Calculating Input Price Ratios for Technology Choice
A firm produces cloth and has two efficient technology options available. Technology A requires 1 worker and 6 tons of coal to produce 100 meters of cloth. Technology B requires 4 workers and 2 tons of coal for the same output. Determine the specific ratio of the wage rate (w) to the price per ton of coal (p) at which a cost-minimizing firm would be indifferent between choosing Technology A and Technology B.
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Simplified Graphical Representation of Technologies
Comparative Input Data for Five Cloth Production Technologies
Axes and Coordinates for the Technology Comparison Graph
Drawing Conclusions from Figure 2.6
A firm can produce 100 meters of cloth using one of five available technologies, each with different requirements for labor (number of workers) and energy (tons of coal), as shown below:
- Technology A: 1 worker, 6 tons of coal
- Technology B: 4 workers, 2 tons of coal
- Technology C: 3 workers, 7 tons of coal
- Technology D: 5 workers, 5 tons of coal
- Technology E: 10 workers, 1 ton of coal
A technology is considered inefficient if another available technology can produce the same output using less of at least one input without using more of any other input. Based on this definition, which of the following technologies is inefficient?
Cost-Minimization for Cloth Production
Evaluating Production Technologies
Consider two methods for producing 100 meters of cloth. Method C requires 3 workers and 7 tons of coal. Method A requires 1 worker and 6 tons of coal. Based on this information, a profit-maximizing firm would always choose Method A over Method C, regardless of the wages paid to workers or the price of coal.
Five distinct technologies are available to produce a standard batch of cloth. Match each named technology to the combination of labor (workers) and energy (tons of coal) it requires.
Strategic Technology Selection Based on Input Costs
Adapting Production Strategy to Input Price Changes
A firm can produce a specific quantity of cloth using one of five available technologies, each requiring a different combination of labor (number of workers) and energy (tons of coal), as detailed in the table below. Note that technologies C and D are inefficient as other technologies use fewer inputs.
Technology Number of Workers Tons of Coal A 1 6 B 4 2 C 3 7 D 5 5 E 10 1 Under which of the following economic conditions would a profit-maximizing firm be most likely to choose Technology E over the other available efficient technologies (A and B)?
Calculating Input Price Ratios for Technology Choice
A company produces a standard amount of cloth and is currently using a technology that requires 4 workers and 2 tons of coal. If the price of coal were to increase significantly while the cost of labor stayed the same, a profit-maximizing company would logically consider switching to an available technology that uses more workers but less coal.