# 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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View this answer**Part (a)**

{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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Chapter 3 / Lesson 71Understand 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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