Final answer:
The level of production where average total cost is minimized is at the intersection of the average total cost (ATC) and average variable cost (AVC) curves. The level of output where average variable cost is equal to marginal cost is at the intersection of the average variable cost (AVC) and marginal cost (MC) curves.
Step-by-step explanation:
The average total cost (ATC) is minimized at the level of production where it intersects with the average variable cost (AVC). To determine this level, we need to analyze the given cost function and calculate the ATC and AVC. In this case, the cost function is c(y) = 7y² + 112. Average total cost (ATC) is calculated by dividing the total cost by the quantity produced, while average variable cost (AVC) is calculated by dividing the variable cost by the quantity produced.
To find the level of production where ATC is minimized, we need to find the minimum point on the ATC curve. Typically, the ATC curve is U-shaped, so the minimum point is at the bottom of the U-shape where it intersects with the AVC curve. At this level of production, the average variable cost is equal to the marginal cost (MC).
To find the level of output where AVC is equal to MC, we need to find the point on the AVC curve that intersects with the MC curve. The MC curve represents the additional cost of producing one additional unit of output. The intersection of the MC curve and the AVC curve represents the level of output where average variable cost is equal to marginal cost.