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Conditional dynamic sourcing

solve_sourcing_adjustment chooses origin quantities for one unit of a CES composite at each date. Delivered prices are exogenous. It minimizes

\[\sum_{t=0}^{T-1}\delta^t\left[p_t'q_t+ \frac{\kappa}{2}\sum_o\frac{(q_{to}-q_{t-1,o})^2}{\alpha_o}\right]\]

subject to CES production of at least one unit:

\[F(q_t)=\left[\sum_o\alpha_o(q_{to}/\alpha_o)^{(\sigma-1)/\sigma} \right]^{\sigma/(\sigma-1)}\ge1.\]

For sigma=1, use the Cobb–Douglas limit. Shares are strictly positive and sum to one; baseline origin prices are one and initial quantities default to the shares. CES is concave, its superlevel feasible set is convex, and adjustment costs are convex. Free disposal is permitted. There is no production requirement or switching cost after the last date: horizon choice is part of the model.

import pandas as pd
from puremacro.trade import solve_sourcing_adjustment

prices = pd.DataFrame({"domestic": [1., 1., 1., 1.],
                       "imported": [1., 1.3, 1.3, 1.]})
result = solve_sourcing_adjustment(
    prices, pd.Series({"domestic": .7, "imported": .3}),
    elasticity=3., adjustment_cost=2., discount=.99,
)
print(result.accounts)
print(result.diagnostics)

Accounts separate procurement, adjustment resources, total cost, output and the frictionless CES index. Numerical acceptance requires production feasibility, reconstructed KKT stationarity and complementarity. A failed optimization or an unresolved artificial quantity floor raises, preserving the failure.

This model supplies a conditional sourcing mechanism. It does not determine national wages, output, trade balances, worker mobility or tariff recycling. Passing total unit costs into household prices is an explicit transmission assumption, as in the observed household study. The existing dynamic MRIO equilibrium has a different economic closure; the two models are not interchangeable.