Production and Factor Demand

Production and Factor Demand#

In the standard model, production combines a composite of primary factors with intermediate inputs.

Composite factor production#

For good \(i\),

\[Y_i = b_i \prod_h F_{h,i}^{\beta_{h,i}}.\]

Here:

  • \(Y_i\) is composite factor output;

  • \(F_{h,i}\) is demand for factor \(h\);

  • \(\beta_{h,i}\) is the calibrated factor share; and

  • \(b_i\) is a scale parameter.

Cost minimisation implies factor demand:

\[F_{h,i} = \frac{\beta_{h,i}\,p_i^y\,Y_i}{p_h^f}.\]

Intermediate inputs#

Intermediate demand is Leontief:

\[X_{i,j} = a^x_{i,j} Z_j,\]

and composite-factor demand is:

\[Y_i = a_i^y Z_i.\]

The zero-profit unit-cost condition is:

\[p_j^z = a_j^y p_j^y + \sum_i a^x_{i,j} p_i^q.\]

These relationships correspond to eqpy, eqF, eqX, eqY, and eqpzs in the standard model implementation.

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