A firm needs to produce 100 meters of cloth. It has access to four different production technologies, each requiring a different combination of labor and coal, as shown in the table below. If the wage for a worker is £8 and the price of coal is £6 per ton, which technology should the firm choose to minimize its production costs?

Evaluating a Production Decision After a Wage Increase

A textile firm is considering two methods to produce a standard batch of cloth. Method A requires 3 workers and 4 tons of coal. Method B requires 2 workers and 5 tons of coal. The price of coal is fixed at £6 per ton. If the wage for a worker increases from £4 to £8, it would be a cost-minimizing decision for the firm to switch from using Method A to Method B.

Impact of Wage Increase on Technology Choice

Evaluating Technology Choice After a Wage Increase

A firm can use different technologies to produce a set amount of output. Given a wage of £8 per worker and a coal price of £6 per ton, match each production technology with its correct total cost.

A manufacturing firm is evaluating two production methods to produce a specific quantity of goods.

• Method X uses 4 workers and 2 tons of coal.
• Method Y uses 2 workers and 5 tons of coal.

The price of coal is fixed at £6 per ton. To minimize costs, the firm would be indifferent between Method X and Method Y when the wage per worker is £____.

Evaluating a Strategic Production Shift

A textile factory manager must choose a technology to produce a standard batch of cloth. The price of coal is £6 per ton. The manager has two options:

• Technology A: Requires 6 workers and 2 tons of coal.
• Technology B: Requires 2 workers and 7 tons of coal.

Previously, when the wage was lower, the manager correctly used Technology A. Now, the wage has increased to £8 per worker. The manager makes the following claim: "Even with the higher wage, Technology A is still the better choice because it uses significantly less coal."

Which of the following provides the most accurate evaluation of the manager's claim from a cost-minimization perspective?

A firm produces a standard batch of cloth using a technology that requires 4 workers and 3 tons of coal. Initially, the wage is £4 per worker and the price of coal is £6 per ton. The wage then increases to £8 per worker, while the price of coal remains unchanged. Which of the following alternative technologies, if it became available, would represent a logical switch for the firm to minimize its costs in the new price environment?