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

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 la

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