A mathematical model of the economics of electric vehicles compared to traditional liquid/gas-powered cars

Here are some key variables that would need to be included in the model:

1. Vehicle purchase price - This would include the purchase price of the EV and the gas-powered car, as well as any applicable tax credits or incentives.
2. Fuel cost - This would include the cost of electricity for the EV and the cost of gasoline for the gas-powered car. It would also factor in the fuel efficiency of each vehicle, measured in miles per gallon (MPG) for the gas-powered car and miles per kilowatt-hour (miles/kWh) for the EV.
3. Maintenance and repair costs - This would include the cost of routine maintenance, such as oil changes and tire rotations, as well as any major repairs that may be needed over the life of the vehicle.
4. Resale value - This would consider the estimated resale value of each vehicle after a certain number of years, as well as any potential tax implications of selling the vehicles.
5. Financing costs - This would include the interest rate on any loans or financing used to purchase the vehicles, as well as any fees or charges associated with the financing.

Using these variables, we could create a mathematical model that calculates the total cost of ownership for an EV and a gas-powered car over a certain period, such as five or ten years. The model could be used to compare the total cost of ownership of the two vehicles and determine the payback period for the initial investment in the EV. By adjusting the variables in the model, we could also analyze the impact of different factors, such as changes in fuel prices or maintenance costs, on the total cost of ownership of each vehicle.

The mathematical expression for comparing the total cost of ownership of an electric vehicle (EV) and a gas-powered car over a certain period of time could be:

Total Cost of Ownership (TCO) = Purchase Price + Fuel Cost + Maintenance and Repair Costs + Financing Costs - Resale Value

Where:

Purchase Price: The initial purchase price of the EV and the gas-powered car

Fuel Cost: The cost of fuel over the specified period, including the cost of electricity for the EV and the cost of gasoline for the gas-powered car.

It is calculated as:

Fuel Cost = (Total Miles Driven / Vehicle Efficiency) * Fuel Cost per Unit

Where Total Miles Driven is the estimated number of miles driven over the specified period, Vehicle Efficiency is the fuel efficiency of the vehicle in miles per gallon (MPG) for the gas-powered car and miles per kilowatt-hour (miles/kWh) for the EV, and Fuel Cost per Unit is the cost of fuel per gallon for the gas-powered car and cost of electricity per kilowatt-hour for the EV.

Maintenance and Repair Costs: The estimated cost of routine maintenance and any major repairs over the specified period.

Financing Costs: The cost of financing the vehicles over the specified period, including interest and fees.

Resale Value: The estimated resale value of the vehicles at the end of the specified period.

The TCO value can be calculated separately for the EV and the gas-powered car, and then compared to determine which vehicle has the lower total cost of ownership over the specified period. The payback period for the initial investment in the EV can also be calculated by subtracting the TCO of the gas-powered car from the TCO of the EV and dividing by the difference in initial purchase price.