Firm Equations

Firms

open_cge.firms

open_cge.firms.eqD(gamma, deltad, eta, Q, pq, pd)[source]

Demand for domestically produced goods from importers.

\[D_{i} = \left(\gamma_{i}^{\eta_{i}}\delta^{d}_{i}\frac{pq_{i}}{pd_{i}}\right)^{\frac{1}{1-\eta_{i}}}Q_{i}\]
Parameters

  • gamma (1D numpy array) – Scale parameter for CES production function

  • deltad (1D numpy array) – Share parameter for use of domestically produced good i in produciton Armington good i

  • eta (1D numpy array) – The elasticity of substitution between imports and domestically supplied good i

  • Q (1D numpy array) – The domestic supply of good i, the Armington good

  • pq (1D numpy array) – price of the Armington good (domestic + imports) for each good i

  • pd (1D numpy array) – price of domesically produced good i

Returns

Demand for domestically produced good i from importers

Return type

D (1D numpy array)

open_cge.firms.eqDex(theta, xid, tauz, phi, pz, pd, Z)[source]

Demand for domestic goods by exporters.

\[D_{i} = \left(\theta_{i}^{\phi_{i}}\xi^{D}_{i}(1+\tau^{z}_{i}\frac{pz_{i}}{pd_{i}})\right)^{\frac{1}{1-\phi_{i}}}Z_{i}\]
Parameters

  • theta (1D numpy array) – Scaling coefficient of the ith good transformation from domestic output to exports

  • xid (1D numpy array) – Share parameter for the share of domestically produced good i used by firms exporting good i

  • tauz (1D numpy array) – Ad valorem tax rate on commodity i

  • phi (1D numpy array) – Transformation elasticity parameter between exports and domestic production of good i

  • pz (1D numpy array) – price of output good i

  • pd (1D numpy array) – price of domesically produced good i

  • Z (1D numpy array) – Output from exporters CET production function

Returns

Demand for domestic good i by exporters.

Return type

D (1D numpy array)

open_cge.firms.eqE(theta, xie, tauz, phi, pz, pe, Z)[source]

Supply of exports.

\[E_{i} = \left(\theta_{i}^{\phi_{i}}\xi^{E}_{i}(1+\tau^{z}_{i}\frac{pz_{i}}{pe_{i}})\right)^{\frac{1}{1-\phi_{i}}}Z_{i}\]
Parameters

  • theta (1D numpy array) – Scaling coefficient of the ith good transformation from domestic output to exports

  • xie (1D numpy array) – Share parameter for the share of exports of good i used by firms exporting good i

  • tauz (1D numpy array) – Ad valorem tax rate on commodity i

  • phi (1D numpy array) – Transformation elasticity parameter between exports and domestic production of good i

  • pz (1D numpy array) – price of output good i

  • pe (1D numpy array) – Price of commodity i exports in domestic currency

  • Z (1D numpy array) – Output from exporters CET production function

Returns

Exports of good i

Return type

E (1D numpy array)

open_cge.firms.eqFsh(R, Kf, er)[source]

Domestic profits that are repatriated to foreign owners of capital.

\[Fsh = R \cdot Kf \cdot \varepsilon\]
Parameters

  • R (float) – Real return on domestic capital

  • Kf (float) – Foreign holdings of domestic capital

  • er (float) – The real exchange rate (foreign/domestic)

Returns

Fsh = Repatriated profits

open_cge.firms.eqM(gamma, deltam, eta, Q, pq, pm, taum)[source]

Demand for imports.

\[M_{i} = \left(\gamma^{\eta_{i}}_{i}\delta^{m}_{i}\frac{pq_{i}}{(1+\tau^{m}_{i})pm_{i}}\right)^{\frac{1}{1-\eta_{i}}}Q_{i}\]
Parameters

  • gamma (1D numpy array) – Scale parameter for CES production function

  • deltam (1D numpy array) – Share parameter for use of imports of good i in produciton Armington good i

  • eta (1D numpy array) – The elasticity of substitution between imports and domestically supplied good i

  • Q (1D numpy array) – The domestic supply of good i, the Armington good

  • pq (1D numpy array) – price of the Armington good (domestic + imports) for each good i

  • pm (1D numpy array) – The price of good i imports in domestic currency.

  • taum (1D numpy array) – Tariff rate on good i

Returns

Demand for imports of good i

Return type

M (1D numpy array)

open_cge.firms.eqQ(gamma, deltam, deltad, eta, M, D)[source]

CES production function for the importing firm.

\[Q(i) = \gamma_{i}\left[\delta^{m}_{i}M^{\eta_{i}}_{i} + \delta^{d}_{i}D^{\eta_{i}}_{i}\right]^{\frac{1}{\eta_{i}}}\]
Parameters

  • gamma (1D numpy array) – Scale parameter for CES production function

  • deltam (1D numpy array) – Share parameter for use of imports of good i in produciton Armington good i

  • deltad (1D numpy array) – Share parameter for use of domestically produced good i in produciton Armington good i

  • eta (1D numpy array) – The elasticity of substitution between imports of good i and domestically supplied good i

  • M (1D numpy array) – The imports of good i

  • D (1D numpy array) – The domestic supply of good i from domestic production

Returns

The domestic supply of good Q(i), the Armington good

Return type

Q (1D numpy array)

open_cge.firms.eqX(ax, Z)[source]

Demand for intermediate inputs.

\[X_{h,i} = ax_{h,j}Z_{j}\]
Parameters

  • ax (2D numpy array) – Fixed proportions of factor h used in production of good i (Leontief production function)

  • Z (1D numpy array) – Output of industry j

Returns

Demand for factor h used in the

production of good i

Return type

X (2D numpy array)

open_cge.firms.eqXv(lam, XXv)[source]

Investment demand for each good i

\[Xv_{j} = \lambda_{i}XXv\]
Parameters

  • lam (1D numpy array) – Fixed shares of investment for each good i

  • XXv (float??) – Total investment

Returns

Investment demand for each good i

Return type

Xv (1D numpy array)

open_cge.firms.eqY(ay, Z)[source]

Value added.

\[Y_{i} = ay_{i,j}Z_{j}\]
Parameters

  • ay (1D numpy array) – leontief production parameter, share of output of industry j in value added of good i

  • Z (1D numpy array) – Output of industry j

Returns

Value added of good i

Return type

Y (1D numpy array)

open_cge.firms.eqZ(theta, xie, xid, phi, E, D)[source]

Exporting firm production function.

\[Z_{i} = \theta_{i}\left[\xi_{i}^{E}E_{i}^{\phi_{i}} + \xi_{i}^{D}D_{i}^{\phi_{i}}\right]^{\frac{1}{\phi_{i}}}\]
Parameters

  • theta (1D numpy array) – Scaling coefficient of the ith good transformation from domestic output to exports

  • xie (1D numpy array) – Share parameter for the share of exports of good i used by firms exporting good i

  • xie – Share parameter for the share of domestically produced good i used by firms exporting good i

  • phi (1D numpy array) – Elasticity of substitution between exports (??) and domestically produced goods by firms exporting good i

  • E (1D numpy array) – Exports of good i

  • D (1D numpy array) – Domestically produced good i

Returns

Output from exporters CET production function

Return type

Z (1D numpy array)

open_cge.firms.eqpd(gamma, deltad, eta, Q, pq, D)[source]

Price of domestically produced goods from importers.

\[pd_{i} = \left(\gamma_{i}^{\eta_{i}}\delta^{d}_{i}pq_{i}\right)\left(\frac{D_{i}}{Q_{i}}\right)^{\eta_{i}-1}\]
Parameters

  • gamma (1D numpy array) – Scale parameter for CES production function

  • deltad (1D numpy array) – Share parameter for use of domestically produced good i in produciton Armington good i

  • eta (1D numpy array) – The elasticity of substitution between imports and domestically supplied good i

  • Q (1D numpy array) – The domestic supply of good i, the Armington good

  • pq (1D numpy array) – price of the Armington good (domestic + imports) for each good i

  • D (1D numpy array) – Demand for domestically produced good i from importers

Returns

price of domesically produced good i

Return type

pd (1D numpy array)

open_cge.firms.eqpe(er, pWe)[source]

World export price equation.

\[pe_{i} = \varepsilon \cdot pWe_{i}\]
Parameters

  • er (float) – The real exchange rate (foreign/domestic)

  • pWe (1D numpy array) – The export price of good i in domestic currency

Returns

The world export price of good i exports in foreign currency

Return type

pe (1D numpy array)

open_cge.firms.eqpm(er, pWm)[source]

World import price equation.

\[pm_{i} = \varepsilon \cdot pWm_{i}\]
Parameters

  • er (float) – The real exchange rate (foreign/domestic)

  • pWm (1D numpy array) – The world import price of good i in domestic currency.

Returns

The world import price of good i imports in foreign currency.

Return type

pm (1D numpy array)

open_cge.firms.eqpy(b, F, beta, Y)[source]

Production function.

\[Y_{i} = b_{i}\prod_{h}F_{h,i}^{\beta_{h,i}}\]
Parameters

  • b (1D numpy array) – Scale parameter for each good i

  • F (2D numpy array) – The use of factor h in the production of good i

  • beta (2D numpy array) – Cost share parameter for factor h in production of good i

  • Y (1D numpy array) – Value added for each good i

Returns

The difference between Y and the

production function evaluated at F.

Return type

py_error (1D numpy array)

open_cge.firms.eqpz(ay, ax, py, pq)[source]

Output prices.

\[pz_{i} = ay_{i}py_{i} + \sum_{i}ax_{h,i}pq_{i}\]
Parameters

  • ay (1D numpy array) – Leontief production parameter, share of output of industry j in value added of good i

  • ax (2D numpy array) – Fixed proportions of factor h used in production of good i (leontief production function)

  • py (1D numpy array) – The price of value added for each good i

  • pq (1D numpy array) – price of the Armington good (domestic + imports) for each good i

Returns

price of output good i

Return type

pz (1D numpy array)