To determine which production technique is the most economically efficient, we need to calculate the total cost for each technique by considering the given prices for labor and capital. We'll use the following prices:
- Labor cost: \[tex]$2 per unit
- Capital cost: \$[/tex]3 per unit
The production techniques are as follows:
1. Technique 1 uses 4 units of labor and 2 units of capital
2. Technique 2 uses 3 units of labor and 3 units of capital
3. Technique 3 uses 2 units of labor and 5 units of capital
4. Technique 4 uses 5 units of labor and 1 unit of capital
Let's calculate the total costs for each technique:
### Technique 1:
- Labor cost: [tex]\( 4 \text{ units} \times \$2/\text{unit} = \$8 \)[/tex]
- Capital cost: [tex]\( 2 \text{ units} \times \$3/\text{unit} = \$6 \)[/tex]
- Total cost: [tex]\( \$8 + \$6 = \$14 \)[/tex]
### Technique 2:
- Labor cost: [tex]\( 3 \text{ units} \times \$2/\text{unit} = \$6 \)[/tex]
- Capital cost: [tex]\( 3 \text{ units} \times \$3/\text{unit} = \$9 \)[/tex]
- Total cost: [tex]\( \$6 + \$9 = \$15 \)[/tex]
### Technique 3:
- Labor cost: [tex]\( 2 \text{ units} \times \$2/\text{unit} = \$4 \)[/tex]
- Capital cost: [tex]\( 5 \text{ units} \times \$3/\text{unit} = \$15 \)[/tex]
- Total cost: [tex]\( \$4 + \$15 = \$19 \)[/tex]
### Technique 4:
- Labor cost: [tex]\( 5 \text{ units} \times \$2/\text{unit} = \$10 \)[/tex]
- Capital cost: [tex]\( 1 \text{ unit} \times \$3/\text{unit} = \$3 \)[/tex]
- Total cost: [tex]\( \$10 + \$3 = \$13 \)[/tex]
We summarize the total costs for each technique:
1. Technique 1: \[tex]$14
2. Technique 2: \$[/tex]15
3. Technique 3: \[tex]$19
4. Technique 4: \$[/tex]13
The technique with the lowest total cost is Technique 4, with a total cost of \$13. Therefore, the economically most efficient technique in producing product [tex]\( A \)[/tex] is:
4
