**2. Methodology**

### *2.1. CAFEs and CAFE Targets for Automobile Manufacturers*

The CAFE of each automobile manufacturer, *C* (km/L), was estimated based on the number of new vehicle sales and the published fuel economy values using the following equation:

$$C = \frac{X}{\sum\_{i=1}^{N} x\_i} \tag{1}$$

where *X* is the number of new vehicle sales of a particular automobile manufacturer *j*, *zi* (km/L) is the fuel economy value of vehicle model *i* of the automobile manufacturer, and *xi* is the number of vehicle model *i* that the automobile manufacturer sold for the year. Furthermore, *N* is the number of different vehicle models sold by the relevant automobile manufacturer. As the CAFE obtained from Equation (1) increases, the fuel economy of the 'average vehicle' sold by the relevant automobile manufacturer improves. The CAFE target, *C*-(km/L), is calculated as follows [4]:

$$\widetilde{\mathbf{C}} = \frac{X}{\sum\_{k=1}^{M} \mathbf{x}\_k} \tag{2}$$

where *zk* (km/L) is the target fuel economy value for a predefined passenger vehicle weight category *k*, *xk* is the total number of sales of vehicle models belonging to vehicle weight category *k* by a particular automobile manufacturer, and *M* is the number of vehicle weight categories.
