per unit of labour. Households also make shopping trips to subcenter j with a
travel time αdtj , per unit of differentiated good, where αd denotes the number
of shopping trips per unit of consumption, for i, j =1, ..n. These two trips are
treated as independent (trip chaining is not considered here). The intermediary
(homogenous) goods needed in the subcenters are transported from the center
to the subcenter with a travel time per unit of intermediary good of αhti, where
αh denotes the number of freight trips per unit of production. We first neglect
congestion; in this case transportation cost ti is independent of the number of
drivers using the road. Later, we treat congestion by recognizing that the trans-
portation cost increases with the number of cars and trucks and decreases with
road capacity.
2.1 The production possibilities
There are N households who all work and each household supplies a fixed
amount, (1 + θ) units of labour time. The production of one unit of the differ-
entiated good requires one unit of labour time. The remaining labour time of
the household θ is devoted to the production of the homogeneous good. Each
worker household consumes one unit of the differentiated good, the rest of his
income is spent on the homogenous good.
We assume linear production technologies. The homogeneous good is pro-
duced using labour in a one to one ratio (one unit of the homogeneous good is
produced during one unit of time). The homogeneous good is either consumed
directly or used as input for the differentiated good and for the transport ser-
vices (fixed and variable input). The production of the differentiated good in
subcenter i requires a fixed set-up cost F (in the form of inputs of the ho-
mogeneous good) per subcenter and an intermediate input equal to c1 units
of the homogeneous good per unit of the differentiated good. Moreover, each
subcenter requires some road infrastructure. The production of this road infras-
tructure requires K units of the homogeneous good. The total consumption of
the homogeneous good is denoted by G.
We can present the total production possibilities of the economy by compar-
ing the net inputs and the total uses of the homogeneous good. We have the
following identity for the supply and the demand for labour:
(1 + θ) N = D + c1D + nF + (αw + αd + αh) X tiDi + nK + G, (1)
i=1...n
where the LHS represents the total supply of labour. The first term in the RHS
represents the direct use of labour in the production of the differentiated good
(DwithD= N)) while the remaining terms represent the use of the homoge-
neous good as input into the production of the differentiated good (c1D + nF),
to pay for the transportation costs αw + αd + αh i=1...n tiDi and to pay for
the infrastructure cost nK . The remaining production of the homogeneous good
(G) is used as the final consumption good by the household..