | 8.88 | 8.36 | 9.86 |
21 | 35 | 35 | 35.99 | 41.5 | 25.94 | 7.2 | 6.96 | 7.56 |
22 | 36 | 36 | 39.1 | 39.99 | 27.36 | 7.78 | 8.66 | 8.46 |
23 | 37 | 37 | 37.59 | 47.47 | 24.85 | 7.9 | 6.86 | 9.18 |
24 | 38 | 38 | 32.74 | 46.34 | 34.39 | 8.9 | 6.76 | 6 |
25 | 39 | 39 | 41.11 | 39.73 | 35.21 | 7.7 | 9.16 | 6.6 |
26 | 40 | 40 | 39.13 | 50.35 | 29.02 | 9.04 | 7.68 | 9.18 |
27 | 15 | 15 | 20.63 | 11.64 | 14.71 | 6 | 13.44 | 6.38 |
28 | 16 | 16 | 24.06 | 11.99 | 14.81 | 5 | 12.96 | 6.32 |
29 | 17 | 17 | 18.56 | 15.67 | 17.15 | 7.96 | 11.1 | 6.24 |
30 | 18 | 18 | 23.01 | 15.57 | 16.27 | 6.5 | 11.76 | 6.98 |
31 | 19 | 19 | 24.62 | 14.78 | 20.11 | 7.04 | 14.66 | 6.38 |
32 | 20 | 20 | 21.32 | 19.26 | 19.44 | 8.54 | 11 | 6.8 |
33 | 21 | 21 | 28.65 | 14.13 | 26.64 | 5.32 | 13.96 | 4.14 |
34 | 22 | 22 | 23.68 | 19.77 | 23.61 | 7.9 | 11.16 | 5.66 |
35 | 23 | 23 | 25.7 | 18.23 | 28.96 | 7.86 | 13.46 | 4.88 |
36 | 24 | 24 | 32.56 | 19.58 | 22.08 | 7.02 | 14.6 | 7.92 |
37 | 25 | 25 | 31.22 | 21.64 | 23.29 | 7.12 | 12.52 | 7.18 |
38 | 26 | 26 | 26.8 | 21.88 | 33.17 | 8.6 | 12.48 | 4.78 |
39 | 27 | 27 | 35.71 | 22.64 | 24.55 | 6 | 11.72 | 6.66 |
40 | 28 | 28 | 31.96 | 22.97 | 32.26 | 7.7 | 12.98 | 5.44 |
41 | 29 | 29 | 34.42 | 21.31 | 38.27 | 6.44 | 12.94 | 4.06 |
42 | 30 | 30 | 39.78 | 23.07 | 31.38 | 6.84 | 14.84 | 6.46 |
43 | 31 | 31 | 40.92 | 24.26 | 31.67 | 5.8 | 12.26 | 5.6 |
44 | 32 | 32 | 42.76 | 21.79 | 40.91 | 5.82 | 14.7 | 4.38 |
45 | 33 | 33 | 39.9 | 29.41 | 30.62 | 7.26 | 11.88 | 7.08 |
46 | 34 | 34 | 51.7 | 25.11 | 31.8 | 5.5 | 14.7 | 6.96 |
47 | 35 | 35 | 42.57 | 27.14 | 40.61 | 7.02 | 13.62 | 5.3 |
48 | 36 | 36 | 37.69 | 34.62 | 35.95 | 8.9 | 11.24 | 6.72 |
49 | 37 | 37 | 52.75 | 31.61 | 29.65 | 5.46 | 11.4 | 7.68 |
50 | 38 | 38 | 40.59 | 31.42 | 47.44 | 7.2 | 11.12 | 4.28 |
51 | 39 | 39 | 46.13 | 35.72 | 35.67 | 7.24 | 11.18 | 7 |
52 | 40 | 40 | 62.79 | 29.59 | 35.82 | 5.02 | 13.9 | 6.94 |
53 | 15 | 15 | 21.7 | 17.4 | 7.52 | 4.94 | 7.32 | 12.28 |
54 | 16 | 16 | 19.51 | 20.41 | 8.62 | 7.42 | 8.04 | 13.86 |
55 | 17 | 17 | 20.63 | 22.12 | 8.96 | 7.62 | 8.02 | 14.52 |
56 | 18 | 18 | 23.8 | 25.95 | 7.49 | 5 | 5.16 | 13.92 |
57 | 19 | 19 | 22.04 | 27.67 | 9.09 | 5.74 | 5.02 | 11.62 |
58 | 20 | 20 | 30.34 | 27.83 | 7.47 | 4 | 5.06 | 14.86 |
59 | 21 | 21 | 25.53 | 29.35 | 10.03 | 5.32 | 5.16 | 11.4 |
60 | 22 | 22 | 31.6 | 26.93 | 10.33 | 4.32 | 5.96 | 11.5 |
61 | 23 | 23 | 29.6 | 27.46 | 12.71 | 5.8 | 7.24 | 11.2 |
62 | 24 | 24 | 36.56 | 28.11 | 11.18 | 4.42 | 6.88 | 12.72 |
63 | 25 | 25 | 38.57 | 27.34 | 12.62 | 5.16 | 8.84 | 13.72 |
64 | 26 | 26 | 27.61 | 41.75 | 12.19 | 7.46 | 5.24 | 13.94 |
65 | 27 | 27 | 28.67 | 45.12 | 12.03 | 7.52 | 5.04 | 14.92 |
66 | 28 | 28 | 38.99 | 30.97 | 15.69 | 5.66 | 8.48 | 11.8 |
67 | 29 | 29 | 33.62 | 42.04 | 13.98 | 6.92 | 6.08 | 13.88 |
68 | 30 | 30 | 33.13 | 44.57 | 14.84 | 7.12 | 5.74 | 13.08 |
69 | 31 | 31 | 45.37 | 38.07 | 14.18 | 4.84 | 6.8 | 13.58 |
70 | 32 | 32 | 48.17 | 34.01 | 17.31 | 4.88 | 8.4 | 11.62 |
71 | 33 | 33 | 40.64 | 49.71 | 14.09 | 5.7 | 5.14 | 14.16 |
72 | 34 | 34 | 38.16 | 51.49 | 16.08 | 7.02 | 5.64 | 13.86 |
73 | 35 | 35 | 41.48 | 45.1 | 19.25 | 7.84 | 8.12 | 13.82 |
74 | 36 | 36 | 47.09 | 45.54 | 18.03 | 6.46 | 7.68 | 14.28 |
75 | 37 | 37 | 56.62 | 40.7 | 18.7 | 5.34 | 9 | 14.04 |
76 | 38 | 38 | 43.21 | 46.21 | 23.85 | 7.82 | 8.26 | 11.24 |
77 | 39 | 39 | 51.58 | 43.55 | 22.93 | 6.44 | 8.98 | 11.94 |
78 | 40 | 40 | 60.46 | 44.62 | 20.11 | 5.46 | 8.92 | 14.24 |
79 | 15 | 15 | 9.44 | 23.85 | 14.46 | 13.22 | 5.08 | 5.72 |
80 | 16 | 16 | 11.65 | 21.35 | 16.11 | 12.96 | 7.26 | 6.32 |
81 | 17 | 17 | 13.44 | 25.56 | 12.77 | 11.7 | 6.28 | 8.88 |
82 | 18 | 18 | 12.83 | 24.97 | 17.64 | 11 | 5.74 | 5.4 |
83 | 19 | 19 | 11.98 | 32.78 | 16.23 | 12.52 | 4.38 | 6.26 |
84 | 20 | 20 | 14 | 31.82 | 16.46 | 13.38 | 5.82 | 7.9 |
85 | 21 | 21 | 15.04 | 34.56 | 15.96 | 11.74 | 5.04 | 7.82 |
86 | 22 | 22 | 13.86 | 35.39 | 20.83 | 13.66 | 5.18 | 6.04 |
87 | 23 | 23 | 16.7 | 36.15 | 18.28 | 13.24 | 6.1 | 8.5 |
88 | 24 | 24 | 17.7 | 32.46 | 23.23 | 11.64 | 6.52 | 6.04 |
89 | 25 | 25 | 19.54 | 31.22 | 25.11 | 12 | 7.9 | 6.38 |
90 | 26 | 26 | 17.21 | 39.93 | 24.46 | 13.38 | 5.68 | 6.32 |
91 | 27 | 27 | 20.57 | 39.5 | 22.21 | 12.78 | 6.78 | 8.34 |
92 | 28 | 28 | 20.63 | 35.98 | 29.34 | 12.12 | 7.2 | 5.72 |
93 | 29 | 29 | 20.4 | 35.64 | 34.98 | 13.36 | 7.92 | 5.06 |
94 | 30 | 30 | 20.04 | 51.12 | 23.99 | 11.8 | 4.48 | 6.82 |
95 | 31 | 31 | 21.96 | 46.46 | 27.34 | 11.96 | 5.66 | 6.6 |
96 | 32 | 32 | 24.85 | 48.97 | 24.03 | 11.12 | 5.72 | 8.26 |
97 | 33 | 33 | 24.62 | 47.89 | 28.3 | 12.4 | 6.48 | 7.52 |
98 | 34 | 34 | 21.03 | 63.09 | 27 | 13.64 | 4.28 | 7.26 |
99 | 35 | 35 | 23.3 | 48.39 | 38.19 | 14.22 | 6.88 | 5.68 |
100 | 36 | 36 | 26.19 | 53.54 | 30.89 | 11.12 | 5.48 | 6.54 |
101 | 37 | 37 | 22.41 | 63.35 | 33.94 | 12.18 | 4.1 | 5.34 |
102 | 38 | 38 | 22.68 | 65.8 | 35.07 | 12.44 | 4.06 | 5.32 |
103 | 39 | 39 | 28.79 | 59.11 | 31.89 | 13.42 | 6.58 | 8.5 |
104 | 40 | 40 | 24.12 | 64.61 | 40.2 | 14.5 | 5.2 | 5.68 |
105 | 15 | 15 | 18.65 | 15.52 | 10.64 | 9.22 | 13.08 | 12.74 |
106 | 16 | 16 | 18.69 | 15.01 | 14.33 | 10.22 | 15.12 | 9.98 |
107 | 17 | 17 | 19.58 | 15.34 | 16.51 | 10.7 | 16.3 | 9.34 |
108 | 18 | 18 | 22.67 | 16.66 | 14.9 | 9.16 | 15.04 | 10.72 |
109 | 19 | 19 | 23.03 | 19.28 | 14.35 | 10.24 | 14.42 | 12.76 |
110 | 20 | 20 | 29.7 | 16.76 | 15.7 | 7.42 | 16.62 | 11.22 |
111 | 21 | 21 | 28.17 | 18.94 | 16.7 | 7.92 | 14.44 | 10.46 |
112 | 22 | 22 | 29.48 | 21.06 | 15.97 | 7.8 | 13.24 | 11.46 |
113 | 23 | 23 | 24.69 | 23.57 | 20.07 | 10.82 | 13.06 | 9.86 |
114 | 24 | 24 | 27.35 | 24.36 | 19.63 | 10.92 | 14.3 | 11.52 |
115 | 25 | 25 | 31.61 | 22.35 | 21.76 | 9.04 | 15.54 | 10.02 |
116 | 26 | 26 | 35.73 | 23.53 | 19.94 | 7.74 | 14.46 | 10.98 |
117 | 27 | 27 | 31.98 | 23.68 | 26.44 | 10.32 | 16.8 | 9.22 |
118 | 28 | 28 | 35.6 | 25.65 | 23.27 | 8.32 | 13.98 | 9.8 |
119 | 29 | 29 | 32.51 | 28.1 | 26.07 | 9.98 | 13.54 | 9.24 |
120 | 30 | 30 | 39.9 | 26.58 | 24.8 | 8.02 | 14.78 | 10.02 |
121 | 31 | 31 | 35.26 | 28.59 | 29.56 | 10.72 | 15.68 | 9.42 |
122 | 32 | 32 | 39.65 | 30.4 | 25.99 | 10.46 | 16.34 | 12.28 |
123 | 33 | 33 | 46.67 | 27.93 | 27.11 | 7.76 | 16.22 | 10.5 |
124 | 34 | 34 | 44.15 | 29.71 | 29.64 | 8.62 | 15.7 | 9.84 |
125 | 35 | 35 | 43.33 | 29.91 | 33.69 | 9.56 | 16.9 | 9.18 |
126 | 36 | 36 | 49.25 | 32.78 | 27.51 | 7.48 | 13.8 | 10.6 |
127 | 37 | 37 | 46.52 | 37.21 | 27.03 | 9.46 | 14.06 | 12.8 |
128 | 38 | 38 | 43.77 | 36.86 | 32.88 | 10.78 | 15.08 | 10.78 |
129 | 39 | 39 | 50.76 | 35.66 | 31.55 | 9.38 | 16.24 | 11.72 |
130 | 40 | 40 | 48.84 | 41.63 | 28.8 | 9.76 | 13.46 | 12.98 |
131 | 15 | 15 | 17.16 | 20.45 | 7.97 | 9.06 | 8.42 | 15.94 |
132 | 16 | 16 | 15.22 | 24.11 | 9.36 | 12.84 | 8.54 | 16.24 |
133 | 17 | 17 | 18.6 | 22.21 | 10.12 | 10.78 | 10 | 15.76 |
134 | 18 | 18 | 19.31 | 22.37 | 11.79 | 10.34 | 9.94 | 13.2 |
135 | 19 | 19 | 22.51 | 22.68 | 11.63 | 9.36 | 10.6 | 14.54 |
136 | 20 | 20 | 19.93 | 27.44 | 12.53 | 10.58 | 8.3 | 13.04 |
137 | 21 | 21 | 20.54 | 29.89 | 12.81 | 11.48 | 8.44 | 14.3 |
138 | 22 | 22 | 20.91 | 32.77 | 13.09 | 10.6 | 7.14 | 13.14 |
139 | 23 | 23 | 23.56 | 32.04 | 13.62 | 11.96 | 9.52 | 16.28 |
140 | 24 | 24 | 25.94 | 32.53 | 13.8 | 10.78 | 9.44 | 16.18 |
141 | 25 | 25 | 25.18 | 39.34 | 12.84 | 10.44 | 7.06 | 16.48 |
142 | 26 | 26 | 29.18 | 32.85 | 15.72 | 10.14 | 10.08 | 15 |
143 | 27 | 27 | 30.87 | 34.8 | 15.51 | 10.44 | 10.36 | 16.76 |
144 | 28 | 28 | 28.87 | 40.25 | 15.76 | 10.92 | 8.44 | 15.9 |
145 | 29 | 29 | 32.35 | 38.83 | 16.29 | 9.22 | 8.5 | 14.76 |
146 | 30 | 30 | 31.86 | 39.24 | 18.52 | 12.1 | 10.82 | 16.36 |
147 | 31 | 31 | 31.86 | 43.26 | 18.24 | 10.08 | 8.04 | 13.88 |
148 | 32 | 32 | 35.38 | 44.98 | 17.02 | 9.98 | 8.6 | 16.86 |
149 | 33 | 33 | 28.95 | 51.95 | 20.21 | 12.22 | 7.02 | 13.32 |
150 | 34 | 34 | 33.35 | 52.48 | 18.51 | 10.56 | 7.08 | 15.08 |
151 | 35 | 35 | 37.87 | 49.62 | 18.9 | 10.22 | 8.5 | 16.54 |
152 | 36 | 36 | 37.1 | 48.45 | 22.19 | 11.26 | 9.4 | 14.72 |
153 | 37 | 37 | 43.42 | 44 | 23.04 | 9.1 | 10.24 | 13.7 |
154 | 38 | 38 | 44.36 | 46.63 | 22.79 | 9.5 | 10.24 | 14.86 |
155 | 39 | 39 | 46.44 | 46.05 | 24.1 | 9.2 | 10.62 | 14.22 |
156 | 40 | 40 | 39.84 | 60.26 | 22.07 | 11.36 | 7.98 | 16.26 |
157 | 15 | 15 | 13.32 | 16.17 | 15.75 | 14.04 | 12.78 | 8.24 |
158 | 16 | 16 | 14.73 | 19.4 | 13.32 | 13.4 | 11.08 | 10.78 |
159 | 17 | 17 | 15.48 | 21.2 | 13.77 | 13.2 | 10.42 | 10.82 |
160 | 18 | 18 | 12.51 | 23.77 | 19.73 | 16.94 | 9.1 | 7.08 |
161 | 19 | 19 | 16.49 | 22.98 | 17.24 | 14.64 | 11.32 | 9.92 |
162 | 20 | 20 | 16.46 | 25.2 | 18.37 | 16.06 | 11.12 | 10.08 |
163 | 21 | 21 | 16.88 | 27.71 | 18.62 | 15.3 | 9.76 | 9.74 |
164 | 22 | 22 | 19.63 | 22.57 | 24.84 | 13.22 | 12.82 | 7.16 |
165 | 23 | 23 | 17.6 | 28.29 | 24.38 | 16.64 | 10.88 | 8.1 |
166 | 24 | 24 | 20.47 | 28.86 | 22.5 | 15.36 | 11.72 | 9.82 |
167 | 25 | 25 | 22.94 | 29.7 | 21.56 | 13.38 | 11.28 | 10.28 |
168 | 26 | 26 | 21.37 | 35.53 | 21.22 | 15.02 | 9.44 | 10.82 |
169 | 27 | 27 | 24.05 | 31.73 | 24.67 | 14.14 | 11.66 | 9.8 |
170 | 28 | 28 | 21.09 | 37.08 | 27.13 | 16.72 | 9.84 | 8.88 |
171 | 29 | 29 | 23.47 | 36.23 | 27.66 | 14.84 | 10.18 | 8.74 |
172 | 30 | 30 | 26.03 | 32.92 | 31.67 | 14.6 | 12.66 | 8.28 |
173 | 31 | 31 | 25.97 | 36.81 | 30.41 | 16.72 | 12.68 | 9.92 |
174 | 32 | 32 | 29.15 | 35.74 | 30.64 | 13.12 | 11.8 | 8.84 |
175 | 33 | 33 | 28.01 | 39.78 | 31.05 | 15.52 | 11.74 | 9.82 |
176 | 34 | 34 | 29.45 | 39.4 | 33.03 | 15.38 | 12.48 | 9.6 |
177 | 35 | 35 | 29.05 | 42.96 | 33.08 | 16.44 | 11.86 | 10.08 |
178 | 36 | 36 | 28.17 | 42.57 | 39.29 | 16.98 | 11.94 | 8.2 |
179 | 37 | 37 | 30.1 | 42.64 | 39.7 | 13.92 | 10.56 | 7.18 |
180 | 38 | 38 | 34.57 | 44.43 | 33.96 | 15 | 12.76 | 10.94 |
181 | 39 | 39 | 28.81 | 53.05 | 37.34 | 16.94 | 9.44 | 8.92 |
182 | 40 | 40 | 31.66 | 47.12 | 43.18 | 16.54 | 11.84 | 8.2 |
183 | 15 | 15 | 15.73 | 17.33 | 11.26 | 10.84 | 11.06 | 11.48 |
184 | 16 | 16 | 15.89 | 17.83 | 13.64 | 12.72 | 12.7 | 10.88 |
185 | 17 | 17 | 18.39 | 19.89 | 12.02 | 10.92 | 11.38 | 12.86 |
186 | 18 | 18 | 21.02 | 19.66 | 12.76 | 10.24 | 12.66 | 13.16 |
187 | 19 | 19 | 20.28 | 22.49 | 13.44 | 10.34 | 10.46 | 11.98 |
188 | 20 | 20 | 20.47 | 23.16 | 15.45 | 10.54 | 10.42 | 10.48 |
189 | 21 | 21 | 19.98 | 24.21 | 18.03 | 13.8 | 12.58 | 11.12 |
190 | 22 | 22 | 24.11 | 26.03 | 15.06 | 10.8 | 11.28 | 13.42 |
191 | 23 | 23 | 22.66 | 27.96 | 17.39 | 12.1 | 10.8 | 11.8 |
192 | 24 | 24 | 22.52 | 28.75 | 19.82 | 13.9 | 11.92 | 11.54 |
193 | 25 | 25 | 23.15 | 30.45 | 20.51 | 13.36 | 11.06 | 11 |
194 | 26 | 26 | 25.21 | 32.37 | 19.4 | 13.46 | 11.46 | 13.08 |
195 | 27 | 27 | 26.42 | 31.38 | 22.03 | 12.26 | 11.44 | 10.84 |
196 | 28 | 28 | 27.42 | 33.18 | 22.18 | 11.08 | 10.12 | 10.16 |
197 | 29 | 29 | 30.93 | 31.12 | 23.78 | 11.14 | 12.64 | 10.84 |
198 | 30 | 30 | 30.96 | 34.77 | 22.89 | 12.56 | 12.52 | 12.8 |
199 | 31 | 31 | 29.97 | 39.42 | 22.52 | 12.9 | 10.68 | 12.9 |
200 | 32 | 32 | 33.53 | 39.06 | 22.19 | 11.56 | 11.04 | 13.42 |
201 | 33 | 33 | 34.44 | 36.34 | 26.79 | 10.98 | 11.78 | 10.54 |
202 | 34 | 34 | 36.4 | 39.95 | 24.22 | 11.46 | 11.74 | 13.22 |
203 | 35 | 35 | 36.6 | 44.49 | 22.95 | 11.32 | 10.28 | 14 |
204 | 36 | 36 | 38.21 | 41.67 | 26.52 | 12.52 | 12.92 | 13.74 |
205 | 37 | 37 | 41.71 | 39.98 | 27.91 | 11.52 | 13.84 | 13.2 |
206 | 38 | 38 | 36.31 | 46.52 | 29.64 | 12.44 | 10.62 | 11.28 |
207 | 39 | 39 | 38.96 | 46.8 | 29.52 | 12.18 | 11.22 | 12.06 |
208 | 40 | 40 | 43.37 | 48.06 | 27.14 | 10.84 | 10.98 | 13.44 |
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