# Production Function and Cobb Douglas Equation

Assume Firm Y's production function is given by the following Cobb Douglas equation

Q = 0.5 x L^0.6 x K^0.5

where L denotes labor and K denotes capital.

The production function exhibits (increasing/decreasing/constant) returns to scale.

1. If labor hours increase by 10%, what is the percentage change in output (provide a numerical answer)?

2. If capital decreases by 10%, what is the percentage change in output (provide a numerical answer)?

3. If the number of labor hours increases by 10% and the number of hours of capital used decreases by 10%, what is the percentage change in output?

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#### Solution Preview

The production function exhibits (increasing/decreasing/constant) returns to scale.

Sum of exponents of L and K=0.6+0.5=1.1

In the case of the Cobb Douglas function if sum of exponents is greater than 1, production function exhibits increasing returns to scale.

If labor hours increase by 10%, what is the percentage change in ...

#### Solution Summary

This solution analyzes the given production function and predicts the effect of changes in input values on output level.

Cobb-Douglas Production Function

Hi,

I am fairly new to economics with only a basic understand of the topic and because of this I am struggling to answer (and understand the explanation for the answer) a question about the Cobb Douglas production function.

Q. Under what conditions does a Cobb-Douglas production function (q=AL^(alpha)K^(beta)) exhibit decreasing, constant or increasing returns to scale?

Alongside this, can someone please breakdown for me how and why '(alpha) + (beta) > 1' would indicate increasing returns. All answers online and in the textbook have been out of my depth in terms of understanding.

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