Figure 1 plots three Cobb-Douglas production functions for different values of α and β, given z and K.Refer to figure 1. Which production function do you think makes more sense to describe the economy, considering most economies are labor-intensive at the aggregate level, and that firms' optimizing behavior implies maximizing the marginal product of labor? Explain which values you would choose for α and β and why.(Note: The transcription does not include a description of Figure 1 as no graphical details are provided in the image.) **Figure 1: Cobb-Douglas Production Functions for Different Capital and Labor Shares**This graph illustrates the Cobb-Douglas production functions with varying capital and labor share parameters. The x-axis represents the labor input, ranging from 0 to 20, while the y-axis depicts the output level, extending from 0 to 7.Three curves are plotted to show different combinations of the parameters α (capital share) and β (labor share):1. **Blue Curve (α = 0.3, β = 0.7):** This curve, positioned highest on the graph, demonstrates a production function with a lower capital share and a higher labor share. As labor input increases, the output rises at a relatively faster rate compared to the other curves. 2. **Red Curve (α = 0.5, β = 0.5):** Located in the middle, this is an example of a balanced capital and labor share. The output increases moderately with the increment in labor input. 3. **Green Curve (α = 0.7, β = 0.3):** This curve is positioned lowest, illustrating a higher capital share and a lower labor share. The increase in output is slower as labor input grows compared to the other two curves.The graph visually depicts how different ratios of capital and labor shares can influence the output in a Cobb-Douglas production function.

Answered: Refer to figure 1. function do you…

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Figure 1 plots three Cobb-Douglas production functions for different values of α and β, given z and K.

Refer to figure 1. Which production function do you think makes more sense to describe the economy, considering most economies are labor-intensive at the aggregate level, and that firms' optimizing behavior implies maximizing the marginal product of labor? Explain which values you would choose for α and β and why.

(Note: The transcription does not include a description of Figure 1 as no graphical details are provided in the image.)

**Figure 1: Cobb-Douglas Production Functions for Different Capital and Labor Shares**

This graph illustrates the Cobb-Douglas production functions with varying capital and labor share parameters. The x-axis represents the labor input, ranging from 0 to 20, while the y-axis depicts the output level, extending from 0 to 7.

Three curves are plotted to show different combinations of the parameters α (capital share) and β (labor share):

1. **Blue Curve (α = 0.3, β = 0.7):** This curve, positioned highest on the graph, demonstrates a production function with a lower capital share and a higher labor share. As labor input increases, the output rises at a relatively faster rate compared to the other curves.

2. **Red Curve (α = 0.5, β = 0.5):** Located in the middle, this is an example of a balanced capital and labor share. The output increases moderately with the increment in labor input.

3. **Green Curve (α = 0.7, β = 0.3):** This curve is positioned lowest, illustrating a higher capital share and a lower labor share. The increase in output is slower as labor input grows compared to the other two curves.

The graph visually depicts how different ratios of capital and labor shares can influence the output in a Cobb-Douglas production function.

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The production function determines the output of the firm, produced from using the labour and capital as inputs. The share of capital $α$ and the share of labour $β$ in the production function are the output elasticity of these inputs. These values are constants for a production function and are determined by the technology at that time.

Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production.

In the question we have three different production function, with different shares of capital and labour in the economy. As given the economies are labour intensive, and firms optimize, where the marginal product of labour is maximum.

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