# Consider a production function for an economy: Y = 20 (L^{0.5}K^{0.4}N^{0.1}) where L is labor, K...

## Question:

Consider a production function for an economy: {eq}\displaystyle Y = 20 (L^{0.5}K^{0.4}N^{0.1}) {/eq} where {eq}L {/eq} is labor, {eq}K {/eq} is capital, and {eq}N {/eq} is land. In this economy the factors of production are in fixed supply with {eq}L = 100,\ K = 100 {/eq}, and {eq}N = 100 {/eq}.

a) What is the level of output in this country?

b) Does this production function exhibit constant returns to scale? Demonstrate by an example.

c) If the economy is competitive so that factors of production are paid the value of their marginal products, what share of total income will go to land?

## Returns to scale:

The concept of returns to scale is a long-run concept. Under this, all the factors are variable and none is a fixed factor. There are different phases of returns to scale.

## Answer and Explanation: 1

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View this answer**a)** The level of output in this country is:

{eq}\begin{align*} Y &= 20\left( {{L^{0.5}}{K^{0.4}}{N^{0.1}}} \right)\\ &= 20\left(...

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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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