Let's break down the calculation for the monthly bill of the customer for both companies under the given situation (a).

First Company:

• Charges: $3 per month per kilowatt (kW) of installed capacity
• Credit: $0.03 per kilowatt-hour (kWh) for excess electricity exported to the grid

For a customer who:

• Owns a 3-kW system
• Exports 150 kWh to the grid

1. Cost for Installed Capacity: $$\text{Cost} = 3 , \text{kW} \times 3 , \frac{$}{\text{kW}} = 9 , $$$

2. Credit for Exported Electricity: $$\text{Credit} = 150 , \text{kWh} \times 0.03 , \frac{$}{\text{kWh}} = 4.50 , $$$

3. Monthly Bill: $$\text{Monthly Bill} = \text{Cost} - \text{Credit} = 9 - 4.50 = 4.50 , $$$

Thus, the monthly bill for a customer of the first company is $4.50.

Do you have any questions on this? Would you like me to proceed with part (b) or the second company calculation for part (a)?

Here are 5 relative questions for you to consider:

1. What is the overall cost structure for larger systems?
2. How does exporting more kWh affect the final bill in both companies?
3. How would the bill change if the first company raised the per kWh credit?
4. What would happen if the system produced no excess electricity?
5. How does the flat rate model compare in terms of risk for customers?

Tip: Always check the break-even point to understand which company is more favorable in different usage scenarios.