Figure 1. Comparison of index formulas: final Chained Consumer Price Index for All Urban Consumers (C-CPI-U) , Consumer Price Index for All Urban Consumers (CPI-U), Geometric Young formula, and constant elasticity of substitution (CES) formula with sigmas 0 to 0.999, 2000–12
Index period Final C-CPI-U CPI-U Geometric Young CES = 0.0 CES = 0.1 CES = 0.2 CES = 0.3 CES = 0.4 CES = 0.5 CES = 0.6 CES = 0.7 CES = 0.8 CES = 0.9 CES = 0.999

Jan 2000

100.337 100.332 100.256 100.334 100.327 100.320 100.313 100.306 100.298 100.291 100.283 100.274 100.265 100.256

Feb 2000

100.887 100.914 100.781 100.915 100.903 100.890 100.877 100.864 100.851 100.838 100.824 100.810 100.795 100.781

Mar 2000

101.631 101.727 101.552 101.729 101.712 101.696 101.679 101.662 101.645 101.627 101.609 101.590 101.571 101.552

Apr 2000

101.649 101.803 101.621 101.804 101.788 101.771 101.754 101.736 101.719 101.700 101.682 101.662 101.642 101.621

May 2000

101.683 101.888 101.690 101.889 101.872 101.854 101.835 101.816 101.797 101.777 101.757 101.735 101.713 101.690

Jun 2000

102.111 102.453 102.128 102.455 102.425 102.395 102.365 102.334 102.302 102.270 102.236 102.201 102.166 102.129

Jul 2000

102.305 102.659 102.274 102.660 102.626 102.591 102.555 102.519 102.481 102.443 102.403 102.362 102.319 102.275

Aug 2000

102.297 102.675 102.284 102.677 102.642 102.607 102.571 102.535 102.497 102.457 102.417 102.374 102.330 102.284

Sep 2000

102.796 103.225 102.814 103.227 103.190 103.153 103.115 103.076 103.036 102.995 102.952 102.908 102.862 102.814

Oct 2000

102.899 103.386 102.976 103.388 103.352 103.315 103.277 103.239 103.199 103.158 103.115 103.071 103.025 102.977

Nov 2000

102.834 103.462 102.973 103.463 103.421 103.379 103.335 103.289 103.242 103.194 103.143 103.089 103.032 102.973

Dec 2000

102.624 103.384 102.862 103.385 103.341 103.296 103.250 103.202 103.152 103.100 103.045 102.988 102.927 102.863

Jan 2001

103.303 104.052 103.358 104.053 103.992 103.931 103.868 103.803 103.737 103.668 103.596 103.521 103.441 103.359

Feb 2001

103.658 104.480 103.776 104.482 104.422 104.361 104.298 104.233 104.166 104.096 104.022 103.945 103.863 103.777

Mar 2001

103.894 104.736 104.064 104.738 104.682 104.624 104.565 104.504 104.440 104.374 104.303 104.229 104.150 104.065

Apr 2001

104.201 105.129 104.389 105.131 105.069 105.005 104.940 104.872 104.802 104.728 104.651 104.569 104.482 104.390

May 2001

104.557 105.572 104.731 105.573 105.503 105.430 105.356 105.278 105.198 105.115 105.027 104.934 104.836 104.732

Jun 2001

104.830 105.800 104.941 105.801 105.731 105.659 105.584 105.506 105.424 105.339 105.249 105.153 105.051 104.942

Jul 2001

104.494 105.460 104.557 105.461 105.387 105.311 105.232 105.150 105.064 104.974 104.879 104.779 104.672 104.558

Aug 2001

104.604 105.499 104.576 105.501 105.426 105.350 105.270 105.187 105.100 105.008 104.911 104.807 104.696 104.578

Sep 2001

104.940 105.929 104.956 105.930 105.851 105.769 105.685 105.597 105.505 105.409 105.307 105.198 105.081 104.957

Oct 2001

104.654 105.581 104.661 105.583 105.509 105.433 105.354 105.271 105.185 105.094 104.997 104.893 104.782 104.662

Nov 2001

104.366 105.395 104.381 105.396 105.314 105.229 105.141 105.050 104.954 104.853 104.747 104.634 104.512 104.382

Dec 2001

103.869 104.988 103.899 104.989 104.901 104.809 104.715 104.617 104.514 104.406 104.291 104.170 104.039 103.900

Jan 2002

104.166 105.262 104.146 105.263 105.172 105.079 104.982 104.882 104.776 104.665 104.548 104.423 104.290 104.147

Feb 2002

104.502 105.669 104.507 105.670 105.576 105.478 105.377 105.272 105.162 105.047 104.925 104.795 104.657 104.509

Mar 2002

105.068 106.239 105.106 106.240 106.148 106.053 105.955 105.853 105.746 105.633 105.514 105.388 105.252 105.108

Apr 2002

105.634 106.842 105.715 106.843 106.752 106.658 106.561 106.460 106.353 106.241 106.123 105.996 105.861 105.716

May 2002

105.573 106.819 105.688 106.820 106.729 106.635 106.537 106.436 106.329 106.217 106.098 105.971 105.835 105.690

Jun 2002

105.582 106.906 105.729 106.917 106.821 106.722 106.619 106.512 106.400 106.282 106.157 106.024 105.882 105.730

Jul 2002

105.737 107.024 105.781 107.028 106.927 106.822 106.713 106.600 106.483 106.359 106.228 106.089 105.940 105.782

Aug 2002

106.034 107.354 106.076 107.359 107.254 107.146 107.034 106.918 106.797 106.669 106.535 106.392 106.240 106.078

Sep 2002

106.254 107.545 106.252 107.549 107.444 107.334 107.221 107.104 106.981 106.852 106.716 106.572 106.417 106.254

Oct 2002

106.405 107.750 106.438 107.752 107.645 107.535 107.420 107.301 107.177 107.046 106.908 106.762 106.606 106.439

Nov 2002

106.326 107.748 106.375 107.750 107.637 107.521 107.401 107.277 107.146 107.010 106.865 106.713 106.550 106.377

Dec 2002

106.046 107.507 106.068 107.508 107.390 107.268 107.141 107.010 106.874 106.730 106.579 106.420 106.250 106.070

Jan 2003

106.495 107.955 106.457 107.961 107.837 107.709 107.577 107.440 107.297 107.147 106.989 106.823 106.646 106.459

Feb 2003

107.256 108.811 107.226 108.815 108.683 108.547 108.406 108.261 108.110 107.952 107.785 107.610 107.424 107.228

Mar 2003

107.938 109.470 107.833 109.471 109.334 109.193 109.047 108.897 108.741 108.578 108.407 108.227 108.037 107.835

Apr 2003

107.682 109.204 107.611 109.205 109.073 108.936 108.796 108.650 108.498 108.339 108.172 107.997 107.810 107.613

May 2003

107.521 109.044 107.435 109.045 108.912 108.776 108.634 108.487 108.334 108.174 108.005 107.827 107.638 107.437

Jun 2003

107.617 109.180 107.513 109.181 109.043 108.901 108.754 108.601 108.442 108.276 108.102 107.917 107.722 107.515

Jul 2003

107.730 109.292 107.553 109.292 109.148 108.999 108.846 108.686 108.520 108.347 108.165 107.973 107.770 107.555

Aug 2003

108.160 109.696 107.872 109.695 109.543 109.387 109.225 109.058 108.884 108.702 108.512 108.311 108.099 107.875

Sep 2003

108.478 110.035 108.163 110.036 109.879 109.718 109.551 109.379 109.200 109.013 108.818 108.612 108.394 108.165

Oct 2003

108.354 109.953 108.101 109.953 109.798 109.638 109.474 109.303 109.127 108.942 108.749 108.545 108.330 108.103

Nov 2003

107.980 109.642 107.722 109.643 109.482 109.316 109.145 108.968 108.784 108.593 108.393 108.182 107.959 107.724

Dec 2003

107.821 109.515 107.530 109.516 109.348 109.177 109.000 108.816 108.626 108.429 108.221 108.004 107.774 107.533

Jan 2004

108.450 110.074 108.039 110.074 109.902 109.725 109.542 109.354 109.158 108.955 108.743 108.521 108.287 108.041

Feb 2004

109.061 110.679 108.609 110.680 110.504 110.323 110.138 109.946 109.747 109.541 109.325 109.099 108.861 108.611

Mar 2004

109.695 111.385 109.276 111.386 111.206 111.022 110.832 110.636 110.434 110.223 110.004 109.774 109.532 109.279

Apr 2004

110.011 111.732 109.563 111.730 111.546 111.357 111.162 110.961 110.753 110.537 110.312 110.076 109.826 109.565

May 2004

110.560 112.355 110.053 112.355 112.156 111.953 111.745 111.531 111.309 111.080 110.841 110.592 110.329 110.056

Jun 2004

110.786 112.718 110.347 112.727 112.521 112.310 112.094 111.872 111.643 111.406 111.160 110.902 110.632 110.350

Jul 2004

110.651 112.574 110.210 112.583 112.379 112.170 111.955 111.734 111.505 111.269 111.022 110.765 110.495 110.213

Aug 2004

110.706 112.605 110.221 112.615 112.409 112.198 111.981 111.758 111.528 111.289 111.040 110.781 110.508 110.224

Sep 2004

111.014 112.823 110.466 112.832 112.629 112.421 112.207 111.987 111.760 111.524 111.278 111.021 110.751 110.469

Oct 2004

111.580 113.452 110.993 113.462 113.247 113.028 112.804 112.573 112.335 112.089 111.834 111.567 111.287 110.996

Nov 2004

111.577 113.514 111.008 113.514 113.296 113.073 112.844 112.610 112.368 112.118 111.859 111.589 111.306 111.011

Dec 2004

111.156 113.094 110.612 113.094 112.879 112.659 112.434 112.202 111.963 111.716 111.458 111.190 110.909 110.615

Jan 2005

111.350 113.305 110.826 113.305 113.092 112.873 112.648 112.417 112.178 111.931 111.674 111.405 111.123 110.829

Feb 2005

111.925 113.966 111.421 113.966 113.745 113.520 113.289 113.052 112.806 112.553 112.289 112.014 111.725 111.425

Mar 2005

112.637 114.853 112.198 114.852 114.620 114.383 114.140 113.891 113.635 113.370 113.096 112.810 112.512 112.201

Apr 2005

113.371 115.630 112.805 115.629 115.378 115.123 114.862 114.596 114.323 114.041 113.750 113.449 113.134 112.809

May 2005

113.290 115.536 112.761 115.536 115.291 115.042 114.787 114.526 114.258 113.981 113.695 113.397 113.087 112.765

Jun 2005

113.246 115.572 112.743 115.572 115.324 115.070 114.811 114.545 114.272 113.990 113.698 113.394 113.076 112.747

Jul 2005

113.684 116.088 113.051 116.087 115.817 115.542 115.262 114.975 114.681 114.378 114.066 113.742 113.404 113.055

Aug 2005

114.295 116.683 113.469 116.683 116.392 116.097 115.797 115.491 115.179 114.859 114.530 114.190 113.837 113.473

Sep 2005

115.577 118.112 114.393 118.112 117.757 117.402 117.044 116.685 116.321 115.953 115.577 115.194 114.799 114.397

Oct 2005

115.748 118.373 114.700 118.373 118.026 117.678 117.327 116.973 116.614 116.250 115.878 115.497 115.105 114.704

Nov 2005

114.890 117.436 114.138 117.436 117.136 116.832 116.524 116.210 115.889 115.561 115.223 114.875 114.514 114.141

Dec 2005

114.418 116.923 113.728 116.922 116.636 116.345 116.049 115.746 115.436 115.118 114.790 114.450 114.097 113.732

Jan 2006

115.208 117.821 114.480 117.814 117.513 117.208 116.897 116.581 116.257 115.924 115.582 115.229 114.862 114.484

Feb 2006

115.412 118.081 114.777 118.076 117.779 117.478 117.172 116.859 116.539 116.210 115.871 115.521 115.157 114.781

Mar 2006

116.023 118.758 115.405 118.751 118.449 118.143 117.832 117.514 117.189 116.856 116.512 116.157 115.789 115.408

Apr 2006

116.945 119.723 116.142 119.723 119.395 119.063 118.726 118.384 118.036 117.679 117.313 116.937 116.547 116.147

May 2006

117.460 120.311 116.560 120.312 119.964 119.613 119.259 118.899 118.533 118.160 117.778 117.385 116.980 116.565

Jun 2006

117.731 120.571 116.777 120.570 120.220 119.866 119.508 119.144 118.774 118.397 118.010 117.613 117.202 116.782

Jul 2006

118.060 120.922 116.967 120.922 120.555 120.185 119.811 119.432 119.046 118.653 118.250 117.837 117.410 116.971

Aug 2006

118.324 121.192 117.222 121.192 120.824 120.453 120.078 119.698 119.311 118.916 118.512 118.096 117.667 117.227

Sep 2006

117.815 120.586 116.947 120.585 120.255 119.920 119.579 119.233 118.879 118.516 118.143 117.759 117.361 116.951

Oct 2006

117.134 119.937 116.480 119.936 119.626 119.311 118.990 118.662 118.326 117.982 117.626 117.259 116.877 116.484

Nov 2006

116.910 119.748 116.299 119.748 119.439 119.125 118.806 118.479 118.144 117.800 117.445 117.078 116.697 116.303

Dec 2006

117.016 119.928 116.383 119.927 119.609 119.286 118.956 118.620 118.276 117.922 117.558 117.181 116.790 116.387

Jan 2007

117.330 120.286 116.720 120.287 119.968 119.643 119.312 118.974 118.627 118.271 117.905 117.525 117.131 116.724

Feb 2007

117.877 120.930 117.319 120.929 120.606 120.277 119.941 119.599 119.248 118.888 118.517 118.133 117.734 117.323

Mar 2007

118.913 122.031 118.245 122.030 121.688 121.341 120.987 120.627 120.259 119.881 119.493 119.092 118.677 118.250

Apr 2007

119.666 122.824 118.832 122.823 122.457 122.087 121.712 121.330 120.941 120.544 120.136 119.716 119.282 118.836

May 2007

120.292 123.574 119.318 123.573 123.177 122.777 122.373 121.964 121.549 121.125 120.692 120.248 119.791 119.323

Jun 2007

120.439 123.813 119.506 123.813 123.413 123.009 122.601 122.187 121.767 121.338 120.899 120.449 119.985 119.511

Jul 2007

120.377 123.782 119.433 123.781 123.381 122.977 122.567 122.152 121.729 121.297 120.854 120.398 119.927 119.438

Aug 2007

120.288 123.555 119.354 123.554 123.170 122.781 122.387 121.985 121.575 121.157 120.727 120.285 119.828 119.358

Sep 2007

120.638 123.895 119.698 123.894 123.511 123.122 122.728 122.326 121.917 121.499 121.070 120.628 120.171 119.703

Oct 2007

120.885 124.160 119.972 124.158 123.775 123.388 122.995 122.595 122.187 121.770 121.341 120.900 120.444 119.976

Nov 2007

121.481 124.898 120.448 124.897 124.485 124.069 123.647 123.220 122.786 122.342 121.889 121.424 120.944 120.453

Dec 2007

121.295 124.814 120.359 124.813 124.401 123.985 123.564 123.137 122.702 122.258 121.804 121.337 120.856 120.364

Jan 2008

121.867 125.434 120.927 125.433 125.017 124.596 124.170 123.737 123.297 122.848 122.388 121.917 121.430 120.932

Feb 2008

122.250 125.799 121.280 125.798 125.380 124.958 124.531 124.098 123.656 123.206 122.746 122.273 121.785 121.286

Mar 2008

123.323 126.890 122.226 126.888 126.456 126.019 125.577 125.129 124.673 124.208 123.733 123.246 122.744 122.231

Apr 2008

124.116 127.659 122.861 127.658 127.211 126.760 126.304 125.842 125.373 124.895 124.407 123.907 123.393 122.867

May 2008

125.171 128.734 123.656 128.733 128.255 127.773 127.288 126.797 126.300 125.794 125.279 124.753 124.212 123.661

Jun 2008

126.307 130.031 124.585 130.030 129.511 128.991 128.467 127.938 127.404 126.862 126.311 125.750 125.175 124.591

Jul 2008

126.918 130.714 125.114 130.712 130.179 129.644 129.104 128.561 128.011 127.454 126.888 126.311 125.721 125.120

Aug 2008

126.594 130.192 124.844 130.191 129.687 129.180 128.669 128.152 127.627 127.095 126.553 125.998 125.429 124.850

Sep 2008

126.551 130.012 124.775 130.010 129.519 129.024 128.524 128.019 127.506 126.984 126.453 125.909 125.351 124.781

Oct 2008

125.500 128.699 123.794 128.698 128.243 127.784 127.319 126.847 126.368 125.879 125.379 124.867 124.339 123.799

Nov 2008

123.044 126.234 121.313 126.233 125.784 125.330 124.869 124.402 123.925 123.438 122.938 122.421 121.882 121.319

Dec 2008

121.557 124.929 119.703 124.927 124.450 123.967 123.478 122.981 122.474 121.956 121.424 120.875 120.304 119.709

Jan 2009

122.095 125.472 120.272 125.471 124.996 124.516 124.029 123.534 123.030 122.514 121.985 121.439 120.871 120.278

Feb 2009

122.598 126.096 120.960 126.095 125.626 125.151 124.670 124.182 123.684 123.175 122.652 122.113 121.551 120.966

Mar 2009

122.803 126.403 121.238 126.401 125.930 125.452 124.969 124.477 123.977 123.465 122.940 122.397 121.833 121.245

Apr 2009

123.053 126.718 121.560 126.716 126.245 125.768 125.285 124.794 124.294 123.783 123.259 122.717 122.154 121.566

May 2009

123.427 127.084 121.950 127.082 126.614 126.140 125.659 125.171 124.674 124.165 123.643 123.104 122.542 121.956

Jun 2009

124.485 128.176 123.010 128.174 127.704 127.228 126.745 126.254 125.754 125.243 124.717 124.174 123.608 123.016

Jul 2009

124.293 127.973 122.756 127.971 127.495 127.014 126.526 126.031 125.525 125.009 124.478 123.929 123.358 122.762

Aug 2009

124.620 128.260 122.999 128.258 127.778 127.293 126.801 126.301 125.791 125.270 124.735 124.182 123.606 123.005

Sep 2009

124.706 128.340 123.064 128.338 127.857 127.370 126.877 126.375 125.864 125.342 124.805 124.250 123.673 123.070

Oct 2009

124.791 128.463 123.221 128.461 127.984 127.501 127.012 126.514 126.007 125.487 124.954 124.402 123.827 123.227

Nov 2009

124.788 128.554 123.272 128.552 128.072 127.585 127.092 126.590 126.079 125.556 125.018 124.462 123.883 123.279

Dec 2009

124.544 128.328 123.008 128.326 127.842 127.353 126.856 126.351 125.836 125.308 124.767 124.207 123.623 123.015

Jan 2010

124.987 128.767 123.455 128.767 128.283 127.794 127.299 126.794 126.280 125.753 125.212 124.653 124.070 123.461

Feb 2010

124.972 128.799 123.431 128.798 128.310 127.815 127.314 126.804 126.284 125.752 125.206 124.641 124.052 123.438

Mar 2010

125.442 129.327 123.979 129.327 128.841 128.348 127.849 127.341 126.823 126.293 125.748 125.185 124.598 123.986

Apr 2010

125.620 129.552 124.189 129.552 129.064 128.570 128.070 127.560 127.041 126.510 125.963 125.399 124.810 124.196

May 2010

125.678 129.653 124.263 129.650 129.160 128.664 128.161 127.649 127.128 126.594 126.045 125.478 124.887 124.270

Jun 2010

125.521 129.526 124.064 129.524 129.026 128.523 128.012 127.493 126.964 126.423 125.867 125.292 124.694 124.070

Jul 2010

125.536 129.554 124.020 129.551 129.048 128.539 128.023 127.497 126.962 126.414 125.850 125.267 124.660 124.026

Aug 2010

125.756 129.732 124.168 129.730 129.224 128.712 128.192 127.664 127.126 126.574 126.008 125.422 124.811 124.174

Sep 2010

125.830 129.808 124.231 129.805 129.296 128.782 128.260 127.729 127.189 126.636 126.069 125.483 124.873 124.237

Oct 2010

125.969 129.969 124.423 129.967 129.461 128.949 128.431 127.903 127.366 126.816 126.251 125.668 125.062 124.430

Nov 2010

125.920 130.024 124.459 130.022 129.514 129.001 128.481 127.951 127.412 126.860 126.294 125.709 125.100 124.466

Dec 2010

126.143 130.247 124.672 130.245 129.737 129.223 128.701 128.172 127.631 127.078 126.511 125.924 125.314 124.678

Jan 2011

126.778 130.868 125.247 130.870 130.357 129.839 129.313 128.778 128.233 127.675 127.102 126.510 125.894 125.253

Feb 2011

127.363 131.513 125.857 131.510 130.995 130.473 129.945 129.407 128.859 128.298 127.722 127.127 126.508 125.864

Mar 2011

128.585 132.796 127.032 132.793 132.268 131.736 131.197 130.649 130.091 129.519 128.932 128.326 127.695 127.039

Apr 2011

129.483 133.650 127.812 133.642 133.105 132.563 132.012 131.453 130.884 130.303 129.708 129.096 128.465 127.819

May 2011

129.999 134.279 128.341 134.274 133.727 133.174 132.613 132.044 131.465 130.873 130.268 129.646 129.004 128.347

Jun 2011

129.846 134.136 128.240 134.130 133.588 133.040 132.485 131.920 131.345 130.758 130.156 129.538 128.900 128.247

Jul 2011

129.983 134.255 128.327 134.252 133.707 133.156 132.597 132.029 131.451 130.860 130.255 129.633 128.991 128.334

Aug 2011

130.351 134.625 128.651 134.622 134.073 133.518 132.954 132.382 131.799 131.204 130.594 129.967 129.321 128.658

Sep 2011

130.635 134.829 128.841 134.826 134.276 133.719 133.154 132.581 131.996 131.400 130.788 130.160 129.512 128.847

Oct 2011

130.373 134.551 128.599 134.549 134.002 133.449 132.888 132.318 131.738 131.144 130.536 129.911 129.266 128.605

Nov 2011

130.196 134.437 128.461 134.435 133.887 133.331 132.768 132.196 131.613 131.018 130.407 129.780 129.132 128.468

Dec 2011

129.844 134.106 128.119 134.104 133.554 132.998 132.434 131.861 131.277 130.680 130.068 129.439 128.791 128.126

Jan 2012

130.438 134.696 128.631 134.706 134.147 133.581 133.008 132.426 131.833 131.227 130.607 129.969 129.312 128.638

Feb 2012

130.953 135.289 129.090 135.287 134.715 134.137 133.551 132.956 132.351 131.733 131.101 130.452 129.782 129.097

Mar 2012

131.905 136.317 129.900 136.314 135.718 135.116 134.507 133.890 133.263 132.624 131.971 131.301 130.612 129.907

Apr 2012

132.284 136.728 130.239 136.726 136.122 135.513 134.897 134.272 133.638 132.992 132.331 131.654 130.958 130.247

May 2012

132.154 136.568 130.149 136.566 135.971 135.370 134.762 134.145 133.518 132.878 132.224 131.553 130.862 130.156

Jun 2012

131.956 136.368 130.067 136.366 135.785 135.198 134.602 133.998 133.383 132.755 132.112 131.452 130.771 130.074

Jul 2012

131.731 136.145 129.865 136.143 135.565 134.981 134.388 133.786 133.173 132.547 131.906 131.247 130.568 129.872

Aug 2012

132.430 136.903 130.446 136.901 136.304 135.700 135.089 134.469 133.838 133.195 132.537 131.861 131.165 130.454

Sep 2012

132.988 137.514 130.939 137.512 136.901 136.285 135.661 135.029 134.386 133.731 133.061 132.375 131.668 130.946

Oct 2012

132.892 137.460 130.935 137.459 136.854 136.243 135.625 134.998 134.360 133.710 133.045 132.363 131.661 130.943

Nov 2012

132.208 136.809 130.455 136.807 136.222 135.630 135.030 134.421 133.800 133.167 132.519 131.852 131.166 130.463

Dec 2012

131.770 136.441 130.143 136.439 135.860 135.275 134.681 134.078 133.463 132.835 132.192 131.531 130.849 130.151

Source: U.S. Bureau of Labor Statistics.