Question

The table below shows how output changes as inputs change for three different output levels. The wage rate is \(£ 5\) and the rental rate of capital is \(£ 2\). $$ \begin{array}{|l|l|l|c|c|l|c|} \hline & \text { Column } 1 & \text { Column } 2 & \text { Column } 3 & \text { Column } 4 & \text { Column } 5 & \text { Column } 6 \\ \hline \text { Caplral input } & 4 & 2 & 7 & 4 & 11 & 8 \\ \hline \text { Labour input } & 5 & 6 & 10 & 12 & 15 & 16 \\ \hline \text { Output } & 4 & 4 & 8 & 8 & 12 & 12 \\ \hline \end{array} $$ a. For each output level in the above table, which technique of production is more capital intensive? b. Refer to columns 2,3 and 6 . Does the firm switch towards or away from more capital-intensive techniques as output rises?

Short answer

Technique in Column 1, 3, and 5 are more capital intensive. Initially away, then towards capital-intensive techniques.

Step-by-step solution

Calculate Capital-Labor Ratios

To determine which technique is more capital intensive, we need to calculate the capital-labor ratio for each column. The capital-labor ratio is calculated as follows:\[\text{Capital-Labor Ratio} = \frac{\text{Capital Input}}{\text{Labor Input}}\]For Column 1:\[\frac{4}{5} = 0.8\]For Column 2:\[\frac{2}{6} \approx 0.33\]For Column 3:\[\frac{7}{10} = 0.7\]For Column 4:\[\frac{4}{12} \approx 0.33\]For Column 5:\[\frac{11}{15} \approx 0.73\]For Column 6:\[\frac{8}{16} = 0.5\]

Identify More Capital Intensive Techniques

For each output level, compare the capital-labor ratios calculated in Step 1: - Output Level 4: Columns 1 and 2 - Column 1 has a ratio of 0.8, Column 2 has a ratio of 0.33. - Thus, Column 1 is more capital intensive. - Output Level 8: Columns 3 and 4 - Column 3 has a ratio of 0.7, Column 4 has a ratio of 0.33. - Thus, Column 3 is more capital intensive. - Output Level 12: Columns 5 and 6 - Column 5 has a ratio of 0.73, Column 6 has a ratio of 0.5. - Thus, Column 5 is more capital intensive.

Analyze Trends For Output Increase

Examine the capital-labor ratios from the more capital-intensive columns at each output level to determine the trend as output increases: - Output Level 4 uses Column 1 with a ratio of 0.8. - Output Level 8 uses Column 3 with a ratio of 0.7. - Output Level 12 uses Column 5 with a ratio of 0.73. Comparing these ratios, the capital intensity decreases slightly from Output 4 to Output 8 (0.8 to 0.7) but increases from Output 8 to Output 12 (0.7 to 0.73). Therefore, initially, the firm shifts slightly away from more capital-intensive techniques but then moves towards them again as output continues to rise.

Key concepts

Capital Intensity

The concept of capital intensity refers to the level of capital input used in comparison to labor input in a production process. It's often represented by the capital-labor ratio. This ratio is key to understanding how a business allocates its resources.

• A higher ratio indicates a more capital-intensive production process, meaning more machinery, tools, or other equipment is used relative to human labor.
• This can lead to increased productivity if the machinery or technology significantly enhances output.

In the exercise, the capital-labor ratio was calculated for different production techniques across several output levels. This helped identify which techniques were more capital-intensive. For example, Column 1, with a ratio of 0.8, was more capital-intensive compared to Column 2, with a ratio of 0.33, at the same output level. Changes in capital intensity can influence the cost structure and efficiency of production, so businesses must choose an optimal balance that maximizes their competitive advantage.

Production Techniques

Production techniques are the methods or processes a company uses to convert inputs into outputs. The choice of production technique can significantly affect both the quality and quantity of outputs.

• Different techniques can either be labor-intensive or capital-intensive, heavily affecting the overall cost and productivity of production.
• Choosing the right production technique depends on factors like technology, available resources, and cost of inputs.

In our case study, the exercise explored various techniques across different columns, each with distinct levels of capital and labor inputs for producing the same output levels. By comparing these techniques, it was evident how varying the mix of capital and labor affected the capital intensity and, potentially, the efficiency and scalability of production. For instance, as output increased, the firm initially shifted away from capital-intensive techniques, only to move back to them at higher output levels due to possible improvements in cost-effectiveness or technological efficiency.

Labor Input

Labor input pertains to the amount of human effort, measured in worker hours or number of workers, that is used in the production process. It is a critical component in determining the efficiency and effectiveness of production.

• High labor input can suggest a labor-intensive production process, which might involve more manual effort or skilled labor.
• The cost of labor can significantly impact the overall production costs, influencing how a business balances labor and capital inputs.

In the given exercise, varying the labor input across columns gave insights into how the production process could be more or less labor-driven. For instance, Columns 2 and 4 had lower capital input but higher labor input for a given output, highlighting a reliance on human resources rather than machinery. A firm's strategic choice between using more labor or more capital can define its long-term sustainability, especially when considering fluctuating wage rates or advancements in automation technology.