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"text": "and the price of reexport good is the weighted average of the import prices from the regions where its components came from:"
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"text": "P_{IM^{X},t}=\\left(\\sum_{CO\\neq H}\\nu_{IM^{X}}^{H,CO}\\left(\\frac{P_{IM,t}^{H,CO}}{\\Gamma_{IM^{X}}^{H,CO\\dagger}\\left(IM_{t}^{X,CO}/EX_{t}\\right)}\\right)^{1-\\mu_{IMX}}\\right)^{\\frac{1}{1-\\mu_{IMX}}}.",
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"latex": "P_{I M^{X},t}=\\left(\\sum_{C O\\neq H}\\nu_{I M^{X}}^{H,C O}\\left(\\frac{P_{I M,t}^{H,C O}}{\\Gamma_{I M^{X}}^{H,C O\\dagger}\\left(I M_{t}^{X,C O}/E X_{t}\\right)}\\right)^{1-\\mu_{I M X}}\\right)^{\\frac{1}{1-\\mu_{I M X}}}.",
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"alt": "P sub IM to the power of X, t equals the sum of sub CO is not equal to H 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 capital gamma sub IM to the power of X to the power of H, CO dagger of IM sub t to the power of X, CO over EX sub t to the power of 1 minus mu sub IMX to the power of 1 over 1 minus mu sub IMX .",
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"text": "(37)",
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"text": "A.5 Intermediate goods",
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"text": "Non-tradable[p39.5.1] and tradable[p39.5.2] intermediate goods are produced using a Cobb-Douglas technologies:",
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"text": "\\begin{array}{ccl}{Y_{N,t}}&{=}&{z_{N,t}K_{G,t}^{\\alpha_{G}}K_{N,t}^{\\alpha_{N}}N_{N,t}^{1-\\alpha_{N}}-\\psi_{N}}\\\\ \\end{array}",
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"notation": "latex",
"alt": "begin array ccl Y sub N, t & equals & z sub N, t K sub G, t to the power of alpha sub G K sub N, t to the power of alpha sub N N sub N, t to the power of 1 minus alpha sub N minus psi sub N end array",
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{
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"text": "\\begin{array}{ccl}{Y_{T,t}}&{=}&{z_{T,t}K_{G,t}^{\\alpha_{G}}K_{T,t}^{\\alpha_{T}}N_{T,t}^{1-\\alpha_{T}}-\\psi_{T}}\\\\ \\end{array}",
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"type": "text",
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"text": "(38)",
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},
{
"id": "p39.9",
"order": 11,
"type": "text",
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"text": "(39)",
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},
{
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"type": "text",
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"text": "where[p39.10.1] and[p39.10.2] are fixed costs. The inputs are homogenous capital services,[p39.10.3] and[p39.10.4], and labour services,[p39.10.5] and[p39.10.6]. Capital services are supplied by domestic households under perfect competition, yielding that demand for capital is determined by its marginal product being equal to the rental rate, while labour demand is determined by the marginal product of labour at intermediate goods firm being equal to the cost of labour determined by labour packers, as described in the main text.[p39.10.7] and[p39.10.8] are sector-specific productivity shocks.",
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"inline": true,
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"notation": "latex",
"alt": "K sub NTt",
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}
},
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"order": 17,
"type": "formula",
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"text": "N_{N,t}",
"attrs": {
"latex": "N_{N,t}",
"inline": true,
"text_offset": 136,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "N sub N, t",
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}
},
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"text": "N_{N,t}",
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"latex": "N_{N,t}",
"inline": true,
"text_offset": 150,
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}
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"text": "z_{N,t}",
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"latex": "z_{N,t}",
"inline": true,
"text_offset": 534,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "z sub N, t",
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}
},
{
"id": "p39.10.8",
"order": 20,
"type": "formula",
"bbox": {
"l": 67.9013,
"t": 533.501,
"r": 526.175,
"b": 433.6645
},
"text": "z_{T,t}",
"attrs": {
"latex": "z_{T,t}",
"inline": true,
"text_offset": 548,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "z sub T, t",
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}
}
]
},
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"id": "p39.11",
"order": 21,
"type": "text",
"bbox": {
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"b": 403.4256
},
"text": "Note that the labour market clearing implies that the total labour services provided must equal to the labour demanded by intermediate goods firms:"
},
{
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"order": 22,
"type": "formula",
"bbox": {
"l": 250.7309,
"t": 387.8262,
"r": 342.6256,
"b": 374.6267
},
"text": "n_{t}=N_{N,t}+N_{T,t}.",
"attrs": {
"block_label": "display_formula",
"latex": "n_{t}=N_{N,t}+N_{T,t}.",
"notation": "latex",
"alt": "n sub t equals N sub N, t plus N sub T, t .",
"mathml": ""
}
},
{
"id": "p39.13",
"order": 23,
"type": "text",
"bbox": {
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"b": 375.3466
},
"text": "(40)",
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}
},
{
"id": "p39.14",
"order": 24,
"type": "text",
"bbox": {
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"r": 526.6549,
"b": 265.4305
},
"text": "Goods markets for non-tradable and tradable goods clear by equating supply and demand. Demand for non-tradable goods comes from demands for non-tradable consumption and investment goods,[p39.14.1] and[p39.14.2]), and from government[p39.14.3], which is fully biased towards non-tradable goods. Demand for tradable goods comes from demands for tradable consumption and investment goods[p39.14.4] and from trading partners' imports[p39.14.5].[p39.14.6],[p39.14.7], and[p39.14.8] are price dispersions in non-tradable, tradable, and export sectors:",
"children": [
{
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"order": 25,
"type": "formula",
"bbox": {
"l": 67.9013,
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},
"text": "(NT_{C,t}",
"attrs": {
"latex": "(NT_{C,t}",
"inline": true,
"text_offset": 186,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "NT sub C, t",
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},
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"text": "NT_{I,t}",
"attrs": {
"latex": "NT_{I,t}",
"inline": true,
"text_offset": 200,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "NT sub I, t",
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},
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"type": "formula",
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},
"text": "(G_t)",
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"latex": "(G_t)",
"inline": true,
"text_offset": 232,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "G sub t",
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},
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"text": "(HT_{C,t}, HT_{I,t})",
"attrs": {
"latex": "(HT_{C,t}, HT_{I,t})",
"inline": true,
"text_offset": 384,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "HT sub C, t, HT sub I, t",
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}
},
{
"id": "p39.14.5",
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"type": "formula",
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"text": "(IM_{CO,H,t})",
"attrs": {
"latex": "(IM_{CO,H,t})",
"inline": true,
"text_offset": 429,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "IM sub CO, H, t",
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}
},
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"type": "formula",
"bbox": {
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"text": "s_{N,t}",
"attrs": {
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"inline": true,
"text_offset": 440,
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"notation": "latex",
"alt": "s sub N, t",
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},
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"type": "formula",
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"text": "s_{HT,t}",
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"notation": "latex",
"alt": "s sub HT, t",
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},
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"text": "s_{X,t}^{H,CO}",
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"inline": true,
"text_offset": 466,
"text_span": 10,
"bbox_estimated": true,
"notation": "latex",
"alt": "s sub X, t to the power of H, CO",
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}
}
]
},
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"type": "formula",
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},
"text": "\\begin{array}{rlr}{Y_{N,t}}&{=}&{s_{N,t}\\left(NT_{C,t}+NT_{I,t}+G_{t}\\right)}\\end{array}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{array}{r l r}{Y_{N,t}}&{=}&{s_{N,t}\\left(N T_{C,t}+N T_{I,t}+G_{t}\\right)}\\end{array}",
"notation": "latex",
"alt": "begin array rlr Y sub N, t & equals & s sub N, t of NT sub C, t plus NT sub I, t plus G sub t end array",
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}
},
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},
"text": "\\begin{array}{c} Y_{T,t}=s_{HT,t}(HT_{C,t}+HT_{I,t})+\\displaystyle\\sum_{CO\\neq H}s_{X,t}^{H,CO}IM_{CO,H,t}\\end{array}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{array}{c} Y_{T,t}=s_{HT,t}(HT_{C,t}+HT_{I,t})+\\displaystyle\\sum_{CO\\neq H}s_{X,t}^{H,CO}IM_{CO,H,t}\\end{array}",
"notation": "latex",
"alt": "begin array c Y sub T, t equals s sub HT, t of HT sub C, t plus HT sub I, t plus displaystyle the sum of sub CO is not equal to H s sub X, t to the power of H, CO IM sub CO, H, t end array",
"mathml": ""
}
},
{
"id": "p39.17",
"order": 35,
"type": "text",
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"text": "(41)",
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},
{
"id": "p39.18",
"order": 36,
"type": "text",
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"text": "(42)",
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},
{
"id": "p39.19",
"order": 37,
"type": "heading",
"bbox": {
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"r": 189.0679,
"b": 157.6744
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"text": "A.6 Price setting",
"attrs": {
"block_label": "paragraph_title"
}
},
{
"id": "p39.20",
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"type": "text",
"bbox": {
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"text": "Price setting follows the standard Calvo (1983) framework. Intermediate goods firms, however, set prices differently, depending on the market to which they are pricing their goods. This applies to non-tradable, home tradable and to export goods, in the latter case also for each export market separately (the so-called local currency pricing framework). Prices that are not reset are indexed to a composite of past inflation and inflation target.",
"children": [
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"order": 39,
"type": "link",
"bbox": {
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},
"text": "Calvo",
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"action_type": "/Named"
}
},
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"text": "(1983)",
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},
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"id": "p39.21",
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"type": "footer",
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"text": "38",
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}