Modern biofuel mandates establish targets for carbon intensities of the motor fuel that is sold in a jurisdiction. British Columbia has the Low Carbon Fuel Act which establishes a Low Carbon Fuel Standard (LCFS). The federal government of Canada has the Clean Fuel Regulations (CFR) since 2022. Originally such mandates were simple blending mandates, for example 5% ethanol content in gasoline. This is still the practice in some jurisdictions. However, the current generation of biofuel mandates sets specific carbon intensity targets that need to be met.

British Columbia's LCFS establishes a baseline emission intensity for fuels: 93.67 gCO2e/MJ for gasoline and 94.38 gCO2e/MJ for diesel. The physical units are grams of carbon dioxide (equivalent) per Megajoule. The overall target is a reduction of 30% in the carbon intensity of motor fuels by 2030. The mandated carbon intensities for the following years are shown in the table below.

The federal targets under the Clean Fuel Regulations are weaker; for 2030 they target 81.0 gCO2e/MJ for gasoline and 79.0 gCO2e/MJ for diesel, with baseline carbon intensities for gasoline of 95 gCO2e/MJ and 93 gCO2e/M for diesel. Also useful to know is the energy density of these fuels: 34.69 MJ/L for gasoline and 38.65 MJ/L for diesel. For gasoline, a target of 81 gCO2e/MJ translates into 2.81 kilograms of CO2 per litre, relative to the baseline of 3.30 kg/L. Note that the carbon intensity that is used as a baseline is measured on a life-cycle basis. Typically, a motor vehicle emits about 2.3 kg/L of carbon dioxide through combustion. The difference to the baseline is determined by the "upstream" emissions.

Let us explore the economics of the mandate through a simple mirco-economic model. Fuel suppliers must blend fuels (or offer them separately) at a ratio \(\theta\) to achieve the mandated carbon intensity target \(\bar{e}\). Fossil fuels have the initial carbon intensity \(e_f\) and the average of supplied biofuels have emission intensity \(e_b\). Then the mandate requires meeting the target \[\bar{e}=\theta e_b+(1-\theta)e_f\] which in turn implies that the required blending (market share) ratio for biofuels is \[\theta=\frac{e_f-\bar{e}}{e_f-e_b}\]

Producing biofuels is more costly then producing fossil fuels—otherwise the market would already be dominated by biofuels. Producing biofuels becomes increasingly costly with lower carbon intensity, although in the long term innovation may (and very likely will) change that. One can capture the cost structure as a function that depends on the emission intensity \(e_b\) of the biofuel relative to the emission intensity \(e_f\) of the fossil fuel: \[ c_b = c^\circ_b\cdot\exp\left(\frac{e_f-e_b}{\beta}\right) > c_f \] Parameter \(c^\circ_b\) is the initial cost of producing biofuel without emission reductions, and parameter \(\beta>0\) identifies the increase in costs when the emission intensity of biofuel is pushed towards zero. The higher the \(\beta\), the flatter the cost trajectory for biofuels. Production cost increase at an increasing rate as emission intensities are lowered. The producers thus face combined total production cost of \[ C= \theta c_b +(1-\theta) c_f\] The producer knows the blending ratio \(\theta\) given the choice of emission intensity \(e_b\), but that emision intensity still needs to be determined. The biofuel producer still need to find the cost-minimal solution. This turns out to be \[ e_b =e_f-\beta\Lambda\] where \(\Lambda\equiv 1+W(-c_f/c^\circ_b/\exp(1))\) is a positive constant defined by the Lambert-W function. For \(c_f/c^\circ_b\) increasing from 1 to 2, \(\Lambda\) increases concavely from 1 to 1.77; without an initial cost mark-up, \(\Lambda=1\). Essentially, \(\Lambda\) captures the initial cost mark-up.

With the optimal emission intensity \(e_b\), the production cost becomes \(c_b=c^\circ_b\exp(\Lambda)\), which means that the initial cost gap gets magnified.

Interestingly, the above result for the optimal \(e_b\) is independent of the policy stringency. The optimal emission intensity \(e_b\) for biofuels is technology-driven rather than policy-driven. Essentially, the biofuels technology is driven to the point where the the average cost mark-up per unit of emission intensity reduction is equal to the marginal cost increase. Inserting this result back into the blending ratio, we find the market share of biofuels as \[\theta=\frac{e_f-\bar{e}}{\beta\Lambda} \] Here the policy stringency matters. Lowering \(\bar{e}\) will increase the market share \(\theta\) of biofuels. Similarly, a flatter cost structure for biofuels—finding lower carbon-intensive fuels is not too hard—will also allow for a higher market share of biofuels.

Note that the market share of biofuels cannot exceed one. If the policy target \(\bar{e}\) falls below the optimal \(e_b\), then fossil fuels are completely displaced and \(e_b\) must become equal to \(\bar{e}\), and only biofuels are produced.

But what is the optimal policy stringency? Let's push the policy to the extreme and ask what happens when biofuels replace fossil fuels completely as \(\theta\rightarrow1\). The cost difference divided by the emission intensity difference is an implicit carbon price that we can compare with the social cost of carbon \(\Psi\), suitably expressed in units of (¢/L)/(gCO2e/MJ) by multiplying it with the energy intensity of gasoline \(\Theta=0.003469.\). We find that if \[\frac{c_b-c_f}{e_f-e_b}=\frac{c^\circ_b\exp(\Lambda)-c_f}{\beta\Lambda}<\Psi \Theta \] then it is socially optimal to strive for displacing fossil fuels completely. When \(\Lambda\rightarrow0\), then the implicit carbon price becomes simply \((c^\circ_b-c_f)/\beta\), which means that either a low initial price gap or a flat slope of biofuel cost increases will make this scenario more likely.

The above discussion shows that biofuel mandates can be very effective in displacing fossil fuels. As long as the extra expense for biofuels is below the threshold for the social cost of carbon, the policy is eminently sensible.

Let's do some calculations. If we start with a social cost of carbon of $250/tonne, then \(\Psi\Theta=0.86725\)(¢/L)/(gCO2e/MJ). If we can reduce the carbon intensity of fuels from 95 to 35 gCO2e/MJ, and this comes at a cost markup for biofuels of 30 cents per litre, we get 0.5—well below the social cost of carbon.

At this point there is hardly any notion that biofuels have increased fuel prices. In fact, Navius Research (2023) finds that there was a negative abatement cost for gasoline because blending ethanol raised the octance level. This means there's still plenty of scope to expand biofuels production, supported by rigorous life-cycle analysis of carbon intensities.