{ "document_id": 405, "page": 38, "width_pt": 595.276, "height_pt": 841.89, "engine": "paddleocr_vl", "source_run_id": 530, "item_count": 34, "counts_by_type": { "footer": 1, "formula": 14, "heading": 1, "link": 3, "text": 15 }, "build_ms": 3, "items": [ { "id": "p38.1", "order": 1, "type": "text", "bbox": { "l": 85.8963, "t": 769.8926, "r": 329.4292, "b": 755.2531 }, "text": "The corresponding cost-minimizing prices are:", "children": [] }, { "id": "p38.2", "order": 2, "type": "formula", "bbox": { "l": 128.1247, "t": 743.2535, "r": 350.0636, "b": 717.5744 }, "text": "\\begin{array}{rcl}{P_{C,t}}&{=}&{\\left[\\nu_{C}P_{TT^{C},t}^{1-\\mu_{C}}+\\left(1-\\nu_{C}\\right)P_{NT,t}^{1-\\mu_{C}}\\right]^{\\frac{1}{1-\\mu_{C}}}}\\\\ \\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{r c l}{P_{C,t}}&{=}&{\\left[\\nu_{C}P_{T T^{C},t}^{1-\\mu_{C}}+\\left(1-\\nu_{C}\\right)P_{N T,t}^{1-\\mu_{C}}\\right]^{\\frac{1}{1-\\mu_{C}}}}\\\\ \\end{array}", "notation": "latex", "alt": "begin array rcl P sub C, t & equals & nu sub C P sub TT to the power of C, t to the power of 1 minus mu sub C plus 1 minus nu sub C P sub NT, t to the power of 1 minus mu sub C to the power of 1 over 1 minus mu sub C end array", "mathml": "PC,t=[νCPTTC,t1−μC+(1−νC)PNT,t1−μC]11−μC" }, "children": [] }, { "id": "p38.3", "order": 3, "type": "text", "bbox": { "l": 502.4216, "t": 737.4937, "r": 524.2556, "b": 723.8142 }, "text": "(28)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.4", "order": 4, "type": "formula", "bbox": { "l": 116.128, "t": 714.2145, "r": 377.416, "b": 688.5355 }, "text": "\\begin{array}{rcl}{P_{TT^{C},t}}&{=}&{\\left[\\nu_{TC}P_{HT,t}^{1-\\mu_{TC}}+\\left(1-\\nu_{TC}\\right)P_{IM^{C},t}^{1-\\mu_{TC}}\\right]^{\\frac{1}{1-\\mu_{TC}}}}\\\\ \\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{r c l}{P_{T T^{C},t}}&{=}&{\\left[\\nu_{T C}P_{H T,t}^{1-\\mu_{T C}}+\\left(1-\\nu_{T C}\\right)P_{I M^{C},t}^{1-\\mu_{T C}}\\right]^{\\frac{1}{1-\\mu_{T C}}}}\\\\ \\end{array}", "notation": "latex", "alt": "begin array rcl P sub TT to the power of C, t & equals & nu sub TC P sub HT, t to the power of 1 minus mu sub TC plus 1 minus nu sub TC P sub IM to the power of C, t to the power of 1 minus mu sub TC to the power of 1 over 1 minus mu sub TC end array", "mathml": "PTTC,t=[νTCPHT,t1−μTC+(1−νTC)PIMC,t1−μTC]11−μTC" }, "children": [] }, { "id": "p38.5", "order": 5, "type": "text", "bbox": { "l": 502.4216, "t": 707.9748, "r": 524.0156, "b": 694.0553 }, "text": "(29)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.6", "order": 6, "type": "formula", "bbox": { "l": 114.6884, "t": 683.0157, "r": 478.1883, "b": 634.2974 }, "text": "\\begin{array}{lll}{P_{{IM}^{C},t}}&{=}&{\\displaystyle\\left(\\sum_{CO\\neq H}\\nu_{{IM}^{C}}^{H,CO}\\left(\\frac{P_{{IM},t}^{H,CO}}{\\Gamma_{{IM}^{C}}^{H,CO\\dagger}\\left(IM_{t}^{C,CO}/Q_{C,t}\\right)}\\right)^{1-\\mu_{{IMC}}}\\right)^{\\frac{1}{1-\\mu_{{IMC}}}}.}\\\\ \\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{l l l}{P_{{I M}^{C},t}}&{=}&{\\displaystyle\\left(\\sum_{C O\\neq H}\\nu_{{I M}^{C}}^{H,C O}\\left(\\frac{P_{{I M},t}^{H,C O}}{\\Gamma_{{I M}^{C}}^{H,C O\\dagger}\\left(I M_{t}^{C,C O}/Q_{C,t}\\right)}\\right)^{1-\\mu_{{I M C}}}\\right)^{\\frac{1}{1-\\mu_{{I M C}}}}.}\\\\ \\end{array}", "notation": "latex", "alt": "begin array lll P sub IM to the power of C, t & equals & displaystyle of the sum of sub CO is not equal to H nu sub IM to the power of C to the power of H, CO of frac P sub IM, t to the power of H, CO capital gamma sub IM to the power of C to the power of H, CO dagger of IM sub t to the power of C, CO over Q sub C, t to the power of 1 minus mu sub IMC to the power of frac 1 1 minus mu sub IMC . end array", "mathml": "PIMC,t=(∑CO≠HνIMCH,CO(PIM,tH,COΓIMCH,CO†(IMtC,CO/QC,t))1−μIMC)11−μIMC." }, "children": [] }, { "id": "p38.7", "order": 7, "type": "text", "bbox": { "l": 502.4216, "t": 665.7363, "r": 524.0156, "b": 651.5768 }, "text": "(30)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.8", "order": 8, "type": "heading", "bbox": { "l": 67.9013, "t": 615.8181, "r": 192.9069, "b": 599.4986 }, "text": "A.4 Export goods", "attrs": { "block_label": "paragraph_title" }, "children": [] }, { "id": "p38.9", "order": 9, "type": "text", "bbox": { "l": 67.9013, "t": 590.619, "r": 526.415, "b": 532.781 }, "text": "The model features import-content of exports, which is modelled as in Brzoza-Brzezina et al. (2014), where export firms create a bundle of home-produced tradable goods for export,[p38.9.4] and goods imported for the purpose of reexporting,[p38.9.5], and then export the bundle of both goods. The export bundle is:", "children": [ { "id": "p38.9.1", "order": 10, "type": "link", "bbox": { "l": 437.324, "t": 589.402, "r": 525.406, "b": 576.662 }, "text": "Brzoza-Brzezina", "attrs": { "action_type": "/Named" }, "children": [] }, { "id": "p38.9.2", "order": 11, "type": "link", "bbox": { "l": 69.87, "t": 575.44, "r": 97.246, "b": 562.216 }, "text": "et al.", "attrs": { "action_type": "/Named" }, "children": [] }, { "id": "p38.9.3", "order": 12, "type": "link", "bbox": { "l": 101.844, "t": 575.44, "r": 131.573, "b": 562.216 }, "text": "(2014),", "attrs": { "action_type": "/Named" }, "children": [] }, { "id": "p38.9.4", "order": 13, "type": "formula", "bbox": { "l": 67.9013, "t": 590.619, "r": 526.415, "b": 532.781 }, "text": "HT_{X,t}", "attrs": { "latex": "HT_{X,t}", "inline": true, "text_offset": 179, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "HT sub X, t", "mathml": "HTX,t" }, "children": [] }, { "id": "p38.9.5", "order": 14, "type": "formula", "bbox": { "l": 67.9013, "t": 590.619, "r": 526.415, "b": 532.781 }, "text": "IM_{X,t}", "attrs": { "latex": "IM_{X,t}", "inline": true, "text_offset": 239, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "IM sub X, t", "mathml": "IMX,t" }, "children": [] } ] }, { "id": "p38.10", "order": 15, "type": "formula", "bbox": { "l": 166.994, "t": 521.2614, "r": 426.1226, "b": 488.8626 }, "text": "EX_{t}=\\left\\lceil\\nu_{X}^{\\frac{1}{\\mu_{X}}}HT_{X,t}^{\\frac{\\mu_{X}-1}{\\mu_{X}}}+(1-\\nu_{X})^{\\frac{1}{\\mu_{X}}}IM_{X,t}^{\\frac{\\mu_{x}-1}{\\mu_{X}}}\\right\\rceil^{\\frac{\\mu_{X}}{\\mu_{X}-1}}.", "attrs": { "block_label": "display_formula", "latex": "E X_{t}=\\left\\lceil\\nu_{X}^{\\frac{1}{\\mu_{X}}}H T_{X,t}^{\\frac{\\mu_{X}-1}{\\mu_{X}}}+(1-\\nu_{X})^{\\frac{1}{\\mu_{X}}}I M_{X,t}^{\\frac{\\mu_{x}-1}{\\mu_{X}}}\\right\\rceil^{\\frac{\\mu_{X}}{\\mu_{X}-1}}.", "notation": "latex", "alt": "EX sub t equals lceil nu sub X to the power of 1 over mu sub X HT sub X, t to the power of mu sub X minus 1 over mu sub X plus 1 minus nu sub X to the power of 1 over mu sub X IM sub X, t to the power of mu sub x minus 1 over mu sub X rceil to the power of mu sub X over mu sub X minus 1 .", "mathml": "EXt=⌈νX1μXHTX,tμX−1μX+(1−νX)1μXIMX,tμx−1μX⌉μXμX−1." }, "children": [] }, { "id": "p38.11", "order": 16, "type": "text", "bbox": { "l": 502.6615, "t": 510.4618, "r": 524.2556, "b": 496.3023 }, "text": "(31)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.12", "order": 17, "type": "text", "bbox": { "l": 68.1412, "t": 482.6228, "r": 526.175, "b": 453.8238 }, "text": "Analogously to demands for goods in the consumption bundle, we have the demands for home tradable goods for exports and imported goods for reexports:", "children": [] }, { "id": "p38.13", "order": 18, "type": "formula", "bbox": { "l": 191.9471, "t": 430.7846, "r": 369.2583, "b": 399.3458 }, "text": "\\begin{array}{ccc}{HT_{X,t}}&{=}&{\\nu_{X}\\left(\\displaystyle\\frac{MC_{T,t}}{MC_{X,t}}\\right)^{-\\mu_{X}}EX_{t}}\\\\ \\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{c c c}{H T_{X,t}}&{=}&{\\nu_{X}\\left(\\displaystyle\\frac{M C_{T,t}}{M C_{X,t}}\\right)^{-\\mu_{X}}E X_{t}}\\\\ \\end{array}", "notation": "latex", "alt": "begin array ccc HT sub X, t & equals & nu sub X of displaystyle MC sub T, t over MC sub X, t to the power of minus mu sub X EX sub t end array", "mathml": "HTX,t=νX(MCT,tMCX,t)−μXEXt" }, "children": [] }, { "id": "p38.14", "order": 19, "type": "text", "bbox": { "l": 502.6615, "t": 422.145, "r": 524.2556, "b": 408.2255 }, "text": "(32)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.15", "order": 20, "type": "formula", "bbox": { "l": 191.7072, "t": 395.9859, "r": 402.3691, "b": 364.067 }, "text": "\\begin{array}{lcl}{IM_{X,t}}&{=}&{\\left(1-\\nu_{X}\\right)\\left(\\cfrac{P_{IM^{X},t}}{MC_{X,t}}\\right)^{-\\mu_{X}}EX_{t}.}\\\\ \\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{l c l}{I M_{X,t}}&{=}&{\\left(1-\\nu_{X}\\right)\\left(\\cfrac{P_{I M^{X},t}}{M C_{X,t}}\\right)^{-\\mu_{X}}E X_{t}.}\\\\ \\end{array}", "notation": "latex", "alt": "begin array lcl IM sub X, t & equals & 1 minus nu sub X times cfrac P sub IM to the power of X, t MC sub X, t to the power of minus mu sub X EX sub t . end array", "mathml": "IMX,t=(1−νX)(PIMX,tMCX,t)−μXEXt." }, "children": [] }, { "id": "p38.16", "order": 21, "type": "text", "bbox": { "l": 502.6615, "t": 387.3462, "r": 524.2556, "b": 373.6667 }, "text": "(33)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.17", "order": 22, "type": "text", "bbox": { "l": 68.1412, "t": 353.9874, "r": 526.175, "b": 324.9484 }, "text": "Imported goods for the purpose of reexports are a bundle of imported goods from all other regions, subject to adjustment costs:", "children": [] }, { "id": "p38.18", "order": 23, "type": "formula", "bbox": { "l": 73.8996, "t": 300.4693, "r": 517.7774, "b": 252.951 }, "text": "IM_{X,t}=\\left[\\sum_{CO\\neq H}\\left(\\nu_{IM_{X}}^{H,CO}\\right)^{\\frac{1}{\\mu_{IMX}}}\\left(IM_{X,CO,t}\\left(1-\\Gamma_{IM^{X}}^{H,CO}\\left(\\frac{IM_{X,CO,t}}{EX_{t}}\\right)\\right)\\right)^{\\frac{\\mu_{IMX}-1}{\\mu_{IMX}}}\\right]^{\\frac{\\mu_{IMX}}{\\mu_{IMX}-1}}.", "attrs": { "block_label": "display_formula", "latex": "I M_{X,t}=\\left[\\sum_{C O\\neq H}\\left(\\nu_{I M_{X}}^{H,C O}\\right)^{\\frac{1}{\\mu_{I M X}}}\\left(I M_{X,C O,t}\\left(1-\\Gamma_{I M^{X}}^{H,C O}\\left(\\frac{I M_{X,C O,t}}{E X_{t}}\\right)\\right)\\right)^{\\frac{\\mu_{I M X}-1}{\\mu_{I M X}}}\\right]^{\\frac{\\mu_{I M X}}{\\mu_{I M X}-1}}.", "notation": "latex", "alt": "IM sub X, t equals the sum of sub CO is not equal to H of nu sub IM sub X to the power of H, CO to the power of 1 over mu sub IMX of IM sub X, CO, t of 1 minus capital gamma sub IM to the power of X to the power of H, CO of IM sub X, CO, t over EX sub t to the power of mu sub IMX minus 1 over mu sub IMX to the power of mu sub IMX over mu sub IMX minus 1 .", "mathml": "IMX,t=[∑CO≠H(νIMXH,CO)1μIMX(IMX,CO,t(1−ΓIMXH,CO(IMX,CO,tEXt)))μIMX−1μIMX]μIMXμIMX−1." }, "children": [] }, { "id": "p38.19", "order": 24, "type": "text", "bbox": { "l": 502.6615, "t": 254.3909, "r": 524.0156, "b": 240.7114 }, "text": "(34)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.20", "order": 25, "type": "text", "bbox": { "l": 85.8963, "t": 239.5115, "r": 377.8959, "b": 225.832 }, "text": "These give rise to bilateral demands for reexport goods:", "children": [] }, { "id": "p38.21", "order": 26, "type": "formula", "bbox": { "l": 74.8594, "t": 201.3528, "r": 517.5374, "b": 162.9542 }, "text": "IM_{X,CO,t}=\\nu_{IM^{X}}^{H,CO}\\left(\\frac{P_{IM,t}^{H,CO}}{P_{IM^{X},t}\\Gamma_{IM^{X}}^{H,CO\\dagger}\\left(IM_{X,CO,t}/EX_{t}\\right)}\\right)^{-\\mu_{IMX}}\\frac{IM_{X,t}}{1-\\Gamma_{IM^{X}}^{H,CO}\\left(IM_{X,CO,t}/EX_{t}\\right)}", "attrs": { "block_label": "display_formula", "latex": "IM_{X,CO,t}=\\nu_{IM^{X}}^{H,CO}\\left(\\frac{P_{IM,t}^{H,CO}}{P_{IM^{X},t}\\Gamma_{IM^{X}}^{H,CO\\dagger}\\left(IM_{X,CO,t}/EX_{t}\\right)}\\right)^{-\\mu_{IMX}}\\frac{IM_{X,t}}{1-\\Gamma_{IM^{X}}^{H,CO}\\left(IM_{X,CO,t}/EX_{t}\\right)}", "notation": "latex", "alt": "IM sub X, CO, t equals nu sub IM to the power of X to the power of H, CO of P sub IM, t to the power of H, CO over P sub IM to the power of X, t capital gamma sub IM to the power of X to the power of H, CO dagger of IM sub X, CO, t over EX sub t to the power of minus mu sub IMX IM sub X, t over 1 minus capital gamma sub IM to the power of X to the power of H, CO of IM sub X, CO, t over EX sub t", "mathml": "IMX,CO,t=νIMXH,CO(PIM,tH,COPIMX,tΓIMXH,CO†(IMX,CO,t/EXt))−μIMXIMX,t1−ΓIMXH,CO(IMX,CO,t/EXt)" }, "children": [] }, { "id": "p38.22", "order": 27, "type": "text", "bbox": { "l": 502.9014, "t": 164.3941, "r": 524.0156, "b": 151.4346 }, "text": "(35)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.23", "order": 28, "type": "text", "bbox": { "l": 67.9013, "t": 150.2346, "r": 525.6952, "b": 106.3162 }, "text": "The real price (in terms of consumption goods) of the export good is just its marginal cost,[p38.23.1], which is the weighted average of (real) marginal costs of home tradable goods,[p38.23.2], and the relative price of imported goods for reexport,[p38.23.3]:", "children": [ { "id": "p38.23.1", "order": 29, "type": "formula", "bbox": { "l": 67.9013, "t": 150.2346, "r": 525.6952, "b": 106.3162 }, "text": "MC_{X,t}", "attrs": { "latex": "MC_{X,t}", "inline": true, "text_offset": 92, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "MC sub X, t", "mathml": "MCX,t" }, "children": [] }, { "id": "p38.23.2", "order": 30, "type": "formula", "bbox": { "l": 67.9013, "t": 150.2346, "r": 525.6952, "b": 106.3162 }, "text": "MC_{T,t}", "attrs": { "latex": "MC_{T,t}", "inline": true, "text_offset": 182, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "MC sub T, t", "mathml": "MCT,t" }, "children": [] }, { "id": "p38.23.3", "order": 31, "type": "formula", "bbox": { "l": 67.9013, "t": 150.2346, "r": 525.6952, "b": 106.3162 }, "text": "P_{IM^{X},t}", "attrs": { "latex": "P_{IM^{X},t}", "inline": true, "text_offset": 248, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "P sub IM to the power of X, t", "mathml": "PIMX,t" }, "children": [] } ] }, { "id": "p38.24", "order": 32, "type": "formula", "bbox": { "l": 175.1517, "t": 95.2766, "r": 419.6444, "b": 68.1576 }, "text": "\\begin{array}{r}{MC_{X,t}=\\left[\\nu_{X}MC_{T,t}^{1-\\mu_{X}}+(1-\\nu_{X})P_{IM^{X},t}^{1-\\mu_{X}}\\right]^{\\frac{1}{1-\\mu_{X}}},}\\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{r}{M C_{X,t}=\\left[\\nu_{X}M C_{T,t}^{1-\\mu_{X}}+(1-\\nu_{X})P_{I M^{X},t}^{1-\\mu_{X}}\\right]^{\\frac{1}{1-\\mu_{X}}},}\\end{array}", "notation": "latex", "alt": "begin array r MC sub X, t equals nu sub X MC sub T, t to the power of 1 minus mu sub X plus 1 minus nu sub X P sub IM to the power of X, t to the power of 1 minus mu sub X to the power of 1 over 1 minus mu sub X, end array", "mathml": "MCX,t=[νXMCT,t1−μX+(1−νX)PIMX,t1−μX]11−μX," }, "children": [] }, { "id": "p38.25", "order": 33, "type": "text", "bbox": { "l": 502.4216, "t": 88.0769, "r": 524.2556, "b": 74.3973 }, "text": "(36)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" }, "children": [] }, { "id": "p38.26", "order": 34, "type": "footer", "bbox": { "l": 290.32, "t": 51.1182, "r": 305.4359, "b": 39.3586 }, "text": "37", "attrs": { "block_label": "number" }, "children": [] } ], "ai_page_review": { "model": "claude-opus-4-8", "applied": true, "changed": true, "reviewed_at": "2026-08-21T10:46:26+00:00" } }