Technology A-prime: Input Coordinates (1, 3)

Technological Dominance of A-prime

A firm can produce a specific quantity of output using one of three different production methods, each with different input requirements:

• Method A: Requires 1 worker and 6 tons of coal.
• Method B: Requires 4 workers and 2 tons of coal.
• Method A-prime: Requires 1 worker and 3 tons of coal.

First, identify if any method uses strictly more of at least one input and no less of any other input compared to another, making it an inefficient choice regardless of price. Then, assuming the price of hiring a worker is £5 and the price of a ton of coal is £20, which of the remaining methods is the most cost-effective for the firm to use?

A firm is evaluating three different methods to produce 100 metres of cloth. The input requirements for each method are:

• Method A: 1 worker and 6 tons of coal
• Method B: 4 workers and 2 tons of coal
• Method A-prime: 1 worker and 3 tons of coal

The firm calculates that, at current input prices, the total cost of using Method A is exactly the same as the total cost of using Method B. Given this information, which of the following statements is a logical conclusion?

Evaluating a Production Technology Claim

Evaluating a New Production Technology

A firm can produce a fixed quantity of output using either Technology A (requiring 1 worker and 6 tons of coal) or Technology B (requiring 4 workers and 2 tons of coal). An isocost line represents all combinations of inputs that result in the same total cost. If both Technology A and Technology B are on the same isocost line, what must be true about the relationship between the wage (the price of one worker) and the price of one ton of coal?

A firm can produce a specific quantity of output using either Technology A (requiring 1 worker and 6 tons of coal) or Technology B (requiring 4 workers and 2 tons of coal). Initially, the economic conditions are such that Technology A is the most cost-effective option. Later, due to market changes, the firm finds that Technology B has become the cheaper option. What change in the relative prices of the inputs best explains this switch?

A firm uses a production model with the number of workers on the horizontal axis and tons of coal on the vertical axis. The firm is analyzing two distinct economic scenarios, each represented by a line showing input combinations for a specific total cost:

• Scenario 1: A line representing a total cost of £40 passes through the points (1 worker, 6 tons of coal) and (4 workers, 0 tons of coal).
• Scenario 2: A line representing a total cost of £80 passes through the points (4 workers, 2 tons of coal) and (8 workers, 0 tons of coal).

A new production technology, 'A-prime', is introduced, which requires 1 worker and 3 tons of coal. Which statement correctly analyzes the economic impact of this new technology?

If a firm can produce a specific output using either Technology A (requiring 1 worker and 6 tons of coal) or Technology A-prime (requiring 1 worker and 3 tons of coal), then Technology A-prime will always be a more cost-effective choice for that output, regardless of the prevailing prices of workers and coal.

Cost Analysis of Production Technologies

A firm's production costs are represented on a graph where the horizontal axis measures the number of workers and the vertical axis measures tons of coal. An isocost line on this graph shows all combinations of workers and coal that have the same total cost. One such line, representing a total cost of £80, passes through two points: an input combination of 4 workers and 2 tons of coal, and another point on the horizontal axis representing 8 workers and 0 tons of coal. Based on this information, what is the wage (cost per worker) and the price per ton of coal?