Add Armington model case where each location produces only one good.

Author: SebKrantz

src/main/optimal_network.jl

@@ -88,7 +88,10 @@ function optimal_network(param, graph; I0=nothing, Il=nothing, Iu=nothing, verbo
         model = model_partial_mobility(optimizer, auxdata)
         recover_allocation = recover_allocation_partial_mobility    
     elseif param.mobility == 0 && !param.cong
-        if param.beta <= 1 && param.a < 1 && param.duality
+        if all(sum(param.Zjn .> 0, dims = 2) .<= 1) # Armington case
+            model = model_fixed_armington(optimizer, auxdata)
+            recover_allocation = recover_allocation_fixed_armington
+        elseif param.beta <= 1 && param.a < 1 && param.duality
             model = model_fixed_duality(optimizer, auxdata)
             recover_allocation = recover_allocation_fixed_duality
         else

src/models/model_fixed_armington.jl

@@ -0,0 +1,74 @@
+# The primal case, no mobility, no cross-good congestion, and an Armington (1969) world where each location produces only one good
+
+function model_fixed_armington(optimizer, auxdata)
+
+    # Extract parameters
+    param = auxdata.param
+    graph = auxdata.graph
+    kappa_ex_init = auxdata.kappa_ex
+    A = auxdata.edges.A
+    Apos = auxdata.edges.Apos
+    Aneg = auxdata.edges.Aneg
+    psigma = (param.sigma - 1) / param.sigma
+    Lj = param.Lj
+    # Production: Fixed because just one good is produced by each location
+    Yj = dropdims(sum(param.Zjn, dims = 2) .* Lj .^ param.a, dims = 2)
+
+    # Model
+    model = Model(optimizer)
+    set_string_names_on_creation(model, false)
+
+    # Variables
+    @variable(model, Cjn[1:graph.J, 1:param.N] >= 1e-8, container=Array, start = 1e-6)
+    @variable(model, Qin[1:graph.ndeg, 1:param.N], container=Array, start = 0.0)
+
+    # Parameters: to be updated between solves
+    @variable(model, kappa_ex[i = 1:graph.ndeg] in Parameter(i), container=Array)
+    set_parameter_value.(kappa_ex, kappa_ex_init)
+
+    # Defining Utility Funcion: from Cjn + parameters (by operator overloading)
+    @expression(model, Cj, sum(Cjn .^ psigma, dims=2) .^ (1 / psigma))
+    @expression(model, cj, ifelse.(Lj .== 0, 0.0, Cj ./ Lj))
+    @expression(model, uj, ((cj / param.alpha) .^ param.alpha .* (param.hj / (1-param.alpha)) .^ (1-param.alpha)) .^ (1-param.rho) / (1-param.rho))
+    @expression(model, U, sum(param.omegaj .* Lj .* uj))
+    @objective(model, Max, U)
+
+    # Balanced flow constraints
+    @constraint(model, Pjn[j in 1:param.J, n in 1:param.N],
+        Cjn[j, n] + sum(A[j, i] * Qin[i, n] for i in 1:graph.ndeg) -
+        Yj[j] + sum(
+            ifelse(Qin[i, n] > 0, Apos[j, i], Aneg[j, i]) *
+            abs(Qin[i, n])^(1 + param.beta) / kappa_ex[i]
+            for i in 1:graph.ndeg
+        ) <= 0
+    )
+    return model
+end
+
+function recover_allocation_fixed_armington(model, auxdata)
+    param = auxdata.param
+    graph = auxdata.graph
+    model_dict = model.obj_dict
+    results = Dict()
+    # Production: Fixed because just one good is produced by each location
+    Yj = dropdims(sum(param.Zjn, dims = 2) .* param.Lj .^ param.a, dims = 2)
+    WY = param.Zjn .> 0
+
+    results[:welfare] = value(model_dict[:U])
+    results[:Yjn] = WY .* Yj
+    results[:Yj] = Yj
+    results[:Cjn] = value.(model_dict[:Cjn])
+    results[:Cj] = dropdims(value.(model_dict[:Cj]), dims = 2)
+    results[:Ljn] = WY .* param.Lj
+    results[:Lj] = param.Lj
+    results[:cj] = dropdims(value.(model_dict[:cj]), dims = 2)
+    results[:hj] = ifelse.(results[:Lj] .== 0, 0.0, param.Hj ./ results[:Lj])
+    results[:uj] = dropdims(value.(model_dict[:uj]), dims = 2)
+    # Prices
+    results[:Pjn] = shadow_price.(model_dict[:Pjn])
+    results[:PCj] = dropdims(sum(results[:Pjn] .^ (1-param.sigma), dims=2), dims = 2) .^ (1/(1-param.sigma))    
+    # Network flows
+    results[:Qin] = value.(model_dict[:Qin])
+    results[:Qjkn] = gen_network_flows(results[:Qin], graph, param.N)
+    return results
+end