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| - | < | + | ======Introduction====== |
| - | < | + | ===== Structure of the documentation |
| - | <meta http-equiv=Content-Type content=" | + | |
| - | <meta name=ProgId content=Word.Document> | + | The documentation is structured as follows. Sections |
| - | <meta name=Generator content=" | + | |
| - | <meta name=Originator content=" | + | |
| - | <link rel=File-List href=" | + | |
| - | <link rel=Edit-Time-Data | + | |
| - | href=" | + | |
| - | <link rel=OLE-Object-Data | + | |
| - | href=" | + | |
| - | <!--[if !mso]> | + | |
| - | < | + | |
| - | v\:* {behavior: | + | |
| - | o\:* {behavior: | + | |
| - | w\:* {behavior: | + | |
| - | .shape {behavior: | + | |
| - | </ | + | |
| - | <![endif]-->< | + | |
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| - | <link rel=dataStoreItem | + | |
| - | href=" | + | |
| - | target=" | + | |
| - | <link rel=themeData | + | |
| - | href=" | + | |
| - | <link rel=colorSchemeMapping | + | |
| - | href=" | + | |
| - | <!--[if gte mso 9]>< | + | |
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| - | DefSemiHidden=" | + | |
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| - | </ | + | |
| - | </ | + | |
| - | < | + | |
| - | <!-- | + | |
| - | /* Font Definitions */ | + | |
| - | | + | |
| - | {font-family: | + | |
| - | panose-1:5 0 0 0 0 0 0 0 0 0; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family:" | + | |
| - | panose-1:2 4 5 3 5 4 6 3 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family: | + | |
| - | panose-1:2 15 5 2 2 2 4 3 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family: | + | |
| - | panose-1:2 11 6 4 3 5 4 4 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family: | + | |
| - | panose-1:2 4 5 3 5 4 6 3 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | /* Style Definitions */ | + | |
| - | p.MsoNormal, li.MsoNormal, | + | |
| - | {mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-parent: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | h1 | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | page-break-after: | + | |
| - | mso-outline-level: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-themeshade: | + | |
| - | mso-font-kerning: | + | |
| - | mso-fareast-language: | + | |
| - | h2 | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | page-break-after: | + | |
| - | mso-outline-level: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-fareast-language: | + | |
| - | h3 | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | page-break-after: | + | |
| - | mso-outline-level: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoFootnoteText, | + | |
| - | {mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-link:" | + | |
| - | margin: | + | |
| - | margin-bottom: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoCaption, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-fareast-language: | + | |
| - | font-weight: | + | |
| - | span.MsoFootnoteReference | + | |
| - | {mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | vertical-align: | + | |
| - | p.MsoAcetate, | + | |
| - | {mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-link:" | + | |
| - | margin: | + | |
| - | margin-bottom: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraph, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraphCxSpFirst, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-type: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraphCxSpMiddle, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-type: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraphCxSpLast, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-type: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | span.berschrift1Zchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link:" | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-themeshade: | + | |
| - | font-weight: | + | |
| - | span.MTEquationSection | + | |
| - | {mso-style-name: | + | |
| - | mso-style-unhide: | + | |
| - | color: | + | |
| - | display: | + | |
| - | mso-hide: | + | |
| - | mso-ansi-language: | + | |
| - | p.MTDisplayEquation, | + | |
| - | {mso-style-name: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | tab-stops: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-ansi-language: | + | |
| - | mso-fareast-language: | + | |
| - | span.MTDisplayEquationZchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link: | + | |
| - | mso-ansi-language: | + | |
| - | span.berschrift2Zchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link:" | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | font-weight: | + | |
| - | span.berschrift3Zchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link:" | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | font-weight: | + | |
| - | span.FunotentextZchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link: | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | span.SprechblasentextZchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link: | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-bidi-font-family: | + | |
| - | span.SpellE | + | |
| - | {mso-style-name:""; | + | |
| - | mso-spl-e: | + | |
| - | span.GramE | + | |
| - | {mso-style-name:""; | + | |
| - | mso-gram-e: | + | |
| - | .MsoChpDefault | + | |
| - | {mso-style-type: | + | |
| - | mso-default-props: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | .MsoPapDefault | + | |
| - | {mso-style-type: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | /* Page Definitions */ | + | |
| - | | + | |
| - | {mso-footnote-separator: | + | |
| - | mso-footnote-continuation-separator: | + | |
| - | mso-endnote-separator: | + | |
| - | mso-endnote-continuation-separator: | + | |
| - | @page WordSection1 | + | |
| - | {size: | + | |
| - | margin: | + | |
| - | mso-header-margin: | + | |
| - | mso-footer-margin: | + | |
| - | mso-paper-source: | + | |
| - | div.WordSection1 | + | |
| - | {page: | + | |
| - | /* List Definitions */ | + | |
| - | @list l0 | + | |
| - | {mso-list-id: | + | |
| - | mso-list-type: | + | |
| - | mso-list-template-ids: | + | |
| - | @list l0:level1 | + | |
| - | {mso-level-start-at: | + | |
| - | mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | @list l0:level2 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l0:level3 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level4 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level5 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l0:level6 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level7 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level8 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l0:level9 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1 | + | |
| - | {mso-list-id: | + | |
| - | mso-list-type: | + | |
| - | mso-list-template-ids: | + | |
| - | @list l1:level1 | + | |
| - | {mso-level-start-at: | + | |
| - | mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | @list l1:level2 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l1:level3 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1:level4 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1:level5 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l1:level6 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1:level7 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
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| - | text-indent: | + | |
| - | font-family:" | + | |
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| - | {mso-level-number-format: | + | |
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| - | text-indent: | + | |
| - | font-family: | + | |
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| - | {mso-level-number-format: | + | |
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| - | text-indent: | + | |
| - | font-family: | + | |
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| - | {mso-level-number-format: | + | |
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| - | text-indent: | + | |
| - | font-family:" | + | |
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| - | {mso-level-number-format: | + | |
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| - | {mso-level-number-format: | + | |
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| - | @list l2:level8 | + | |
| - | {mso-level-number-format: | + | |
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| - | text-indent: | + | |
| - | font-family:" | + | |
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| - | {mso-level-number-format: | + | |
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| - | {mso-list-id: | + | |
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| - | @list l3:level1 | + | |
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| - | mso-level-text: | + | |
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| - | mso-bidi-font-family:" | + | |
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| - | @list l3:level2 | + | |
| - | {mso-level-number-format: | + | |
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| - | text-indent: | + | |
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| - | ol | + | |
| - | {margin-bottom: | + | |
| - | ul | + | |
| - | {margin-bottom: | + | |
| - | --> | + | |
| - | </ | + | |
| - | <!--[if gte mso 10]> | + | |
| - | < | + | |
| - | /* Style Definitions */ | + | |
| - | | + | |
| - | {mso-style-name:" | + | |
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| - | </ | + | |
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| - | </ | + | |
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| - | <o:idmap v: | + | |
| - | </ | + | |
| - | </ | + | |
| - | <body lang=DE style=' | + | The rest of the document largely follows the workflow of the model: the different steps of building up the national, regional and global data base provide the foundations on which the system rests ([[The_CAPRI_Data_Base|Chapter "The CAPRI Data Base" |
| - | <div class=WordSection1> | + | ===== What is CAPRI ===== |
| + | |||
| + | The Common Agricultural Policy Regional Impact (CAPRI) model is a global partial equilibrium model for the agricultural sector, with a focus on the European Union. It has been designed for ex-ante impact assessment of agricultural, | ||
| - | <h1 style=' | + | **Figure |
| - | style=' | + | |
| - | style=' | + | |
| - | class=MTEquationSection>< | + | |
| - | lang=EN-GB style=' | + | |
| - | SEQ MTEqn \r \h \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | in Agriculture – Generating more economic sophisticated solutions< | + | |
| - | style=' | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | color:# | + | |
| - | mso-fareast-language: | + | |
| - | <h2 style=' | + | {{:fig01.png? |
| - | guide as training material< | + | |
| - | name=" | + | |
| - | style=' | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | color:# | + | |
| - | EN-US; | + | |
| - | <p class=MsoNormal>< | + | The CAPRI modelling system itself consists |
| - | reading material should guide you theoretically through the derivation | + | |
| - | parameter calibration of PMP terms for economically more sophisticated | + | |
| - | programming models. In this <span class=GramE> | + | |
| - | understand how a linear programming works and what the shortcomings are, how | + | |
| - | positive mathematical programming models are calibrated | + | |
| - | models behave if input parameters change.< | + | |
| - | <p class=MsoNormal>< | + | The data bases exploit wherever possible //well-documented, official |
| - | there is a hands on excel (Session_B5_Beginners_Advanced_PMP_example.xlsx) | + | |
| - | GAMS file (Session_B5_Advanced_PMP_example.gms) for the beginners and advanced, | + | |
| - | respectively.< | + | |
| - | title="">< | + | |
| - | footnote'>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
| - | minor-latin; | + | |
| - | mso-bidi-theme-font: | + | |
| - | EN-US; | + | |
| - | With the examples provided | + | |
| - | linear programming model, calibrate | + | |
| - | models | + | |
| - | changes once you are familiar with the price scenarios given here in the guide.< | + | |
| - | <h2 style=' | + | The economic model builds on a //philosophy of model templates// which are structurally identical so that instances for products and regions are generated by populating the template with specific parameter sets. This approach ensures comparability of results across products, activities and regions, allows for low cost system maintenance and enables its integration within a larger modelling network such as SEAMLESS or the DG Clima modelling suite. At the same time, the approach opens up the chance for complementary approaches at different levels, which may shed light on different aspects not covered by CAPRI or help to learn about possible aggregation errors in CAPRI. |
| - | <p class=MsoNormal style=' | + | CAPRI is designed for scenario analysis. It is a comparative static model, which technically means that the market equilibrium simulated for a given point in time does not involve lags or leads of endogenous variables. If several points in time are simulated, these simulatons may be perfomed therefore in any order or in parallel((This does not hold if land use transitions are simulated for environmental indicators but in a “basic” CAPRI run, these may be switched off.)). Comparative static results are best interpreted as the long run outcome of some scenario, after all adjustments to the new equilibrium are completed. By contrast, dynamic or recursive dynamic |
| - | lang=EN-GB style=' | + | |
| - | models | + | |
| - | Farmers must make decisions about the production plan. The decisions are not | + | |
| - | independent from physical | + | |
| - | relied on intuition, experience | + | |
| - | methods like mathematical programming models can enhance | + | |
| - | at least when the production program becomes more complex. Those mathematical | + | |
| - | programming | + | |
| - | farmer. This predictive “power” makes those representative farm models useful | + | |
| - | for policy analysis | + | |
| - | <h2 style=' | + | CAPRI contains two modules, market and supply, which interact (see Figure 1). |
| - | linear programming model < | + | |
| - | <p class=MsoNormal style=' | + | The //supply module// consists of independent aggregate non linear programming |
| - | lang=EN-GB style=' | + | |
| - | method to find the profit maximizing combination | + | Around 55 agricultural inputs produced in about 60 activities are covered in the supply module. The activities include inputs |
| - | is feasible subject | + | |
| - | 1'> | + | Main constraints outside the feed block are arable and grassland – which are treated as imperfect substitutes |
| - | <p class=MsoListParagraphCxSpFirst style=' | + | Market equilibria are calculated by iterations between the supply module and the market module. |
| - | auto;text-align: | + | |
| - | lang=EN-GB style=' | + | The market module for marketable agricultural outputs is a //spatial, non-stochastic global multi-commodity// model for about 65 primary and processed agricultural products. About 80 world regions are modelled, but aggregated to about 40 trade regions that trade bilaterally with each other, with the possibility of simultaneous import and export. It simulates supply, demand, and price changes in global markets considering international trade. |
| - | mso-hansi-font-family: | + | |
| - | EN-GB'>< | + | Agricultural supply is modelled in a simpler way than in the supply module, with behavioural functions for supply and feed demand. These are supplemented with other functions for processing, biofuel use, and human consumption. These functions apply flexible functional forms where calibration algorithms ensure full compliance with micro economic theory including curvature. The parameters are synthetic, i.e. to a large extent taken from the literature and other modelling systems.Consumers and traders are represented by economic agents that follow neo-classical micro-economic theory regarding behaviour, which makes it possible to compute welfare effects. Bi lateral trade flows and attached prices are modelled based on the Armington assumptions (Armington 1969). Policy instruments cover (bi lateral) tariffs, the Tariff Rate Quota (TRQ) mechanism and, for the EU, intervention stocks and subsidized exports. This market module delivers prices used in the supply module and allows for market analysis at global, EU and national scale. |
| - | </span>< | + | |
| - | alternative production activities, their unit of measurement, their resource | + | As the supply models are solved independently at fixed prices, |
| - | requirements | + | |
| - | <p class=MsoListParagraphCxSpMiddle style=' | + | Environmental indicators, primarily for nutrient surpluses and greenhouse gas (GHG) emissions, are calculated in CAPRI and may be directly addressed in some scenarios. Regarding nutrient surpluses, the supply module contains nutrient balance equations for nitrogen, phosphorous and potassium. It considers nutrient uptake by crops following a crop growth function, and supply of nutrients from mineral fertilizer, manure, crop residues, and, for nitrogen, atmospheric deposition and fixation. The balances also contain factors for over-fertilization, |
| - | auto; | + | |
| - | lang=EN-GB style=' | + | CAPRI allows for //modular applications// as e.g. regional supply models for a specific Member State may be run at fixed exogenous prices without any market module. In previous applications farm heterogeneity has been represented by a set of farm types for each NUTS2 region, each with its own supply model. The farm type model layer is currently being replaced with another solution such that it has been switched OFF in recent applications. Equally, the global market model can be run in stand-alone mode as well. |
| - | mso-hansi-font-family: | + | |
| - | EN-GB'>< | + | |
| - | </span>< | + | |
| - | fixed resource constraints< | + | |
| - | <p class=MsoListParagraphCxSpLast style=' | + | //Post-model analysis// includes the calculation of different income indicators as variable costs, revenues, gross margins, etc., both for individual production activities as for regions, according to the methodology of the EAA. A welfare analysis at Member State level, or globally, at country or country block level, covers agricultural profits, tariff revenues, outlays for domestic supports and the money metric measure to capture welfare effects on consumers. Outlays under the first pillar of the CAP are modelled in very high detail. Among the post model analysis options there are some designed to disentangle various contributions to scenario effects as explained in Chapter |
| - | text-align: | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-hansi-font-family: | + | |
| - | EN-GB'>< | + | |
| - | </ | + | |
| - | margins | + | |
| - | <p class=MsoNormal style=' | + | More information about the CAPRI model, including technical documentation, |
| - | lang=EN-GB style=' | + | |
| - | programming | + | |
| - | <p class=MTDisplayEquation style=' | + | ===== CAPRI uses the GAMS software |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
| - | style=' | + | |
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| - | <p class=MTDisplayEquation style=' | + | To solve the large-scale, non-linear optimization problems in the model, CAPRI uses a software called GAMS (General Algebraic Modelling System). GAMS is a programming language designed for solving optimization problems, widely used in economic modelling. Models in GAMS are defined by one or several |
| - | lang=EN-GB>< | + | |
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| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
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| - | <p class=MsoNormal style=' | + | Data used or produced by GAMS is generally stored in a file format called GDX (GAMS Data Exchange). CAPRI database and results are stored in gdx files, which can be loaded into the CAPRI Result Viewer in the Graphical User Interface where you can analyse and export the results. Without GAMS, you can view and analyse scenario results from previous scenario runs, but not run new simulations with CAPRI. |
| - | lang=EN-GB style=' | + | |
| - | <p class=MsoListParagraphCxSpFirst style=' | + | GAMS solves models using third-party solvers that are linked to GAMS. GAMS comes with a large library of such solvers, most of them specializing in particular types of problems or solution algorithms. CAPRI relies on a particular solver called CONOPT. While CAPRI itself |
| - | auto; | + | |
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| - | <p class=MsoListParagraphCxSpMiddle style=' | + | ===== The network |
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| - | activities< | + | |
| - | <p class=MsoListParagraphCxSpMiddle style=' | + | Methodological development, |
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| - | <p class=MsoListParagraphCxSpMiddle style=' | + | The CAPRI modelling network may be defined as a ‘club’: there are currently no fees attached to its use but the entry in the network is controlled by the current club members. The members have agreed on a distribution |
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| - | <p class=MsoListParagraphCxSpMiddle style=' | + | ===== CAPRI development and applications |
| - | auto; | + | |
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| - | resources< | + | |
| - | <p class=MsoListParagraphCxSpMiddle style=' | + | CAPRI – ‘Common Agricultural Policy Regionalised Impact analysis’ is both the acronym for an EU-wide quantitative agricultural sector modelling system and of the first project centred around it((http://www.ilr.uni-bonn.de/ |
| - | auto; | + | |
| - | lang=EN-GB style=' | + | Later, a larger project (EU research FP VI, Nr. 501981: CAPRI-Dynaspat) was conducted under the co-ordination of the team in Bonn to render the system recursive-dynamic, dis-aggregate results in space, include the new Member States and add a labour module and an indicator for energy use. |
| - | mso-hansi-font-family:Calibri;mso-bidi-font-family: | + | |
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| - | <p class=MsoListParagraphCxSpLast style=' | + | A PhD study (Pérez-Dominguez 2005) initiated (non-CO2) GHG accounting and modelling with CAPRI to analyse tradable permits for GHG emissions from agriculture. Subsequently several projects served to improve the representation of trade policies (FP VI, Nr. 502457: “EU MedAgPol”, |
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| - | associated with the resource constraints< | + | |
| - | <p class=MsoNormal style=' | + | In 2006-2008 a first biofuel coverage in CAPRI has been achieved during an interim stay of Wolfgang Britz at JRC-Ispra which has been expanded in later years leading |
| - | lang=EN-GB style=' | + | |
| - | production activity levels that maximize the total gross margin | + | From 2006-2012 CAPRI participated in the LIFE funded EC4MACS((See http://www.ec4macs.eu/home/index.html)), the “European Consortium for Modelling |
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| - | activity levels. The dual variables | + | |
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| - | </o: | + | |
| - | </xml>< | + | |
| - | values give the maximum value a representative farmer is willing to pay to | + | |
| - | enhance | + | |
| - | maximum value of one additional unit of land to increase the most profitable | + | |
| - | production activity.< | + | |
| - | <p class=MsoNormal style=' | + | In line with the shift of the CAP focus towards sustainability, CAPRI contributed to CCAT – EU Cross compliance tool((See https://cordis.europa.eu/project/rcn/84125/factsheet/en )), an FP6 project coordinated by Wageningen University, for an integrated assessment of cross compliance impacts, |
| - | lang=EN-GB style=' | + | |
| - | few assumptions are made. At first, an optimization problem <span class=GramE> | + | |
| - | faced</ | + | |
| - | lang=EN-GB style=' | + | |
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| - | MERGEFORMAT <span style=' | + | |
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| - | It is important to have at least one nonzero constraint </span>< | + | |
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| - | number of production activities </ | + | |
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| - | MERGEFORMAT <span style=' | + | |
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| - | can be find. The model coefficients – gross <span class=GramE> | + | |
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| - | known and constant. This also leads to the fact, that the increase of total | + | |
| - | expected gross margin and the resource requirements per unit are proportional | + | |
| - | to the used production activity level and hence, independent of the activity | + | |
| - | level used. Further it is assumed, that the resources can be used and the | + | |
| - | activities produced in quantities are fractional units. The units of the | + | |
| - | resources or activities are identical. No interaction effects between the | + | |
| - | production activities are allowed, which means, that the total product is the | + | |
| - | sum of their individual products. < | + | |
| - | <h3 style=' | + | GHG abatement options have also been investigated in two studies by the JRC (IES, Ispra((See https:// |
| - | small example< | + | |
| - | <p class=MsoNormal style=' | + | The current two level version of land supply derives from a study on agricultural and trade policy reform impacts on land-use across the EU, with a particular focus on land abandonment (Renwick et al. 2012). |
| - | style=' | + | |
| - | programming model to become familiar with mathematical programming models.< | + | |
| - | <p class=MsoCaption style=' | + | Until summer 2013, again a EU framework project co-ordinated by the team in Bonn called “CAPRI-RD” ensured various updates, and added a layer of regional CGEs, while working on the integration of CAP pillar 2 measures into the system. While the latter have become an essential |
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| - | file sheet “Simple LP”, GAMS file model “LP”)< | + | |
| - | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 | + | Sustainability in its various facets has been the topic driving model developments and extensions that are likely to be pursued in the next years. |
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| - | mso-border-alt: | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | EN-GB'> | + | |
| - | </ | + | |
| - | <td width=75 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
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| - | </ | + | |
| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | mso-border-alt: | + | |
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| - | lang=EN-GB style=' | + | |
| - | </ | + | |
| - | <td width=134 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | lang=EN-GB style=' | + | |
| - | </ | + | |
| - | </ | + | |
| - | < | + | |
| - | <td width=164 nowrap valign=top style=' | + | |
| - | border-top: | + | |
| - | padding:0cm 5.4pt 0cm 5.4pt; | + | |
| - | <p class=MsoNormal style=' | + | |
| - | margin-left: | + | |
| - | class=SpellE>< | + | |
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| - | </ | + | |
| - | <td width=76 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | mso-border-alt: | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | EN-GB'> | + | |
| - | </ | + | |
| - | <td width=67 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | EN-GB'> | + | |
| - | </ | + | |
| - | <td width=59 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | EN-GB'> | + | |
| - | </ | + | |
| - | <td width=75 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | EN-GB'> | + | |
| - | </ | + | |
| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | margin-left: | + | |
| - | lang=EN-GB style=' | + | |
| - | </ | + | |
| - | <td width=134 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | lang=EN-GB style=' | + | |
| - | </ | + | |
| - | </ | + | |
| - | </ | + | |
| - | <p class=MsoCaption style=' | + | * Beginning with a small explorative study in 2011 several studies led to the development and improvement of a “CAPRI water version” used in various projects((See, |
| - | style=' | + | |
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
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| - | yes'> | + | |
| - | < | + | |
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| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | class=GramE> | + | |
| - | has to set the level of four production activities that produce four | + | |
| - | commodities. The objective function is to maximize | + | |
| - | margin. But at the same time the resource constraints must hold. In particular, | + | |
| - | at maximum 200 ha of land are available | + | |
| - | hours of labour. Each production activity has the same requirement to the land. | + | |
| - | This means, one ha of land produces one unit of the commodity. The production | + | |
| - | activities need different amounts of labour. For example, production activity 4 | + | |
| - | needs 87 hours of labour to produce one unit of commodity four. This activity | + | |
| - | has also the greatest expected gross margin of 516 per unit. The combination of | + | |
| - | the production activities that maximizes the total gross margin | + | |
| - | not violate the constraints has to be find.<o:p></o:p></span>< | + | |
| - | <p class=MsoNormal style=' | + | * Several efforts have been undetaken by JRC-Ispra, partly |
| - | lang=EN-GB style=' | + | |
| - | solver | + | |
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| - | class=GramE> | + | |
| - | -5.0pt'>< | + | |
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| - | labour with <span style=' | + | |
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| - | </ | + | |
| - | </ | + | |
| - | class=GramE> | + | |
| - | relative; | + | |
| - | | + | |
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| - | </ | + | |
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| - | resources of land and labour are totally exhausted. The farmer | + | |
| - | only use production activity two and four to maximize his profits. The shadow | + | |
| - | price of land is 391.5 and labour is 1.43. For instance, the representative | + | |
| - | farmer would pay 391.5 for one additional unit of land to enhance his | + | |
| - | production level for one of his preferred production activities.< | + | |
| - | <h3 style=' | + | * Diet shifts |
| - | of the example< | + | |
| + | Apart from the wide area of sustainability aspects of trade modelling have also been repeatedly at the heart of targeted model improvements, | ||
| - | <p class=MsoNormal style=' | + | Two areas of technical developments are also likely to be continued in the future. The first one is the improvement |
| - | lang=EN-GB style=' | + | |
| - | implementation | + | |
| - | farm production plan. The representative farmer has the knowledge about the | + | |
| - | expected gross margins and resource requirements | + | |
| - | and with that, the linear programming model is a useful tool to calculate | + | |
| - | profit maximizing production plan.<a style=' | + | |
| - | name=" | + | |
| - | style=' | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | 115%; | + | |
| - | mso-fareast-font-family: | + | |
| - | minor-latin; | + | |
| - | mso-ansi-language: | + | |
| - | <p class=MsoNormal style=' | + | The historical review has so far focussed on those studies and projects, that left clear marks in the current system as a heritage. In addition, the system was applied to a wide range of numerous different scenarios that often left smaller “traces” in the system but illustrate its capabilities and contributed to improvement |
| - | lang=EN-GB style=' | + | |
| - | activities are part of the production problem. But in reality we observe | + | In 2004 CAPRI was used to generate a baseline in close co-operation |
| - | farmers also use production activities that seem to be less profitable. The | + | |
| - | linear programming model obviously does not consider real farmer’s behaviour | + | |
| - | and produces overspecialisation. There can be several reasons why farmers use | + | |
| - | less profitable production activities. One the one hand there are governmental | + | |
| - | rules or production | + | |
| - | up a less profitable production plan. This could be handled | + | |
| - | constraints. Further reasons for this behaviour can be the risk aversion | + | |
| - | farmer or some costs that the farmer faces for some production activities that | + | |
| - | cannot be observed and with that not be implemented with additional | + | |
| - | constraints. Additionally, implementing more constraints | + | |
| - | programming model will increase the problem | + | |
| - | <p class=MsoNormal style=' | + | Several analyses have investigated potential impact |
| - | lang=EN-GB style=' | + | |
| - | costs for the farmer should be the point we want to investigate | + | As will be clear from this review |
| - | following. The linear programming model is extended and the solution of the | + | |
| - | optimization programme should be more realistic when compared to real world | + | |
| - | behaviour.< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | mathematical programming model < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | overspecialisation and to reflect more realistic behaviour of farmers, positive | + | |
| - | mathematical programming is a methodology that calibrates programming models to | + | |
| - | observed quantities to specify appropriate non-linear objective functions | + | |
| - | (Heckelei, 2002).<a style=' | + | |
| - | title="">< | + | |
| - | footnote'>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
| - | minor-latin; | + | |
| - | mso-bidi-theme-font: | + | |
| - | EN-US; | + | |
| - | These objective functions are modifications of the traditional objective | + | |
| - | function used in linear programming | + | |
| - | interpreted to capture the unobserved behaviour of the farmer and hence, should | + | |
| - | lead to more realistic optimization solutions.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | programming approach can be separated into three steps (Howitt, 1995). At | + | |
| - | first, the optimization model is forced to reproduce observed activity levels. | + | |
| - | Second, the dual values of the calibration constraints are used for the | + | |
| - | modification of the objective function. Third, the new model is employed for | + | |
| - | simulations.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | model builds on the basis of the linear programming model and is extended only | + | |
| - | by additional constraints. These are the calibration constraints:< | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
| - | lang=EN-GB>< | + | |
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| - | production activity levels< | + | |
| - | + | ||
| - | <p class=MsoListParagraphCxSpMiddle style=' | + | |
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| - | associated with the calibration constraints< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | programming model. In the first step, the optimal solution of this positive | + | |
| - | mathematical programme <span class=GramE> | + | |
| - | the observed production activity levels (<span style=' | + | |
| - | top: | + | |
| - | | + | |
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| - | lang=EN-GB style=' | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | distinguished into preferable and marginal activities. Preferable production | + | |
| - | activities (<span style=' | + | |
| - | | + | |
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| - | </ | + | |
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| - | </ | + | |
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| - | marginal activities < | + | |
| - | (<span style=' | + | |
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| - | </ | + | |
| - | </ | + | |
| - | of the calibration constraints are zero for the marginal activities (<span | + | |
| - | style=' | + | |
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| - | </ | + | |
| - | </ | + | |
| - | cost for preferable activities (<span style=' | + | |
| - | mso-text-raise: | + | |
| - | | + | |
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| - | </ | + | |
| - | </ | + | |
| - | the objective function entries and the coefficients of the marginal activities | + | |
| - | (& | + | |
| - | | + | |
| - | < | + | |
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| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | resources only depend on the marginal activities, interaction between the | + | |
| - | production activities are not covered. With the dual values of the calibration | + | |
| - | constraints, | + | |
| - | model is captured.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | mathematical programming approach the dual values of the preferable activities | + | |
| - | (<span style=' | + | |
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| - | </ | + | |
| - | </ | + | |
| - | function. The extension of the former objective function of the linear | + | |
| - | programming model implies a variable cost function which leads to the omission | + | |
| - | of the calibration constraints of the mathematical programming model in the | + | |
| - | first step.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | parameters of a variable cost function such that the economic rule marginal | + | |
| - | revenue equals marginal cost holds at observed activity levels. Most often, a | + | |
| - | quadratic cost function is used.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | function can be specified like:< | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
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| - | + | ||
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| - | auto; | + | |
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| - | </ | + | |
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| - | the linear cost term< | + | |
| - | + | ||
| - | <p class=MsoListParagraphCxSpLast style=' | + | |
| - | text-align: | + | |
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| - | the quadratic cost term< | + | |
| - | + | ||
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| - | margin and the price of the production activity: <span style=' | + | |
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| - | consider the opportunity cost of the fixed resources. But the resource | + | |
| - | constraints of the complete model count for this.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | two contains the quadratic cost function in the objective function:< | + | |
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| - | solution of the linear programming model.< | + | |
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| - | function that satisfy the conditions | + | |
| - | when solving the positive mathematical programming model are infinite. But the | + | |
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| - | changing economic conditions (see Heckelei (2002) for technical proof).< | + | |
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| - | the parameters of the new objective function< | + | |
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| - | parameters of the new objective function.< | + | |
| - | href="# | + | |
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| - | Some of them are presented | + | |
| - | only a few. In the CAPRI training course we will elaborate additional | + | |
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| - | <p class=MsoNormal style=' | + | |
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| - | very simply ((e.g. Howitt and Mean, 1983; <span class=SpellE> | + | |
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| - | the marginal activities are zero. The objective function of that specification | + | |
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| - | the marginal activities are not zero as before and the new objective function | + | |
| - | would be:< | + | |
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| - | the positive mathematical programming approach < | + | |
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| - | new objective function in the positive mathematical programming model is now | + | |
| - | applied and the results are presented regarding the parameters | + | |
| - | functions.< | + | |
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| - | a positive mathematical programming model. It is quite the same as in the | + | |
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| - | it is convenient to split the gross margin into price and cost per unit of a | + | |
| - | level of production activity. Second – and this is important for the positive | + | |
| - | mathematical programming approach – the addition of 4 calibration constraints. | + | |
| - | The model is forced to solve this optimization problem to have the observed | + | |
| - | production activity levels | + | |
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| - | mathematical< | + | |
| - | “PMP reveal dual values”, GAMS file model “Howitt_1”)</ | + | |
| - | + | ||
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| - | only the resource of land is totally exhausted. One should remember that in the | + | |
| - | linear programming model solution both resources are totally exhausted. In this | + | |
| - | case, the marginal activity is x1 and the preferred activities are x2, x3 and | + | |
| - | x4. Therefore, we only have dual values for x2, x3 and x4 and with that; we | + | |
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| - | programming models are intended to do. < | + | |
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| - | behaviour of the two examples regarding prices changes< | + | |
| - | + | ||
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| - | programming model as well as the two positive mathematical programming models | + | |
| - | simulation behaviour regarding price changes. Therefore, we change the prices | + | |
| - | and solve the optimization problems of all three models and compare how | + | |
| - | different the models react.< | + | |
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| - | of the commodities of the production activities. Only p1 and p3 are increasing, | + | |
| - | p2 and p4 are remaining constant. Price p1 increases with 40 units and price p3 | + | |
| - | with 60 units with each scenario step.< | + | |
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| - | solved again with the different sets of prices. For the linear programming | + | |
| - | model, the most profitable levels of production activities for each price | + | |
| - | scenario depict </ | + | |
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| - | the first two price scenarios no adaption of the production programme of the | + | |
| - | representative farmer is profitable. For the other two price scenarios the | + | |
| - | optimal production were changed to x3=123.3 and x4= 76.7 for scenario 3 and | + | |
| - | x3=200 for scenario 4.< | + | |
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| - | production activities of the linear programming model activities (Excel file | + | |
| - | sheet “Simple LP”, GAMS file model “LP”)< | + | |
| - | + | ||
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| - | of production activities of the model with the objective <span class=GramE> | + | |
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| - | the production activities x1, x2, and x4 are declining whereas the level of | + | |
| - | production x4 is increasing. Although the price of commodity of production | + | |
| - | activity x1 is increasing, the optimal level of it is decreasing. This is due | + | |
| - | to the fact that the gross margin of x3 is increasing even higher than for x1 in | + | |
| - | every new price scenario.<a style=' | + | |
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| - | of production activities of the model with the objective <span class=GramE> | + | |
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| - | the level of the production activity x3 is increasing. This is also due to the | + | |
| - | fact that the gross margin of x3 is increasing even higher than for x1 and the | + | |
| - | other production activities with every new price scenario.< | + | |
| - | + | ||
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| - | of simulation< | + | |
| - | + | ||
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| - | style=' | + | |
| - | differences between the linear | + | |
| - | approaches. The reaction of the linear programming model to price changes shows | + | |
| - | erratic adaptions of the production programme induced by price changes. It | + | |
| - | takes a while until the production programme changes when the model is optimized. | + | |
| - | These changes are also very strong. This means that between the second and | + | |
| - | third price scenario the production programme differs completely and the fourth | + | |
| - | price scenario induce a production plan with only one production activity. This | + | |
| - | behaviour seems very unlikely in reality.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
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| - | GOTOBUTTON ZEqnNum923545< | + | |
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| - | ZEqnNum923545 \* Charformat \! \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
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| - | programming approach shows a smoother reaction | + | |
| - | linear programming model. But it can be seen that the adaption of the | + | |
| - | production programme is still relatively erratic. But the reaction to price | + | |
| - | changes seems to be much more likely than in the linear programming model.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | GOTOBUTTON ZEqnNum279523< | + | |
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| - | field-end'></ | + | |
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| - | sophisticated reaction to price changes compared to the other simulated models. | + | |
| - | The adaption of the production plan induced by price changes is very smooth and | + | |
| - | is much more realistic. There is no overspecialisation | + | |
| - | the other two models.< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | linear farm production model and the extension based on the positive | + | |
| - | mathematical programming approach to be able to produce more realistic production | + | |
| - | plans when it comes to profit maximization. The positive mathematical | + | |
| - | programming approach calibrates a programming model to observed production | + | |
| - | behaviour. This is achieved with calibration constraints | + | |
| - | the calibration constraints are used to specify a new objective function that | + | |
| - | reflects observed farm behaviour that cannot be captured | + | |
| - | constraints. These new objective functions capture | + | |
| - | class=SpellE> | + | |
| - | technology, risk behaviour or other non-linear constraints.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | specifications of cost functions. There a many ways to specify these functions | + | |
| - | and each of them imply different behaviour to changing economic circumstances. | + | |
| - | Additionally to the specifications shown in this paper there are others as | + | |
| - | well. The average-cost-approach (Heckelei, 2002) or the use of exogenous supply | + | |
| - | elasticities (Heckelei, 2002; empirically applied by Helming et al., 2001) are | + | |
| - | some of them, which will elaborated in the CAPRI training course in Seville. | + | |
| - | You can also have a closer look at them in the Excel file sheet “PMP2” and | + | |
| - | “PMP4” as well as in the GAMS file models “Howitt_12” and “Elasticities1”, | + | |
| - | respectively.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | objective functions are not unproblematic. As these procedures capture the | + | |
| - | observed behaviour, a change in economic incentives | + | |
| - | other behaviour is not observed and must come from other sources. Other | + | |
| - | shortcomings of these approaches of positive mathematical programming models can | + | |
| - | be found in the literature (see Heckelei (2002) | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | class=SpellE>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mathematical programming model for regional analysis of agricultural policies. | + | |
| - | In: <span class=SpellE> | + | |
| - | Agricultural Economics and Policies, EAAE, Proceedings of the 40th Seminar, | + | |
| - | 26.-28. <span class=SpellE> | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | (1986): Mathematical Programming for Economic Analysis in Agriculture, | + | |
| - | Macmillan Publishing Company.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | estimation of programming models for agricultural supply analysis. <span | + | |
| - | class=SpellE> | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | class=SpellE> | + | |
| - | of Environmental Policy Scenarios in Flemish Agriculture. In: Heckelei, T., | + | |
| - | Witzke, H.P. and <span class=SpellE> | + | |
| - | Sector Modelling and Policy Information Systems. Proceedings of the 65 <span | + | |
| - | class=SpellE>< | + | |
| - | at Bonn University, <span class=SpellE> | + | |
| - | Kiel, pp. 237-245. < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | Mathematical Programming< | + | |
| - | Journal of Agricultural Economics</ | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | Approach | + | |
| - | Agricultural Economics, University of California, Davis. < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | Parametric Programming | + | |
| - | class=GramE> | + | |
| - | of California, Davis. < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | (2001): Analyse der Produktions- und Einkommenseffekte von | + | |
| - | Agrarumwelt-programmen unter Verwendung einer weiterentwickelten Form der | + | |
| - | Positiv Quadratischen Programmierung. <span lang=EN-GB style=' | + | |
| - | EN-GB'> | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | class=SpellE>< | + | |
| - | lang=EN-GB style=' | + | |
| - | Production Models using Positive Mathematical Programming. An | + | |
| - | Agro-environmental Policy Analysis in Southwest Germany. Shaker Verlag, Aachen. | + | |
| - | < | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | <div style=' | + | |
| - | + | ||
| - | <hr align=left size=1 width=" | + | |
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| - | Thünen Institute of Farm Economics< | + | |
| - | + | ||
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| - | GAMS file are already completely working. But you must be familiar how to user | + | |
| - | the solver in excel and how to run a GAMS file. Be careful how to set all the | + | |
| - | constraints to get the desired behaviour | + | |
| - | + | ||
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| - | “solver” add-in in the options.< | + | |
| - | + | ||
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| - | 115%; | + | |
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| - | mso-ansi-language: | + | |
| - | lang=EN-GB style=' | + | |
| - | model is an optimization model, in which an objective function is maximized or | + | |
| - | minimized subject | + | |
| - | problem which is also called | + | |
| - | maximized while land and labour use are constrained. This problem can be | + | |
| - | transformed into a minimization problem (dual model), in which land and labour | + | |
| - | use has to be minimized while the total gross margins of each activity are | + | |
| - | constrained to have a certain minimum. The maximum value of the objective | + | |
| - | function | + | |
| - | function of the dual model. See Hazell & Norton (1986) | + | |
| - | presentation.< | + | |
| - | + | ||
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| - | (1999) or <span class=SpellE> | + | |
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| - | used for optimization and an optimal solution is found, you have to choose | + | |
| - | “sensitivity analysis report” to extract the dual values | + | |
| - | constraints. In the GAMS file you can see that after a model is solved, the | + | |
| - | dual values | + | |
| - | class=SpellE> | + | |
| - | + | ||
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| - | even higher compared | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | </ | + | |
start.txt · Last modified: 2022/11/07 10:23 by 127.0.0.1