Do the following production functions exhibit increasing, constant, or decreasing returns to...
Question:
Do the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume {eq}\bar A {/eq} is some fixed positive number.)
(a) {eq}Y = K^{1/2}L^{1/2} {/eq}
(b) {eq}Y = K^{2/3}L^{2/3} {/eq}
(c) {eq}Y = K^{1/3}L^{1/2} {/eq}
(d) {eq}Y = K + L {/eq}
(e) {eq}Y = K + K^{1/3}L^{1/3} {/eq}
(f) {eq}Y = K^{1/3}L^{2/3} + \bar A {/eq}
(g) {eq}Y = K^{1/3}L^{2/3} - \bar A {/eq}
Return To scale:
Return to scale shows the change in output when two inputs (capital and labor) increase by the same factor. When the increase in outputs is greater than the increase in inputs, there is an increasing return to scale. When the increase in outputs is the same as the increase in inputs, there is a constant return to scale. When the increase in outputs is less than the increase in inputs, there is a decreasing return to scale.
Answer and Explanation: 1
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{eq}Y = K^{1/2}L^{1/2} \\ Y' = (mK)^{1/2}(mL)^{1/2} \\ Y' = mK^{1/2}L^{1/2} \\ Y' = mY {/eq}
There is a constant return to scale.
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Returns to Scale in Economics: Definition & Examples
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Chapter 3 / Lesson 71
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Understand the meaning of returns to scale in economics. Learn about increasing returns to scale, constant returns to scale and decreasing returns to scale.
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