### Production Function Analysis#### 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 |#### Questions:**i) Suppose that $ K $ is fixed at 2. Does this production function exhibit diminishing marginal returns?**To determine if diminishing marginal returns are present when $ K $ is fixed at 2, observe the marginal product of labor as labor increases:- From Labor 1 to Labor 2: $ 15 - 10 = 5 $ (Marginal increase: 5)- From Labor 2 to Labor 3: $ 19 - 15 = 4 $ (Marginal increase: 4)- From Labor 3 to Labor 4: $ 22 - 19 = 3 $ (Marginal increase: 3)- From Labor 4 to Labor 5: $ 24 - 22 = 2 $ (Marginal increase: 2)The marginal product of labor is decreasing as the number of labor units increases, indicating diminishing marginal returns.**ii) Does this production function exhibit constant returns to scale for all values of $ K $ and $ L $?**To determine if the production function exhibits constant returns to scale, we compare the output resulting from proportional increases in both inputs $ K $ and $ L $. - If we double both $ K $ and $ L $, check if the output doubles as well from the initial inputs to twice the initial inputs. For example, starting with $ K = 1 $, $ L = 1 $ (Output = 3), to $ K = 2 $, $ L = 2 $ (Output = 15), and then $ K = 4 $, $ L = 4 $

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 (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?

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 (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?

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
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