Question

What is the relationship between long-run average cost and long-run marginal cost? Discuss.

Short answer

Answer: The relationship between long-run average cost (LRAC) and long-run marginal cost (LRMC) in an economic context is as follows: When LRAC is decreasing, LRMC is lower than LRAC (LRMC < LRAC); when LRAC is increasing, LRMC is higher than LRAC (LRMC > LRAC); and at the minimum point of LRAC, LRMC is equal to LRAC (LRMC = LRAC). This relationship is influenced by economies of scale and diseconomies of scale, and can be visualized through a U-shaped graphical representation where the LRMC curve intersects the LRAC curve at its lowest point.

Step-by-step solution

Defining Long-run Average Cost (LRAC) #

Long-run average cost is the cost per unit of output when all factors of production are variable. In simpler terms, it is the total cost of production divided by the quantity of output in the long run. The long-run average cost curve is a graphical representation of the relationship between output and average cost in the long run, typically U-shaped. It reflects economies of scale (when LRAC decreases as output increases) and diseconomies of scale (when LRAC increases as output increases) at different levels of production.

Defining Long-run Marginal Cost (LRMC)

Long-run marginal cost represents the change in total cost due to producing one additional unit of output in the long run, considering that all factors of production are variable. The long-run marginal cost curve shows the relationship between the quantity of output and the marginal cost of production in the long run. Like the long-run average cost curve, the long-run marginal cost curve can also be U-shaped, reflecting decreasing marginal cost as output increases initially and then increasing marginal cost as output increases further.

Relationship between LRAC and LRMC: Definitions

There is a fundamental relationship between the long-run average cost and long-run marginal cost, based on their definitions, which can be formulated as: If LRAC is decreasing, LRMC must be lower than LRAC (LRMCLRAC); if LRAC is at its minimum point, LRMC is equal to LRAC (LRMC=LRAC).

Relationship between LRAC and LRMC: Economies and Diseconomies of Scale

The relationship between LRAC and LRMC is also influenced by economies and diseconomies of scale. When economies of scale are present (LRAC is decreasing), it means that the firm can produce an additional unit of output with a lower marginal cost than the average cost, making LRMC less than LRAC. Conversely, when diseconomies of scale are present (LRAC is increasing), the marginal cost to produce an additional unit of output is higher than the average cost, making LRMC greater than LRAC.

Graphical Representation of the Relationship between LRAC and LRMC

A graphical representation helps visualize the relationship between LRAC and LRMC. On the graph with output on the horizontal axis and cost on the vertical axis, both the LRAC and LRMC curves are U-shaped. The LRMC curve intersects the LRAC curve at its lowest point, where LRAC stops declining and starts to increase, indicating the point of minimum average cost and the transition from economies of scale to diseconomies of scale. The behavior of both curves leading up to their intersection, and after it, helps illustrate how LRMC is lower than LRAC when LRAC is decreasing and higher than LRAC when LRAC is increasing.