{
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"link": 2,
"text": 12
},
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"items": [
{
"id": "p37.1",
"order": 1,
"type": "heading",
"bbox": {
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"t": 771.8125,
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"b": 755.2531
},
"text": "A.3 Final goods",
"attrs": {
"block_label": "paragraph_title"
},
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{
"id": "p37.2",
"order": 2,
"type": "text",
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"text": "Final goods are consumption goods[p37.2.1] and investment goods[p37.2.2] (to save space, we list equations only for consumption goods, as the equations for investment goods are analogous). They are assembled from tradable goods,[p37.2.3] and non-tradable goods,[p37.2.4] using the constant elasticity of substitution technology:",
"children": [
{
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"text": "Q_{C,t}",
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"latex": "Q_{C,t}",
"inline": true,
"text_offset": 33,
"text_span": 9,
"bbox_estimated": true,
"notation": "latex",
"alt": "Q sub C, t",
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{
"id": "p37.2.2",
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"text": "Q_{I,t}",
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"inline": true,
"text_offset": 63,
"text_span": 9,
"bbox_estimated": true,
"notation": "latex",
"alt": "Q sub I, t",
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},
{
"id": "p37.2.3",
"order": 5,
"type": "formula",
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"text": "TT_{C,t}",
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"latex": "TT_{C,t}",
"inline": true,
"text_offset": 228,
"text_span": 9,
"bbox_estimated": true,
"notation": "latex",
"alt": "TT sub C, t",
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"children": []
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{
"id": "p37.2.4",
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"type": "formula",
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"text": "NT_{C,t}",
"attrs": {
"latex": "NT_{C,t}",
"inline": true,
"text_offset": 261,
"text_span": 9,
"bbox_estimated": true,
"notation": "latex",
"alt": "NT sub C, t",
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}
]
},
{
"id": "p37.3",
"order": 7,
"type": "formula",
"bbox": {
"l": 167.7138,
"t": 677.0159,
"r": 425.6427,
"b": 643.6571
},
"text": "Q_{C,t}=\\left[\\nu_{C}^{\\frac{1}{\\mu_{C}}}TT_{C,t}^{\\frac{\\mu_{C}-1}{\\mu_{C}}}+(1-\\nu_{C})^{\\frac{1}{\\mu_{C}}}NT_{C,t}^{\\frac{\\mu_{C}-1}{\\mu_{C}}}\\right]^{\\frac{\\mu_{C}}{\\mu_{C-1}}},",
"attrs": {
"block_label": "display_formula",
"latex": "Q_{C,t}=\\left[\\nu_{C}^{\\frac{1}{\\mu_{C}}}T T_{C,t}^{\\frac{\\mu_{C}-1}{\\mu_{C}}}+(1-\\nu_{C})^{\\frac{1}{\\mu_{C}}}N T_{C,t}^{\\frac{\\mu_{C}-1}{\\mu_{C}}}\\right]^{\\frac{\\mu_{C}}{\\mu_{C-1}}},",
"notation": "latex",
"alt": "Q sub C, t equals nu sub C to the power of 1 over mu sub C TT sub C, t to the power of mu sub C minus 1 over mu sub C plus 1 minus nu sub C to the power of 1 over mu sub C NT sub C, t to the power of mu sub C minus 1 over mu sub C to the power of mu sub C over mu sub C minus 1,",
"mathml": ""
},
"children": []
},
{
"id": "p37.4",
"order": 8,
"type": "text",
"bbox": {
"l": 502.4216,
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"b": 652.0568
},
"text": "(20)",
"attrs": {
"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
},
"children": []
},
{
"id": "p37.5",
"order": 9,
"type": "heading",
"bbox": {
"l": 68.1412,
"t": 637.8973,
"r": 108.6901,
"b": 625.4177
},
"text": "where:",
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},
{
"id": "p37.6",
"order": 10,
"type": "formula",
"bbox": {
"l": 147.3194,
"t": 627.3376,
"r": 444.3576,
"b": 593.2589
},
"text": "TT_{C,t}=\\left[\\nu_{TC}^{\\frac{1}{\\mu_{TC}}}HT_{C,t}^{\\frac{\\mu_{TC}-1}{\\mu_{TC}}}+(1-\\nu_{TC})^{\\frac{1}{\\mu_{TC}}}IM_{C,t}^{\\frac{\\mu_{TC}-1}{\\mu_{TC}}}\\right]^{\\frac{\\mu_{TC}}{\\mu_{TC}-1}}.",
"attrs": {
"block_label": "display_formula",
"latex": "T T_{C,t}=\\left[\\nu_{T C}^{\\frac{1}{\\mu_{T C}}}H T_{C,t}^{\\frac{\\mu_{T C}-1}{\\mu_{T C}}}+(1-\\nu_{T C})^{\\frac{1}{\\mu_{T C}}}I M_{C,t}^{\\frac{\\mu_{T C}-1}{\\mu_{T C}}}\\right]^{\\frac{\\mu_{T C}}{\\mu_{T C}-1}}.",
"notation": "latex",
"alt": "TT sub C, t equals nu sub TC to the power of 1 over mu sub TC HT sub C, t to the power of mu sub TC minus 1 over mu sub TC plus 1 minus nu sub TC to the power of 1 over mu sub TC IM sub C, t to the power of mu sub TC minus 1 over mu sub TC to the power of mu sub TC over mu sub TC minus 1 .",
"mathml": ""
},
"children": []
},
{
"id": "p37.7",
"order": 11,
"type": "text",
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"b": 601.8986
},
"text": "(21)",
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"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
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"children": []
},
{
"id": "p37.8",
"order": 12,
"type": "text",
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"text": "Tradable goods are a composite bundle of domestic tradable goods,[p37.8.1], and imports,[p37.8.2]. Imports, in turn, are also a composite of imports from other regions CO, denoted by[p37.8.3], and H stands for the home country:",
"children": [
{
"id": "p37.8.1",
"order": 13,
"type": "formula",
"bbox": {
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"text": "HT_{C,t}",
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"latex": "HT_{C,t}",
"inline": true,
"text_offset": 65,
"text_span": 9,
"bbox_estimated": true,
"notation": "latex",
"alt": "HT sub C, t",
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},
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{
"id": "p37.8.2",
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"type": "formula",
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"text": "IM_{C,t}",
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"latex": "IM_{C,t}",
"inline": true,
"text_offset": 88,
"text_span": 9,
"bbox_estimated": true,
"notation": "latex",
"alt": "IM sub C, t",
"mathml": ""
},
"children": []
},
{
"id": "p37.8.3",
"order": 15,
"type": "formula",
"bbox": {
"l": 67.9013,
"t": 588.459,
"r": 525.2153,
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},
"text": "IM_{C,CO,t}",
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"latex": "IM_{C,CO,t}",
"inline": true,
"text_offset": 182,
"text_span": 9,
"bbox_estimated": true,
"notation": "latex",
"alt": "IM sub C, CO, t",
"mathml": ""
},
"children": []
}
]
},
{
"id": "p37.9",
"order": 16,
"type": "formula",
"bbox": {
"l": 78.9383,
"t": 521.7414,
"r": 512.4988,
"b": 472.5432
},
"text": "IM_{C,t}=\\left[\\sum_{CO\\neq H}\\left(\\nu_{IM_{C}}^{H,CO}\\right)^{\\frac{1}{\\mu_{IMC}}}\\left(IM_{C,CO,t}\\left(1-\\Gamma_{IM^{C}}^{H,CO}\\left(\\frac{IM_{C,CO,t}}{Q_{C,t}}\\right)\\right)\\right)^{\\frac{\\mu_{IMC}-1}{\\mu_{IMC}}}\\right]^{\\frac{\\mu_{IMC}}{\\mu_{IMC}-1}}",
"attrs": {
"block_label": "display_formula",
"latex": "I M_{C,t}=\\left[\\sum_{C O\\neq H}\\left(\\nu_{I M_{C}}^{H,C O}\\right)^{\\frac{1}{\\mu_{I M C}}}\\left(I M_{C,C O,t}\\left(1-\\Gamma_{I M^{C}}^{H,C O}\\left(\\frac{I M_{C,C O,t}}{Q_{C,t}}\\right)\\right)\\right)^{\\frac{\\mu_{I M C}-1}{\\mu_{I M C}}}\\right]^{\\frac{\\mu_{I M C}}{\\mu_{I M C}-1}}",
"notation": "latex",
"alt": "IM sub C, t equals the sum of sub CO is not equal to H of nu sub IM sub C to the power of H, CO to the power of 1 over mu sub IMC of IM sub C, CO, t of 1 minus capital gamma sub IM to the power of C to the power of H, CO of IM sub C, CO, t over Q sub C, t to the power of mu sub IMC minus 1 over mu sub IMC to the power of mu sub IMC over mu sub IMC minus 1",
"mathml": ""
},
"children": []
},
{
"id": "p37.10",
"order": 17,
"type": "text",
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},
"text": "(22)",
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"block_label": "formula_number"
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},
{
"id": "p37.11",
"order": 18,
"type": "text",
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"text": "Parameters[p37.11.1],[p37.11.2], and[p37.11.3] are intratemporal elasticities of substitution between the inputs in the production functions, while[p37.11.4],[p37.11.5], and[p37.11.6] are weights (quasi-shares) of the inputs into the production functions, with[p37.11.7]. The function[p37.11.8] is the adjustment cost for bilateral consumption imports of country H from country CO, where[p37.11.9] determines the magnitude of the cost:",
"children": [
{
"id": "p37.11.1",
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"text": "\\mu_{C}",
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"latex": "\\mu_{C}",
"inline": true,
"text_offset": 10,
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"bbox_estimated": true,
"notation": "latex",
"alt": "mu sub C",
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{
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"type": "formula",
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"text": "\\mu_{TC}",
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"latex": "\\mu_{TC}",
"inline": true,
"text_offset": 21,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "mu sub TC",
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},
"children": []
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{
"id": "p37.11.3",
"order": 21,
"type": "formula",
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"text": "\\mu_{IMC}",
"attrs": {
"latex": "\\mu_{IMC}",
"inline": true,
"text_offset": 36,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "mu sub IMC",
"mathml": ""
},
"children": []
},
{
"id": "p37.11.4",
"order": 22,
"type": "formula",
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"text": "\\nu_{C}",
"attrs": {
"latex": "\\nu_{C}",
"inline": true,
"text_offset": 147,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "nu sub C",
"mathml": ""
},
"children": []
},
{
"id": "p37.11.5",
"order": 23,
"type": "formula",
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"l": 67.4214,
"t": 459.5836,
"r": 526.175,
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},
"text": "\\nu_{TC}",
"attrs": {
"latex": "\\nu_{TC}",
"inline": true,
"text_offset": 158,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "nu sub TC",
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},
"children": []
},
{
"id": "p37.11.6",
"order": 24,
"type": "formula",
"bbox": {
"l": 67.4214,
"t": 459.5836,
"r": 526.175,
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"text": "\\nu_{IMC}",
"attrs": {
"latex": "\\nu_{IMC}",
"inline": true,
"text_offset": 173,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "nu sub IMC",
"mathml": ""
},
"children": []
},
{
"id": "p37.11.7",
"order": 25,
"type": "formula",
"bbox": {
"l": 67.4214,
"t": 459.5836,
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},
"text": "\\sum_{CO\\neq H} v_{IMC}^{H,CO} = 1",
"attrs": {
"latex": "\\sum_{CO\\neq H} v_{IMC}^{H,CO} = 1",
"inline": true,
"text_offset": 260,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "the sum of sub CO is not equal to H v sub IMC to the power of H, CO equals 1",
"mathml": ""
},
"children": []
},
{
"id": "p37.11.8",
"order": 26,
"type": "formula",
"bbox": {
"l": 67.4214,
"t": 459.5836,
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},
"text": "\\Gamma_{IMC}^{H,CO} \\left( \\frac{IM_{C,CO,t}}{Q_{C,t}^{C}} \\right)",
"attrs": {
"latex": "\\Gamma_{IMC}^{H,CO} \\left( \\frac{IM_{C,CO,t}}{Q_{C,t}^{C}} \\right)",
"inline": true,
"text_offset": 284,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "capital gamma sub IMC to the power of H, CO of IM sub C, CO, t over Q sub C, t to the power of C",
"mathml": ""
},
"children": []
},
{
"id": "p37.11.9",
"order": 27,
"type": "formula",
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"l": 67.4214,
"t": 459.5836,
"r": 526.175,
"b": 378.2265
},
"text": "\\gamma_{IMC}",
"attrs": {
"latex": "\\gamma_{IMC}",
"inline": true,
"text_offset": 387,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "gamma sub IMC",
"mathml": ""
},
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}
]
},
{
"id": "p37.12",
"order": 28,
"type": "formula",
"bbox": {
"l": 149.7188,
"t": 367.9069,
"r": 442.4381,
"b": 334.7881
},
"text": "\\Gamma_{IM^{C}}^{H,CO}\\left(\\frac{IM_{C,CO,t}}{Q_{C,t}}\\right)\\equiv\\frac{\\gamma_{IM^{C}}}{2}\\left(\\frac{IM_{C,CO,t}/Q_{C,t}}{IM_{C,CO,t-1}/Q_{C,t-1}}-1\\right)^{2}.",
"attrs": {
"block_label": "display_formula",
"latex": "\\Gamma_{I M^{C}}^{H,C O}\\left(\\frac{I M_{C,C O,t}}{Q_{C,t}}\\right)\\equiv\\frac{\\gamma_{I M^{C}}}{2}\\left(\\frac{I M_{C,C O,t}/Q_{C,t}}{I M_{C,C O,t-1}/Q_{C,t-1}}-1\\right)^{2}.",
"notation": "latex",
"alt": "capital gamma sub IM to the power of C to the power of H, CO of IM sub C, CO, t over Q sub C, t equiv gamma sub IM to the power of C over 2 times IM sub C, CO, t over Q sub C, t over IM sub C, CO, t minus 1 over Q sub C, t minus 1 minus 1 squared .",
"mathml": ""
},
"children": []
},
{
"id": "p37.13",
"order": 29,
"type": "text",
"bbox": {
"l": 502.4216,
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"r": 524.2556,
"b": 344.8677
},
"text": "(23)",
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"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
},
"children": []
},
{
"id": "p37.14",
"order": 30,
"type": "text",
"bbox": {
"l": 67.9013,
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"r": 526.6549,
"b": 267.3505
},
"text": "A final good's firm chooses the combination of the tradable and nontradable bundles that minimizes the expenditure[p37.14.3] subject to technology constraints (20) and (21), taking the input prices as given, which yields the following demand functions:",
"children": [
{
"id": "p37.14.1",
"order": 31,
"type": "link",
"bbox": {
"l": 196.752,
"t": 296.139,
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"text": "(20)",
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{
"id": "p37.14.2",
"order": 32,
"type": "link",
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"text": "",
"attrs": {
"action_type": "/Named"
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{
"id": "p37.14.3",
"order": 33,
"type": "formula",
"bbox": {
"l": 67.9013,
"t": 326.1484,
"r": 526.6549,
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},
"text": "P_{HT,t}HT_{C,t} + P_{IMC,t}IM_{C,t} + P_{NT,t}NT_{C,t}",
"attrs": {
"latex": "P_{HT,t}HT_{C,t} + P_{IMC,t}IM_{C,t} + P_{NT,t}NT_{C,t}",
"inline": true,
"text_offset": 114,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "P sub HT, t HT sub C, t plus P sub IMC, t IM sub C, t plus P sub NT, t NT sub C, t",
"mathml": ""
},
"children": []
}
]
},
{
"id": "p37.15",
"order": 34,
"type": "formula",
"bbox": {
"l": 87.5759,
"t": 258.4708,
"r": 355.582,
"b": 225.112
},
"text": "\\begin{array}{rlr}{HT_{C,t}}&{=}&{\\nu_{TC}\\nu_{C}\\left(\\displaystyle\\frac{P_{HT,t}}{P_{TT^{C},t}}\\right)^{-\\mu_{TC}}\\left(\\displaystyle\\frac{P_{TT^{C},t}}{P_{C,t}}\\right)^{-\\mu_{C}}Q_{C,t}}\\end{array}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{array}{r l r}{H T_{C,t}}&{=}&{\\nu_{T C}\\nu_{C}\\left(\\displaystyle\\frac{P_{H T,t}}{P_{T T^{C},t}}\\right)^{-\\mu_{T C}}\\left(\\displaystyle\\frac{P_{T T^{C},t}}{P_{C,t}}\\right)^{-\\mu_{C}}Q_{C,t}}\\end{array}",
"notation": "latex",
"alt": "begin array rlr HT sub C, t & equals & nu sub TC nu sub C of displaystyle P sub HT, t over P sub TT to the power of C, t to the power of minus mu sub TC of displaystyle P sub TT to the power of C, t over P sub C, t to the power of minus mu sub C Q sub C, t end array",
"mathml": ""
},
"children": []
},
{
"id": "p37.16",
"order": 35,
"type": "text",
"bbox": {
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},
"text": "(24)",
"attrs": {
"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
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"children": []
},
{
"id": "p37.17",
"order": 36,
"type": "formula",
"bbox": {
"l": 88.0557,
"t": 223.432,
"r": 388.453,
"b": 190.0732
},
"text": "\\begin{array}{rcl}{IM_{C,t}}&{=}&{\\left(1-\\nu_{TC}\\right)\\nu_{C}\\left(\\cfrac{P_{IM^{C},t}}{P_{TT^{C},t}}\\right)^{-\\mu_{TC}}\\left(\\cfrac{P_{TT^{C},t}}{P_{C,t}}\\right)^{-\\mu_{C}}Q_{C,t}}\\end{array}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{array}{r c l}{I M_{C,t}}&{=}&{\\left(1-\\nu_{T C}\\right)\\nu_{C}\\left(\\cfrac{P_{I M^{C},t}}{P_{T T^{C},t}}\\right)^{-\\mu_{T C}}\\left(\\cfrac{P_{T T^{C},t}}{P_{C,t}}\\right)^{-\\mu_{C}}Q_{C,t}}\\end{array}",
"notation": "latex",
"alt": "begin array rcl IM sub C, t & equals & 1 minus nu sub TC nu sub C of cfrac P sub IM to the power of C, t P sub TT to the power of C, t to the power of minus mu sub TC of cfrac P sub TT to the power of C, t P sub C, t to the power of minus mu sub C Q sub C, t end array",
"mathml": ""
},
"children": []
},
{
"id": "p37.18",
"order": 37,
"type": "text",
"bbox": {
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"b": 200.1529
},
"text": "(25)",
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},
{
"id": "p37.19",
"order": 38,
"type": "formula",
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"l": 88.0557,
"t": 187.6733,
"r": 283.8418,
"b": 156.2344
},
"text": "\\begin{array}{rcl}{NT_{C,t}}&{=}&{\\left(1-\\nu_{C}\\right)\\left(\\displaystyle\\frac{P_{NT,t}}{P_{C,t}}\\right)^{-\\mu_{C}}Q_{C,t}}\\end{array}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{array}{r c l}{N T_{C,t}}&{=}&{\\left(1-\\nu_{C}\\right)\\left(\\displaystyle\\frac{P_{N T,t}}{P_{C,t}}\\right)^{-\\mu_{C}}Q_{C,t}}\\end{array}",
"notation": "latex",
"alt": "begin array rcl NT sub C, t & equals & 1 minus nu sub C times displaystyle P sub NT, t over P sub C, t to the power of minus mu sub C Q sub C, t end array",
"mathml": ""
},
"children": []
},
{
"id": "p37.20",
"order": 39,
"type": "text",
"bbox": {
"l": 502.4216,
"t": 179.0336,
"r": 524.0156,
"b": 165.1141
},
"text": "(26)",
"attrs": {
"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
},
"children": []
},
{
"id": "p37.21",
"order": 40,
"type": "formula",
"bbox": {
"l": 71.2604,
"t": 152.1546,
"r": 524.4955,
"b": 113.036
},
"text": "\\begin{array}{rlr}{IM_{C,CO,t}}&{=}&{\\nu_{IM^{C}}^{H,CO}\\left(\\frac{P_{IM,t}^{H,CO}}{P_{IM^{C},t}\\Gamma_{IM^{C}}^{H,CO\\dagger}\\left(IM_{C,CO,t}/Q_{C,t}\\right)}\\right)^{-\\mu_{IMC}}\\frac{IM_{C,t}}{1-\\Gamma_{IM^{C}}^{H,CO}\\left(IM_{C,CO,t}/Q_{C,t}\\right)}\\mathrm{(27)}}\\end{array}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{array}{r l r}{I M_{C,C O,t}}&{=}&{\\nu_{I M^{C}}^{H,C O}\\left(\\frac{P_{I M,t}^{H,C O}}{P_{I M^{C},t}\\Gamma_{I M^{C}}^{H,C O\\dagger}\\left(I M_{C,C O,t}/Q_{C,t}\\right)}\\right)^{-\\mu_{I M C}}\\frac{I M_{C,t}}{1-\\Gamma_{I M^{C}}^{H,C O}\\left(I M_{C,C O,t}/Q_{C,t}\\right)}\\mathrm{(27)}}\\end{array}",
"notation": "latex",
"alt": "begin array rlr IM sub C, CO, t & equals & nu sub IM to the power of C 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 C, t capital gamma sub IM to the power of C to the power of H, CO dagger of IM sub C, CO, t over Q sub C, t to the power of minus mu sub IMC IM sub C, t over 1 minus capital gamma sub IM to the power of C to the power of H, CO of IM sub C, CO, t over Q sub C, t times 27 end array",
"mathml": ""
},
"children": []
},
{
"id": "p37.22",
"order": 41,
"type": "text",
"bbox": {
"l": 67.9013,
"t": 101.5164,
"r": 525.6952,
"b": 67.1976
},
"text": "The term[p37.22.1] in the bilateral import bundle is the derivative of the adjustment cost.",
"children": [
{
"id": "p37.22.1",
"order": 42,
"type": "formula",
"bbox": {
"l": 67.9013,
"t": 101.5164,
"r": 525.6952,
"b": 67.1976
},
"text": "\\Gamma_{IM^{C}}^{H,CO^{\\dagger}}\\left(\\frac{IM_{C,CO,t}}{Q_{C,t}}\\right)",
"attrs": {
"latex": "\\Gamma_{IM^{C}}^{H,CO^{\\dagger}}\\left(\\frac{IM_{C,CO,t}}{Q_{C,t}}\\right)",
"inline": true,
"text_offset": 8,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "capital gamma sub IM to the power of C to the power of H, CO to the power of dagger of IM sub C, CO, t over Q sub C, t",
"mathml": ""
},
"children": []
}
]
},
{
"id": "p37.23",
"order": 43,
"type": "footer",
"bbox": {
"l": 290.0801,
"t": 51.1182,
"r": 305.1959,
"b": 39.3586
},
"text": "36",
"attrs": {
"block_label": "number"
},
"children": []
}
],
"ai_page_review": {
"model": "claude-opus-4-8",
"applied": true,
"changed": true,
"reviewed_at": "2026-08-21T10:46:32+00:00"
}
}