Question

It would cost the town of Irondale \(\$ 50\) million to build a gaspowered generator that could produce a maximum of 5 megawatts of electricity at 15 cents per hour. Another alternative would be for Irondale to build a \(\$ 100\) million coal-fired generator that could produce a maximum of 15 megawatts of electricity at 5 cents per hour. Irondale should: a. Build the coal-fired generator because its hourly operating costs are so much lower. b. Build the gas-powered generator since it is less expensive to build. c. Build the coal-fired generator because, while it would cost twice as much to build, it would produce three times as much electricity. d. Obtain more information before deciding what to do.

Short answer

d. Obtain more information before deciding what to do.

Step-by-step solution

Analyze Initial Costs

First, we consider the initial cost of each generator. The gas-powered generator will cost \\(50 million to build, while the coal-fired generator will cost \\)100 million. This indicates that the gas-powered generator is less expensive initially.

Calculate Maximum Electricity Output Per Generator

Next, compare the maximum electricity outputs: the gas-powered generator can produce up to 5 megawatts, while the coal-fired generator can produce up to 15 megawatts. Thus, the coal-fired generator has a larger capacity, three times that of the gas-powered generator.

Compare Operating Costs

The operating cost for the gas-powered generator is 15 cents per hour, per megawatt. For the coal-fired generator, it is 5 cents per hour, per megawatt. Therefore, the coal-fired generator is more economical to operate, costing one-third of the gas-powered generator's operating cost per megawatt.

Determine Long-Term Benefits

Consider long-term benefits; the coal-fired generator, although more expensive to build, is more cost-effective in terms of operation and provides three times more output. Hence, over time, the benefits due to lower operating costs and higher capacity might outweigh the initial high cost.

Evaluate Missing Information

Before making a definitive decision, it's prudent to evaluate what other factors might affect Irondale's decision—such as environmental impact, maintenance costs, potential energy demands, or changes in fuel prices. Without this information, it is hard to decide definitively simply based on the given economic factors.

Key concepts

Initial Costs

The initial costs refer to the money spent upfront to build the generator. In Irondale's scenario, constructing a gas-powered generator would require $50 million, whereas a coal-fired generator would double that amount, requiring $100 million.

This upfront expense is significant because it determines how much capital Irondale needs to start the project.

• The gas-powered generator is a lower initial investment.
• The coal-fired generator requires a larger investment, but potentially offers more benefits due to its larger capacity.

In making a decision, considering only initial costs could mislead stakeholders away from the full picture of economic impact over time.

Operating Costs

Operating costs include all the expenses required to run the generator once it is built. For Irondale:

• The gas-powered generator costs 15 cents per megawatt-hour.
• The coal-fired generator costs 5 cents per megawatt-hour.

These costs are crucial when evaluating the total cost of electricity production over time.

Lower operating costs lead to savings in the long term.

This is especially true for the coal-fired generator, which becomes more affordable due to its low per-hour expense compared to the gas-powered generator, assuming fuel prices remain stable.

Electricity Output

Electricity output tells us how much energy each generator can produce at maximum capacity. In this case:

• The gas-powered generator can supply up to 5 megawatts.
• The coal-fired generator can supply up to 15 megawatts—three times more.

This capacity difference is significant. Higher output means meeting greater demand or fewer shortages during peak usage times.

For Irondale, the coal-fired generator's ability to produce more power suggests it is better equipped to satisfy both current needs and any future increases in energy demand.

Long-Term Benefits

Long-term benefits encompass the overall advantages gained from choosing a particular generator after considering both costs and output over time. Factors include:

• Cost-effectiveness thanks to lower operating expenses.
• Greater energy output for community needs.

Although initially more expensive, the coal-fired generator seemingly offers substantial savings and greater energy production in the long run.

By providing a higher capacity at lower operational costs, it allows Irondale to manage its energy requirements more efficiently as time progresses. However, accounting for other considerations, like environmental impacts and technological advancements, is also important to your decision.