Final answer:
To determine the average annual cost of a refrigerator, we must consider the initial purchase price, annual electricity costs, and additional external costs reflected in the manufacturing process. A rational function to model this takes into account these variables over a period of x years, factoring in the potential payback period for more energy-efficient models.
Step-by-step explanation:
To model the average annual cost of a refrigerator kept for x years as a rational function, we need to consider both the initial cost of purchasing the refrigerator and the ongoing costs of running it. The initial manufacture cost of a refrigerator is given, and additional costs such as electricity usage and the cost of externalities related to pollution are mentioned.
The annual cost to run the refrigerator can be estimated using the electricity cost per kWh and the usage rate. If the refrigerator uses 2.4 kWh per day, the cost per year to run it at $0.15 per kWh is calculated as: (2.4 kWh/day) * (365 days/year) * ($0.15/kWh). Now, considering a new, more efficient refrigerator that uses 1.8 kWh per day, similar calculations will apply for the cost per year of running the new refrigerator.
To factor in the external costs of pollution, we can look at how these costs impact the price of refrigerators when they are internalized by the firm. A $100 cost of pollution per refrigerator, when factored into the manufacturing process, increases production costs and is reflected in the market price to some extent, shown by a $50 increase in the final price to consumers according to Table 12.2. This change affects the supply curve and thus the overall cost structure of the refrigerator over its lifetime.
Now, to model the average annual cost for x years, it's a matter of combining these costs with the initial purchase price and any cost savings from utilizing a more efficient model against the less efficient one. We'd also account for the time it takes for the energy savings to 'pay back' the initial higher cost of purchasing a more energy-efficient refrigerator, as indicated by the 9-year payback period mentioned.
In summary, the rational function to model the cost could take the form: Average Annual Cost = (Initial Purchase Price + (Electricity Usage per year * Electricity Cost per kWh + External Costs) * x) / x, where x is the number of years the refrigerator is kept.