### 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

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Chapter1: Making Economics Decisions

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Factors of Production

Factors of production – in simple words means the factors that are used for producing any product or service. This includes the resources which are necessary for the manufacturing of products. Factors of production are also known as the building blocks of the economy.

Question

### 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

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