Choosing a Technology Based on Relative Input Prices

A textile firm is evaluating four different production methods to produce 100 meters of cloth. The resources required for each method are listed below. Assuming the firm's goal is to be as efficient as possible, which method represents an illogical choice that a rational firm would never select, regardless of the specific costs of labor or coal?

Production Efficiency Analysis

A firm is evaluating different technologies to produce one ton of steel. Each technology requires a specific amount of labor (number of workers) and energy (tons of coal). A technology is 'dominated' if another available technology can produce the same output using a smaller quantity of at least one input without using more of any other input.

Technology Data:

• Technology A: 2 workers, 8 tons of coal
• Technology B: 4 workers, 7 tons of coal
• Technology C: 3 workers, 9 tons of coal
• Technology D: 4 workers, 5 tons of coal

Based on the data, match each technology pair with the correct description of their relationship.

A manufacturing firm is assessing two different techniques to produce 1,000 units of a product.

• Technique Alpha requires 2 machine hours and 10 labor hours.
• Technique Beta requires 3 machine hours and 8 labor hours.

Based on this information, Technique Alpha is considered to be the dominant production choice.

Rationale for Eliminating Dominated Technologies

Critique of a Production Decision

A firm is analyzing four production technologies to produce 500 widgets, each requiring a certain number of workers and units of raw material.

• Technology P: 4 workers, 10 units of material
• Technology Q: 5 workers, 8 units of material
• Technology R: 4 workers, 12 units of material
• Technology S: 6 workers, 7 units of material

Based on this data, Technology R is clearly inefficient because it is dominated by Technology ____.

Designing an Inefficient Production Technology

A production manager is analyzing four different methods to assemble one computer server. Each method uses a specific amount of labor (in hours) and a number of standard component units. The manager concludes: 'After reviewing the data, it is clear that Technology Q is the only efficient option we should consider, as it minimizes the number of components used.'

Technology Data (per server):

• Technology P: 10 labor hours, 20 components
• Technology Q: 12 labor hours, 18 components
• Technology R: 10 labor hours, 22 components
• Technology S: 11 labor hours, 20 components

Which of the following statements provides the most accurate evaluation of the manager's conclusion?

A firm wants to choose the most cost-effective way to produce a specific quantity of goods. It has identified several different production technologies, each using different combinations of two inputs (e.g., labor and energy). Arrange the following actions into the correct logical sequence that the firm should follow to make its decision.