Suppose that a firm is using quantity k of capital input and quantity I of labor input to produce output level qo. Further suppose that, at this input combination, the rate of technical substitution (RTS) is 2. Assume also that w = $1 and v = $1, where w and v are the rental rates at which this firm buys its labor and capital services. This firm can reduce its cost of producing output level qo by: reducing labor input use by 1 unit and increase capital input use by ½ unit. reducing labor input use by 1 unit and increase capital input use by ½ unit.. reducing labor input use by 2 units and increase capital input use by 1 unit. reducing capital input use by 2 units and increase labor input use by 1 unit. reducing capital input use by 1 unit and increase labor input use by 1 unit. That is correct. At RTS equal to 2, this firm can trade away 2 units of capital input and use 1 additional unit of labor input instead, and still produce output level qo. At v = $1 per unit of capital and w = $1 per unit of labor, this would reduce the cost of producing output level qo by $1. Therefore, this firm's cost of production could not have been minimized in the first place. A similar argument can be made whenever the RTS of labor (1) for capital (k) differs from the ratio of the input prices, w/v.
Suppose that a firm is using quantity k of capital input and quantity I of labor input to produce output level qo. Further suppose that, at this input combination, the rate of technical substitution (RTS) is 2. Assume also that w = $1 and v = $1, where w and v are the rental rates at which this firm buys its labor and capital services. This firm can reduce its cost of producing output level qo by: reducing labor input use by 1 unit and increase capital input use by ½ unit. reducing labor input use by 1 unit and increase capital input use by ½ unit.. reducing labor input use by 2 units and increase capital input use by 1 unit. reducing capital input use by 2 units and increase labor input use by 1 unit. reducing capital input use by 1 unit and increase labor input use by 1 unit. That is correct. At RTS equal to 2, this firm can trade away 2 units of capital input and use 1 additional unit of labor input instead, and still produce output level qo. At v = $1 per unit of capital and w = $1 per unit of labor, this would reduce the cost of producing output level qo by $1. Therefore, this firm's cost of production could not have been minimized in the first place. A similar argument can be made whenever the RTS of labor (1) for capital (k) differs from the ratio of the input prices, w/v.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.10P
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How would the answer change if w = 5. (see image attached)
Transcribed Image Text:Suppose that a firm is using quantity k of capital input and quantity I of labor input to produce output level 9o.
Further suppose that, at this input combination, the rate of technical substitution (RTS) is 2. Assume also that w
= $1 and v = $1, where w and v are the rental rates at which this firm buys its labor and capital services. This firm
can reduce its cost of producing output level qo by:
reducing labor input use by 1 unit and increase capital input use by ½ unit.
reducing labor input use by 1 unit and increase capital input use by ½ unit..
reducing labor input use by 2 units and increase capital input use by 1 unit.
reducing capital input use by 2 units and increase labor input use by 1 unit.
reducing capital input use by 1 unit and increase labor input use by 1 unit.
That is correct. At RTS equal to 2, this firm can trade away 2 units of capital input and use 1 additional
unit of labor input instead, and still produce output level qo. At v = $1 per unit of capital and w = $1 per
unit of labor, this would reduce the cost of producing output level qo by $1. Therefore, this firm's cost of
production could not have been minimized in the first place. A similar argument can be made whenever
the RTS of labor (I) for capital (k) differs from the ratio of the input prices, w/v.
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