Consider the “Cobb-Douglas” production function given by 𝑌=𝐴𝐾𝛼𝐿1−𝛼 where 𝐴>0 and 0<𝛼<1. Which of the following is FALSE?Group of answer choicesThe marginal product of capital is positiveThe marginal product of labour is positiveThere is diminishing returns to capitalThere is decreasing returns to scale
Question
Consider the “Cobb-Douglas” production function given by 𝑌=𝐴𝐾𝛼𝐿1−𝛼 where 𝐴>0 and 0<𝛼<1. Which of the following is FALSE?Group of answer choicesThe marginal product of capital is positiveThe marginal product of labour is positiveThere is diminishing returns to capitalThere is decreasing returns to scale
Solution
The Cobb-Douglas production function is a particular form of the production function, widely used in economics to represent the technological relationship between the amounts of two or more inputs (particularly physical capital and labor) and the amount of output that can be produced by those inputs.
The statement that is FALSE is: "There is decreasing returns to scale."
Here's why:
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The marginal product of capital is positive: This is TRUE. The marginal product of capital is the increase in output resulting from a one-unit increase in the amount of capital, holding all other inputs constant. In the Cobb-Douglas production function, the exponent on capital (𝛼) is positive, so the marginal product of capital is also positive.
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The marginal product of labour is positive: This is TRUE. Similarly, the marginal product of labor is the increase in output resulting from a one-unit increase in the amount of labor, holding all other inputs constant. In the Cobb-Douglas production function, the exponent on labor (1-𝛼) is positive, so the marginal product of labor is also positive.
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There is diminishing returns to capital: This is TRUE. Diminishing returns to capital means that as we add more capital, holding labor constant, the increase in output from an additional unit of capital becomes smaller. This is a property of the Cobb-Douglas production function because the exponent on capital (𝛼) is less than one.
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There is decreasing returns to scale: This is FALSE. Returns to scale refers to what happens to output when we proportionally increase all inputs. In the Cobb-Douglas production function, if we double both capital and labor, output will also double. This is constant returns to scale, not decreasing returns to scale.
Similar Questions
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