# Transport sectors

The transport sector plays a specific role: it covers both regular transport activities, which are demanded and can be traded like any other service, and international transport of goods. The latter accounts for the difference between fob and cif values of traded goods. Thus, the market clearing equation for a transport sector sector presents two terms. The demand for transport activities other than freight and freight.

$$ Y_{TrT,r,t}=\underbrace{D_{TrT,r,t}+\sum_s\mathit{DEM}_{TrT,r,s,t}}_{\textrm{Regular transport activities}}+\underbrace{\mathit{Tr}_{TrT,r,t}^{Supply}}_{\textrm{Freight}} \\ P_{i,r,s,t}^{\mathit{CIF}}=P_{i,r,s,t}^{\mathit{FOB}}+\mu_{i,r,s}P^{Tr}_{i,r,s,t} $$

The transport sectors **needs to be considered as perfectly competitive** with constant returns to scale.
The two following sections present the modelling of the supply and demand for international transport of goods:

## Transport demand

For each trade flow, we define the corresponding demand for transport through a constant multiplier $\mu_{i,r,s}$

$$ \mathit{Tr}_{i,r,s,t}=\mu_{i,r,s} GnTC_{i,r,s,t} GnMC_{i,r,t} \mathit{DEM}_{i,r,s,t} $$

The freight demand is then brokendown by mode through a Cobb-Douglas specification:

$$ \mathit{Tr}_{TrT,i,r,s,t}^{Mode}=a_{TrT,i,r,s}^{Tr} \mathit{Tr}_{i,r,s,t} \frac{P_{i,r,s,t}^{Tr}}{P_{TrT,t}^{Tr^{Mode}}} $$

Thus, transportation price for a given route is defined as a Cobb-Douglas aggregate price:

$$ P_{i,r,s,t}^{Tr} = \prod_{TrT} {P_{TrT,t}^{{Tr}^{Mode}}}^{a_{TrT,i,r,s}^{Tr}} $$

## Transport supply

Each region contributes to the world supply of freight. The choice between the various transport exporters are made according to a Cobb-Douglas demand function:

$$ \mathit{Tr}_{TrT,r,t}^{Supply} = a_{TrT,r}^{Tr^{Supply}} WorldTr_{TrT,t} \frac{P_{TrT,t}^{Tr^{Mode}}}{P^Y_{TrT,r,t} \left( 1+tax_{Trt,r}^P\right)} $$

These supply is aggregated in a world supply of freight per mode:

$$ World_{TrT,t}^{Tr} = c^{Tr}_{TrT} \prod_r {Tr_{TrT,r,t}^{Supply}}^{a_{TrT,r}^{Tr^{Supply}}} $$

## Freight market clearing

$$ World_{TrT,t}^{Tr} = \sum_{i,r,s} \mathit{Tr}_{TrT,i,r,s,t}^{Mode} $$

## Variables definition

- $DEM_{i,r,s,t}$ : Demand in region $s$ of good $i$ from to region $r$
- $GnMC_{i,r,t}$ : Generalized marginal cost (different than 1 in monopolistic competition)
- $GnTC_{i,r,s,t}$ : Generalized trade cost (iceberg)
- $Tr_{i,r,s,t}$ : Transport demand by export
- $P_{i,r,s,t}^{Tr}$ : Price of transport by export
- $Tr_{TrT,i,r,s,t}^{Mode}$ : Transport demand by export per mode
- $P_{TrT,t}^{Tr^{Mode}}$ : Price of transport per mode
- $\mu_{i,r,s}$ : Transport demand per volume of good
- $WorldTr_{iTrT,t}$ : Transport aggregate per mode
- $Tr_{TrT,r,t}^{Supply}$ : Supply of international transportation sector $i$ in region $r$
- $c^{Tr}_{TrT}$ : Scale coefficient of the Cobb-Douglas
- $a_{TrT,i,r,s}^{Tr}$ and $a_{TrT,r}^{Tr^{Supply}}$ : Share coefficient of the Cobb-Douglas
- $P^Y_{TrT,r,t}$ : Production price

## Emissions from international transportation

Emissions from international transportation are allocated to international freight in a proportionale way:

$$ EmGHG^{Freight}_{g,TrT,r,t,sim} = \left[\sum_i EmGHG^{IC}_{g,i,TrT,r,t,sim} + EmGHG^{Y}_{g,TrT,r,t,sim}\right]\frac{TrSupply_{TrT,r,t,sim}}{Y_{TrT,r,t,sim}} $$

These emissions can enter the emission reduction policy or not, depending on the sector being liste in the `InternationalFreight`

set. In this case, $EmGHG^{Freight}$ is computed, but not added to carbon market emissions and not subject to carbon taxation.