Analyze if the following statements are True or False. Justify your answer.(a) “The difference between the average total cost and the average variable cost is con-stant and equal to the fixed cost for any level of quantity.”(b) “If a production function exhibits increasing return to scale, the average variablecost is increasing and the marginal cost is below the average variable cost.”(c) “The point at which the marginal cost intersects the average variable cost representsthe point at which the average fixed cost is at its minimum.”
Question
Analyze if the following statements are True or False. Justify your answer.(a) “The difference between the average total cost and the average variable cost is con-stant and equal to the fixed cost for any level of quantity.”(b) “If a production function exhibits increasing return to scale, the average variablecost is increasing and the marginal cost is below the average variable cost.”(c) “The point at which the marginal cost intersects the average variable cost representsthe point at which the average fixed cost is at its minimum.”
Solution
(a) False. The difference between the average total cost (ATC) and the average variable cost (AVC) is equal to the average fixed cost (AFC), not the total fixed cost. AFC is calculated by dividing the total fixed cost by the quantity of output. As output increases, AFC decreases because the same amount of fixed costs is spread over a larger number of units.
(b) False. If a production function exhibits increasing returns to scale, it means that doubling all inputs more than doubles the output. However, this does not necessarily imply that the average variable cost is increasing. In fact, under increasing returns to scale, average costs (including AVC) are typically decreasing. Furthermore, the relationship between marginal cost and average variable cost does not depend on returns to scale. When MC is below AVC, AVC is decreasing, and when MC is above AVC, AVC is increasing.
(c) False. The point at which the marginal cost (MC) intersects the average variable cost (AVC) is the point at which AVC is at its minimum, not the average fixed cost (AFC). This is because when MC is less than AVC, AVC is decreasing, and when MC is more than AVC, AVC is increasing. Therefore, AVC is at its minimum when MC equals AVC. AFC, on the other hand, continually decreases as output increases because fixed costs are spread over a larger number of units.
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