Trade-off Between Labor Productivity and Energy Intensity in Competing Technologies

Technology E: Input Coordinates (10, 1) and Coal-to-Labor Ratio

Technology A: An Energy-Intensive Method with Coordinates (1, 6)

Technology B: A Labor-Intensive Method with Coordinates (4, 2)

A graph is used to compare three different technologies (P, Q, and R) available for producing 100 units of a product. The horizontal axis represents the number of workers, and the vertical axis represents the tons of energy required. The input combinations for each technology are as follows: Technology P=(2 workers, 8 tons of energy), Technology Q=(5 workers, 5 tons of energy), and Technology R=(8 workers, 2 tons of energy). If the price of energy were to increase substantially while wages remained constant, which technology would experience the greatest increase in its total production cost?

A graph is used to represent two different production technologies, Technology X and Technology Y, for producing a specific quantity of a good. The horizontal axis measures units of labor, and the vertical axis measures units of energy. Technology X is represented by the point (2, 8), meaning it requires 2 units of labor and 8 units of energy. Technology Y is represented by the point (5, 5), requiring 5 units of labor and 5 units of energy. Which statement correctly analyzes the relationship between these two technologies?

Technology Investment Decision

A graph is used to represent four different production technologies. The horizontal axis measures the number of workers (labor), and the vertical axis measures tons of energy. Given the input requirements for each technology below, match each technology to its correct description.

On a graph where the vertical axis represents units of energy and the horizontal axis represents units of labor, Technology B, which requires 10 units of energy and 5 units of labor to produce a certain output, is considered more energy-intensive than Technology A, which requires 9 units of energy and 3 units of labor for the same output.

Interpreting Technology Rays

Justifying Technology Choice Under Shifting Economic Conditions

A manufacturing firm is analyzing four potential production technologies (Alpha, Beta, Gamma, Delta) for creating a standard product batch. Each technology is defined by its input requirements on a graph where the horizontal axis represents the number of workers (labor) and the vertical axis represents the units of energy consumed. The input combinations are as follows:

• Technology Alpha: (2 workers, 10 units of energy)
• Technology Beta: (8 workers, 4 units of energy)
• Technology Gamma: (4 workers, 8 units of energy)
• Technology Delta: (5 workers, 5 units of energy)

Arrange these technologies in order from the MOST energy-intensive to the LEAST energy-intensive.

On a graph where the horizontal axis represents units of labor and the vertical axis represents units of energy, a ray is drawn from the origin through the point (5, 10) to represent Technology X. Another ray for Technology Y passes through the point (8, 12). For every one unit of labor, Technology X uses ______ more units of energy than Technology Y.

On a graph where the horizontal axis represents units of labor and the vertical axis represents units of energy, two different production technologies, M and N, are each represented by a straight line (ray) starting from the origin. The ray representing Technology M is steeper than the ray representing Technology N. What can be definitively concluded from this information?

Figure 2.4: Graphical Comparison of Fixed-Proportions Technologies