In economics, as opposed to accounting, costs have to include both explicit and implicit cost (see Mankiw 2018 Principles of Microeconomics 8th Ed p 249).
The explicit costs of that fuel is \$0.50 (in yesterday dollars), this is what you explicitly paid for your fuel.
When it comes to implicit 'opportunity' costs things are more difficult. Opportunity cost is defined as value of the next best alternative. Presumably here it is to resell that car fuel on some 2nd hand market for its market price.
One alternative is to resell that fuel today for \$1 per liter (current dollars). Another alternative is to resell it for some future unknown price \$$p$ per liter (in future dollars).
Hence this is what you have to do to solve the riddle:
Step 1
Determine what is the next best alternative. Is it to resell the fuel for \$1 or for expected future price $p$. Since the future price $p$ is in future dollars you also need to do adjustment for time value of money. Hence what you need to first figure out is the relationship between:
$$ 1 \quad ? \quad \frac{E[p]}{1+i} $$
where $?$ is stand in for $=, >, <$, E is expectation operator, it just indicates you have to make best guess of what $p$ is, finally $i$ is your preferred interest rate that should adjust both for inflation and real factors such as your personal 'preferred' level of impatience.
There are three possible outcomes either:
- $$ 1 \quad = \quad \frac{E[p]}{1+i} $$
in that case use which ever you like 1 or $\frac{E[p]}{1+i} $, as opportunity cost per liter, since they are equal.
- $$ 1 \quad > \quad \frac{E[p]}{1+i} $$
in this case opportunity cost per liter is 1 because that is your best alternative.
- $$ 1 \quad < \quad \frac{E[p]}{1+i} $$
in this case you should use $\frac{E[p]}{1+i}$ ass opportunity cost. You will need to form some guess about future price $p$, of course nobody knows future, but $p$ should be the best guess you can make with your information, it could just be random walk (in case you have zero information). Also you need to fill in $i$, $i$ will be rate of inflation + any compensation you believe you should get for postponing consumption, both expressed in decimals.
Step 2
Add all explicit and implicit cost. Since explicit costs were incurred yesterday, in yesterday dollars you have to adjust value of past cots to present otherwise you are comparing apples and oranges.
Hence you need to calculate $0.5(1+i_p)$ first where $i_p$ is your past personalized nominal interest rate, which depends on past inflation and your past impatience etc.
Next you just add them, due to uncertainty you need to do it for all three outcomes above (although outcome 1 and 2 have the same opportunity cost)
For OC from outcome 1 & 2:
Here the economic cost of your gas will be:
$$0.5(1+i_p)+1 = 1.5 + 0.5 i_p$$
So if the interest rate is 5% it would be $\approx \\\$1.53$ per liter.
For OC from outcome 3:
Here the economic cost of your gas will be:
$$0.5(1+i_p)+\frac{E[p]}{1+i} $$
For example, if $i_p$ is 5%, $i$ 10% and $E[p]=2$ then the price per liter will be $\approx \\\$2.34$ per liter.
This is how to get the economic cost of your ride. Unfortunately your riddle has not enough information to fully resolve it but you can fix your riddle by providing parameter values for $i_p$, $i$ and $E[p]$. If you do so you can calculate precisely what the economic cost of your ride is.
PS:
The above is the intertemporal total economic cost of that fuel, but for decision making purposes, whether to take the ride or not take the ride, past non-recoverable costs are sunk ex post. So the past \$0.5 while being part of the total intertemporal economic cost, should not be included in your present day decision making because it happened in past. If you would just be now at a pump thinking whether to pump that \$0.5 per little gas you should include it, but once its pumped the costs are sunk, so you should take a ride if your value of ride is higher than opportunity cost (so in your example \$1 or \$$E[p]/(1+i)$, whichever is larger).
