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| start [2019/10/11 11:27] – alexanderg | start [2019/12/05 12:07] – justinap | ||
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| - | <html xmlns:v=" | + | ===== Structure of the documentation ===== |
| - | xmlns:o=" | + | |
| - | xmlns:w=" | + | |
| - | xmlns:dt=" | + | |
| - | xmlns:m=" | + | |
| - | xmlns=" | + | |
| - | < | + | |
| - | <meta http-equiv=Content-Type content=" | + | The documentation is structured as follows. Sections 1.2-1.3 |
| - | <meta name=ProgId content=Word.Document> | + | |
| - | <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: | + | |
| - | </ | + | |
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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=" | + | |
| - | LatentStyleCount=" | + | |
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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 */ | + | |
| - | | + | |
| - | {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: | + | |
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| - | <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 (Chapter 3). Subsequently the procedure needed to establish a baseline (Chapter 4) is discussed. Chapter 5 deals with the scenario impact analysis, giving descriptions for the regional supply models as well as for the global market model and their interactions in scenario runs. Chapter 6 covers some elements of post model analysis, whereas Chapter 7 covers options for spatial downscaling of the NUTS2 results. At the very end (Chapter 8), some developer tools for stability analysis are described. |
| - | <div class=WordSection1> | ||
| - | <h1 style=' | + | ===== 1.2 What is CAPRI ===== |
| - | style=' | + | |
| - | style=' | + | 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, |
| - | class=MTEquationSection>< | + | |
| - | lang=EN-GB style=' | + | |
| - | SEQ MTEqn \r \h \* MERGEFORMAT <span style=' | + | |
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| - | in Agriculture – Generating more economic sophisticated solutions< | + | |
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| - | <h2 style=' | + | ==== Figure 1. General structure of the CAPRI model ==== |
| - | guide as training material< | + | |
| - | name=" | + | |
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| - | EN-US; | + | |
| - | <p class=MsoNormal>< | + | {{ capri_model_fig01.png | Figure 1. General structure |
| - | reading material should guide you theoretically through the derivation | + | Source: Own illustration |
| - | 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 and how these different | + | |
| - | models behave if input parameters change.< | + | |
| - | <p class=MsoNormal>< | + | The CAPRI modelling system itself consists of specific data bases, a methodology, its software implementation and the researchers involved |
| - | there is a hands on excel (Session_B5_Beginners_Advanced_PMP_example.xlsx) and | + | |
| - | GAMS file (Session_B5_Advanced_PMP_example.gms) for the beginners and advanced, | + | |
| - | respectively.< | + | |
| - | title="">< | + | |
| - | footnote'>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
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| - | EN-US; | + | |
| - | With the examples provided | + | |
| - | linear programming model, calibrate the positive mathematical programming | + | |
| - | models | + | |
| - | changes once you are familiar with the price scenarios given here in the guide.< | + | |
| - | <h2 style=' | + | The data bases exploit wherever possible //well-documented, official and harmonised data sources,// especially data from EUROSTAT, FAOSTAT, OECD and extractions from the Farm Accounting Data Network (FADN)((FADN data are used in the context of so called study contracts with DG AGRI, which define explicitly the scope for which the data can be used, who has access to the data and ensure the data are destroyed after the lifetime of the contract.)) . Specific modules ensure that the data used in CAPRI are mutually compatible and complete in time and space. They cover about 65 agricultural primary and processed products for the EU (see the Annex), from farm type to global scale including input and output coefficients. |
| - | <p class=MsoNormal style=' | + | The economic model builds on a // |
| - | lang=EN-GB style=' | + | |
| - | models is strongly related to the decision making situation | + | |
| - | Farmers must make decisions about the production plan. The decisions are not | + | |
| - | independent from physical or financial constraints. Traditionally, farmers | + | |
| - | relied on intuition, experience | + | |
| - | methods like mathematical programming models can enhance | + | |
| - | at least when the production program becomes more complex. Those mathematical | + | |
| - | programming models predict quite accurately | + | |
| - | farmer. This predictive “power” makes those representative farm models useful | + | |
| - | for policy analysis (Hazell & Norton, 1986).< | + | |
| - | <h2 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 models also trace the adjustment path over time, while considering lagged relationships that are ususally critical in adjustment processes. CAPRI simulations start from a so-called baseline, which is a special applicaiton of the model as discussed in a separate chapter of this documention. The CAPRI baseline integrates projections from external sources, typically the Agricultural Outlook published annually by the European Commission's Directorate-General for Agriculture and Rural Development (DG-AGRI) (European Commission 2017). The parameters describing the reactions in the sector are calibrated to the baseline scenario, making the model behave in accordance with the data and projections. The baseline mirrors the projected agricultural situation up to some point in time and usually assumes status quo policy assumptions (currently: CAP 2014-2020). In a simulated scenario, all conditions in the baseline are maintained – except for the changes to be analysed. |
| - | linear programming model < | + | |
| - | <p class=MsoNormal style=' | + | CAPRI contains two modules, market and supply, |
| - | lang=EN-GB style=' | + | |
| - | method to find the profit maximizing combination of production activities | + | |
| - | is feasible subject to a set of farm constraints. <span style=' | + | |
| - | 1'> | + | |
| - | <p class=MsoListParagraphCxSpFirst style=' | + | The //supply module// consists of independent aggregate non linear programming models representing activities of all farmers at regional or farm type level captured by the Economic Accounts for Agriculture (EAA). The models optimize regional agricultural income, given the prices for inputs and outputs, subsidy levels and other policy measures. These models are a kind of hybrid approach, as they combine a Leontief-technology for variable costs covering a low and high yield variant((The two technological alternatives (for most activities), |
| - | auto; | + | |
| - | lang=EN-GB style=' | + | Around 55 agricultural inputs produced in about 60 activities are covered in the supply module. The activities include inputs to crop and livestock production from other sectors and intermediate inputs produced by the farms such as feed and young animals. The models capture in high detail the premiums paid under CAP, include NPK balances and a module with feeding activities covering nutrient requirements of animals. |
| - | mso-hansi-font-family: | + | |
| - | EN-GB'>< | + | Main constraints outside the feed block are arable and grassland – which are treated as imperfect substitutes |
| - | </ | + | |
| - | alternative production activities, their unit of measurement, | + | |
| - | requirements | + | |
| - | <p class=MsoListParagraphCxSpMiddle 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. |
| - | </ | + | |
| - | fixed resource constraints< | + | As the supply models are solved independently at fixed prices, |
| - | <p class=MsoListParagraphCxSpLast 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, |
| - | text-align: | + | |
| - | 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, |
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| - | EN-GB'>< | + | |
| - | </span>< | + | |
| - | margins | + | |
| - | <p class=MsoNormal 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 |
| - | lang=EN-GB style=' | + | |
| - | programming model for a farm is presented (Hazell & Norton, 1986). < | + | |
| - | <p class=MTDisplayEquation style=' | + | More information about the CAPRI model, |
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| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
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| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
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| - | associated with the resource constraints< | + | |
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| - | production activity levels that maximize the total gross margin (<span | + | |
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| - | activity levels. The dual variables of the resource constraints (<span | + | |
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| - | values give the maximum value a representative farmer is willing to pay to | + | |
| - | enhance the resource constraints. For instance, the shadow price of land is the | + | |
| - | maximum value of one additional unit of land to increase the most profitable | + | |
| - | production activity.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | 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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| - | lang=EN-GB style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | It is important to have at least one nonzero constraint </ | + | |
| - | lang=EN-GB style=' | + | |
| - | style=' | + | |
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| - | MERGEFORMAT <span style=' | + | |
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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=' | + | |
| - | small example< | + | |
| - | + | ||
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| - | programming model to become familiar with mathematical programming models.< | + | |
| - | + | ||
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| - | file sheet “Simple LP”, GAMS file model “LP”)< | + | |
| - | + | ||
| - | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 | + | |
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| - | <td width=278 nowrap colspan=4 valign=top style=' | + | |
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| - | solid windowtext .5pt; | + | |
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| - | line-height: | + | |
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| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | solid windowtext .5pt; | + | |
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| - | solid windowtext .5pt; | + | |
| - | </ | + | |
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| - | <td width=59 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=76 nowrap valign=top style=' | + | |
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| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <td width=67 nowrap valign=top style=' | + | |
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| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | border-left: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=67 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=59 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=75 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | mso-border-alt: | + | |
| - | <td width=134 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <p class=MsoNormal style=' | + | |
| - | margin-left: | + | |
| - | style=' | + | |
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| - | </ | + | |
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| - | <td width=76 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
| - | <td width=67 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
| - | <td width=59 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <td width=75 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <td width=134 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | <td width=164 nowrap valign=top style=' | + | |
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| - | padding:0cm 5.4pt 0cm 5.4pt; | + | |
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| - | <td width=76 nowrap valign=top style=' | + | |
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| - | mso-border-top-alt: | + | |
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| - | <td width=67 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | margin-bottom: | + | |
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| - | <td width=59 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
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| - | <p class=MsoNormal align=center style=' | + | |
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| - | <td width=75 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | <td width=32 nowrap valign=top style=' | + | |
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| - | <td width=76 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | line-height: | + | |
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| - | </ | + | |
| - | <td width=67 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | margin-bottom: | + | |
| - | line-height: | + | |
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| - | </ | + | |
| - | <td width=59 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | <td width=75 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | <td width=32 nowrap valign=top style=' | + | |
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| - | class=GramE> | + | |
| - | has to set the level of four production activities that produce four | + | |
| - | commodities. The objective function is to maximize the expected total gross | + | |
| - | margin. But at the same time the resource constraints must hold. In particular, | + | |
| - | at maximum 200 ha of land are available for each production activity and 10,000 | + | |
| - | 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 and that does | + | |
| - | not violate the constraints has to be find.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | solver in Excel. The expected total gross margin <span style=' | + | |
| - | top: | + | |
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| - | </ | + | |
| - | solver of Excel gives the solution of <span style=' | + | |
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| - | resources of land and labour are totally exhausted. The farmer is advised to | + | |
| - | 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=' | + | |
| - | of the example< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | implementation of the linear programming model to set up a profit maximizing | + | |
| - | farm production plan. The representative farmer has the knowledge | + | |
| - | expected gross margins and resource requirements of each production activity | + | |
| - | and with that, the linear programming | + | |
| - | profit maximizing production plan.<a style=' | + | |
| - | name=" | + | |
| - | style=' | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | 115%; | + | |
| - | mso-fareast-font-family: | + | |
| - | minor-latin; | + | |
| - | mso-ansi-language: | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | activities are part of the production problem. But in reality we observe that | + | |
| - | 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 activity rotation requirements that force the farmer to set | + | |
| - | up a less profitable production plan. This could be handled by additional | + | |
| - | constraints. Further reasons for this behaviour can be the risk aversion of the | + | |
| - | 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, | + | |
| - | programming model will increase the problem of overspecialisation.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | costs for the farmer should be the point we want to investigate in the | + | |
| - | 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 models and have terms that can be | + | |
| - | 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< | + | |
| - | + | ||
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| - | style=' | + | |
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| - | 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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| - | </ | + | |
| - | marginal activities < | + | |
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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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| - | the linear cost term< | + | |
| - | + | ||
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| - | the quadratic cost term< | + | |
| - | + | ||
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| - | of the production activity< | + | |
| - | + | ||
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| - | <span class=GramE> | + | |
| - | margin and the price of the production activity: <span style=' | + | |
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| - | <p class=MsoNormal 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=' | + | |
| - | lang=EN-GB style=' | + | |
| - | two contains the quadratic cost function in the objective function:< | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
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| - | The dual values of </ | + | |
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| - | solution of the linear programming model.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | function that satisfy the conditions to calibrate to observed activity levels | + | |
| - | when solving the positive mathematical programming model are infinite. But the | + | |
| - | different combinations of parameters lead to different response behaviour to | + | |
| - | changing economic conditions (see Heckelei (2002) for technical | + | |
| - | + | ||
| - | <h3 style=' | + | |
| - | the parameters of the new objective function< | + | |
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| - | parameters of the new objective function.< | + | |
| - | href="# | + | |
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| - | 115%; | + | |
| - | mso-fareast-font-family: | + | |
| - | minor-latin; | + | |
| - | mso-ansi-language: | + | |
| - | Some of them are presented in the following (Heckelei, 2002). Here we present | + | |
| - | only a few. In the CAPRI training course we will elaborate additional | + | |
| - | specification rules.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | very simply ((e.g. Howitt | + | |
| - | Paris, 1995)). Just setting <span style=' | + | |
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| - | the marginal activities are zero. The objective function of that specification | + | |
| - | rule would be:< | + | |
| - | + | ||
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| - | function with another rule. He set <span style=' | + | |
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| - | the marginal activities are not zero as before and the new objective function | + | |
| - | would be:< | + | |
| - | + | ||
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| - | lang=EN-GB>< | + | |
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| - | the positive mathematical programming approach < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | new objective function in the positive mathematical programming model is now | + | |
| - | applied and the results are presented regarding the parameters of the cost | + | |
| - | functions.< | + | |
| - | + | ||
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| - | a positive mathematical programming model. It is quite the same as in the | + | |
| - | linear programming model of </ | + | |
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| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | 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 (x1=55; x2=30; x3=85 and x4=30) recalibrated. <span | + | |
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| - | + | ||
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| - | mathematical< | + | |
| - | “PMP reveal dual values”, GAMS file model “Howitt_1”)</ | + | |
| - | + | ||
| - | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 | + | |
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| - | <td width=59 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | border-left: | + | |
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| - | border-left: | + | |
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| - | <td width=76 nowrap valign=top style=' | + | |
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| - | <td width=67 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=59 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=75 nowrap valign=top style=' | + | |
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| - | given the constraints. The solution of this optimization problem reveals that | + | |
| - | 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 | + | |
| - | have only three out of four diagonal elements larger than zero to specify our | + | |
| - | new objective function. </ | + | |
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| - | 115%; | + | |
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| - | model “Howitt_11”)< | + | |
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| - | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 width=" | + | |
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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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| - | yes'> | + | |
| - | < | + | |
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| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | of production activities of the model with the objective <span class=GramE> | + | |
| - | </ | + | |
| - | EN-GB'>< | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | 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.< | + | |
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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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| - | differences between the linear and the positive mathematical programming | + | |
| - | 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.< | + | |
| - | + | ||
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| - | programming approach shows a smoother reaction to price changes compared to the | + | |
| - | 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.< | + | |
| - | + | ||
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| - | lang=EN-GB style=' | + | |
| - | 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 and overreaction like in | + | |
| - | 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 and the dual values of | + | |
| - | the calibration constraints are used to specify a new objective function that | + | |
| - | reflects observed farm behaviour that cannot be captured with additional | + | |
| - | constraints. These new objective functions capture a lot of possible <span | + | |
| - | 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 of the farmer(s) over time inducing | + | |
| - | 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) for an overview).< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | class=SpellE>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mathematical programming | + | |
| - | 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 to Microeconomic Programming Models. Working Paper (6). Department of | + | |
| - | Agricultural Economics, University of California, Davis. < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | Parametric Programming and Comparative Statics. Chapter 11 in Notes <span | + | |
| - | 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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| - | + | ||
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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 of the models!< | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
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| - | “solver” add-in in the options.< | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | <div style=' | + | |
| - | + | ||
| - | <p class=MsoFootnoteText>< | + | |
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| - | class=MsoFootnoteReference>< | + | |
| - | 115%; | + | |
| - | mso-fareast-font-family: | + | |
| - | minor-latin; | + | |
| - | mso-ansi-language: | + | |
| - | lang=EN-GB style=' | + | |
| - | model is an optimization model, in which an objective function is maximized or | + | |
| - | minimized subject to some constraints. In our case we have a maximization | + | |
| - | problem which is also called the primal model. The total gross margin is | + | |
| - | 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 of the primal model is always the same like the value of the objective | + | |
| - | function of the dual model. See Hazell & Norton (1986) for a more detailed | + | |
| - | presentation.< | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | <div style=' | + | |
| - | + | ||
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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 the | + | |
| - | “sensitivity analysis report” to extract the dual values of the calibration | + | |
| - | constraints. In the GAMS file you can see that after a model is solved, the | + | |
| - | dual values are captured as follows: <span class=GramE> | + | |
| - | class=SpellE> | + | |
| - | + | ||
| - | </ | + | |
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| - | even higher compared to the other production activities.< | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | </ | + | |
| - | + | ||
| - | </ | + | |
start.txt · Last modified: 2022/11/07 10:23 by 127.0.0.1