Final answer:
To find the average cost for 4,000 widgets with a total production cost of $5,700 for 700 widgets and a fixed marginal cost of $1.5, calculate the total cost for 4,000 widgets and divide it by 4,000. The average cost comes out to $2.6625 per widget.
Step-by-step explanation:
The student's question involves finding the average cost of producing 4,000 widgets given that the total cost of producing 700 widgets is $5,700 and the marginal cost is a constant $1.5. To calculate the average cost for 4,000 widgets, we first determine the total cost of production for 4,000 widgets and then divide that by the number of widgets.
The total cost for 4,000 widgets can be found by adding the initial total cost provided for 700 widgets to the cost of producing the additional 3,300 widgets at the marginal cost rate. The calculation is as follows:
- Cost to produce the initial 700 widgets: $5,700
- Cost to produce additional 3,300 widgets (3,300 widgets × $1.5/widget): $4,950
- Total cost for 4,000 widgets: $5,700 + $4,950 = $10,650
Now, calculating the average cost:
- Average cost = Total cost for 4,000 widgets / Number of widgets
- Average cost = $10,650 / 4,000
- Average cost = $2.6625 per widget
Therefore, the average cost of producing 4,000 widgets is $2.6625 per widget.