### Production Function Analysis**2. A firm has a production function given by the following table:**| Units of Labor | 1 | 2 | 3 | 4 | 5 ||----------------|----|----|----|----|----|| **K = 1** | 3 | 8 | 12 | 15 | 17 || **K = 2** | 10 | 15 | 19 | 22 | 24 || **K = 3** | 16 | 21 | 25 | 28 | 30 || **K = 4** | 20 | 25 | 28 | 30 | 31 |**(i) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns?**To determine if the production function exhibits diminishing marginal returns when capital \( K \) is fixed at 2, we analyze the incremental output as units of labor \( L \) increase:- From \( L = 1 \) to \( L = 2 \): Output increases from 10 to 15 (Increment of 5)- From \( L = 2 \) to \( L = 3 \): Output increases from 15 to 19 (Increment of 4)- From \( L = 3 \) to \( L = 4 \): Output increases from 19 to 22 (Increment of 3)- From \( L = 4 \) to \( L = 5 \): Output increases from 22 to 24 (Increment of 2)The marginal output diminishes as labor increases, indicating diminishing marginal returns.**(ii) Does this production function exhibit constant returns to scale for all values of K and L?**To evaluate whether the production function exhibits constant returns to scale, we need to check if proportional increases in both \( K \) (capital) and \( L \) (labor) lead to proportional increases in output. Specifically, we compare the output when both inputs are doubled.Let's examine the data for the proportionality check:- When \( K = 2 \) and \( L = 2 \), output is 15.- When \( K = 4 \) and \( L = 4 \), output is 30.Doubling both \( K \) (from 2 to 4) and \( L

Diminishing marginal returns occur when an increase in Labor led to increasing in output at…

2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 15 K=2 K=3 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L? 3 10 16 8 15 21 12 19 25 22 28 17 24 30

2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 15 K=2 K=3 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L? 3 10 16 8 15 21 12 19 25 22 28 17 24 30

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Lesson 7- Production Question 8