Exercise on Technological Redistribution

A firm can produce a specific quantity of goods using any of the three available production methods, each requiring a different combination of labor and capital:

• Method X: 4 workers, 4 units of capital
• Method Y: 2 workers, 8 units of capital
• Method Z: 2 workers, 5 units of capital

If the wage for a worker is $30 and the cost per unit of capital is $10, which method represents the least-cost way to produce the goods?

Production Method Analysis

A firm is evaluating three different methods to produce 1,000 units of a product. All methods produce the exact same output. The input requirements are as follows:

• Method 1: 4 workers and 8 units of material.
• Method 2: 4 workers and 10 units of material.
• Method 3: 2 workers and 12 units of material.

True or False: Method 1 is guaranteed to be the least-cost production method for the firm, regardless of the price of labor or materials.

Choosing the Optimal Production Method

Evaluating Production Technology Choices

A company can produce one unit of output using three different technologies, each with a different combination of labor (workers) and material inputs. Match each technology to the description of the relative input price conditions under which it would be the least-cost production method.

Adapting to Changing Input Costs

A firm produces a standard component using one of three available technologies. All technologies produce the same quantity and quality of output. The input requirements are:

• Technology X: 4 workers, 9 units of capital
• Technology Y: 5 workers, 7 units of capital
• Technology Z: 4 workers, 11 units of capital

The current price of labor is $20 per hour, and the price of capital is $8 per unit. The firm is currently using the least-cost technology. A new market forecast predicts that the price of capital will rise to $15 per unit, while the price of labor will remain unchanged.

Based on this forecast, what is the most logical production decision for the firm?

Evaluating a Technology Adoption Decision

A firm can produce a fixed quantity of output using one of four available production technologies. The input requirements for each technology are listed below:

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

Assuming the firm aims to minimize production costs, which technology will it never select, regardless of the prices of labor and material?

A firm can produce a specific quantity of goods using one of three available production technologies. The input requirements for each are as follows:

• Technology X: Requires 1 worker and 6 tons of coal.
• Technology Y: Requires 1 worker and 3 tons of coal.
• Technology Z: Requires 4 workers and 2 tons of coal.

Given that the wage for a worker is $20 and the price per ton of coal is $10, which statement best analyzes the firm's optimal production choice?

Production Method Cost Analysis

Cost-Effectiveness Analysis of a New Production Technology

A firm has three available methods to produce a certain quantity of output:

• Method Alpha: Requires 2 workers and 8 tons of steel.
• Method Beta: Requires 2 workers and 5 tons of steel.
• Method Gamma: Requires 5 workers and 3 tons of steel.

Statement: Regardless of the wage rate for workers or the price of steel, Method Beta will always be a more cost-effective choice than Method Alpha.

A firm has three available production methods, each using a different combination of labor and capital to produce the same amount of output:

• Method P: 6 hours of labor, 1 unit of capital
• Method Q: 3 hours of labor, 3 units of capital
• Method R: 1 hour of labor, 6 units of capital

Match each input price scenario below to the production method that would be the least expensive to use.

Analysis of a New Production Technology's Viability

A factory can produce a batch of goods using one of three available techniques. Technique 1 requires 2 workers and 9 tons of coal. A newly developed Technique 2 requires 2 workers and 6 tons of coal. Technique 3 requires 5 workers and 4 tons of coal. If the wage for a worker is $40 and the price of coal is $20 per ton, the lowest possible cost to produce the batch of goods is $____.

A company is evaluating its production methods after a new, more efficient technique has been developed. Arrange the following steps in the correct logical order to determine the single most cost-effective production method.

Evaluating a Production Technology Decision

A manufacturing plant manager is reviewing production techniques for a standard component. The plant currently uses two methods to produce the same quantity of output:

• Technique Alpha: Requires 3 workers and 10 units of raw material.
• Technique Beta: Requires 6 workers and 4 units of raw material.

A new process, Technique Gamma, is introduced, which requires 3 workers and 7 units of raw material to produce the same component.

The manager states: "Technique Gamma is clearly superior to Technique Alpha since it uses the same number of workers but less material. Therefore, we should adopt Technique Gamma immediately, as it will be our least-cost production method under any market conditions for labor and materials."

Which of the following statements provides the most accurate critique of the manager's reasoning?