Final answer:
With the cost of labor at $40 and the cost of a machine at $50, the labor-intensive method costs $80, while machine-intensive and neutral methods cost $90 each. Hence, the firm should choose the labor-intensive production method as it is cheaper, assuming one unit of labor and machine per method.
Step-by-step explanation:
When considering the change in production costs, if the cost of labor remains at $40 and the cost of a machine decreases to $50, we need to calculate the total cost for each method of production. Without specific details on how many units of labor and machines are required for each method, we'll assume one unit of each for simplicity. With these costs, a labor-intensive method would cost $80 ($40 labor + $40 machine), a machine-intensive method would cost $90 ($40 labor + $50 machine), and a neutral method—if it uses one unit of each—would cost $90 as well.
Given these calculations, the firm should use the labor-intensive production method since it has the lowest total cost at $80 compared to $90 for the machine-intensive and neutral methods. However, this decision might change depending on the specifics of the firm's production needs and the quantities of labor and machines required for each method.