Question

'The long-run marginal cost curve can be derived from the short-run marginal cost curves'. Discuss.

Short answer

Question: Explain the relationship between the long-run marginal cost curve and the short-run marginal cost curves, and describe the process of deriving the long-run marginal cost curve from a set of short-run marginal cost curves. Answer: The long-run marginal cost curve represents the costs associated with producing additional units of output in the long-run, where all inputs are variable. On the other hand, short-run marginal cost curves represent the costs associated with producing additional units of output in the short-run, with at least one input factor being fixed. The long-run marginal cost curve can be derived from a set of short-run marginal cost curves by identifying the lowest short-run marginal cost among the different curves for each level of output. By plotting these lowest marginal costs for each output level, the long-run marginal cost curve is formed. This curve illustrates the lowest possible marginal costs for producing varying levels of output in the long-run, considering the variable nature of all input factors.

Step-by-step solution

Understanding Marginal Cost

Marginal cost is the cost associated with producing an additional unit of output. It is an important concept in economics because it helps firms determine the optimal level of production, where the marginal cost equals the marginal revenue.

Understanding Short-run and Long-run

In economics, the short-run and long-run are distinguished based on the time horizon and the flexibility of input factors. In the short-run, at least one input factor (usually capital) is fixed, while in the long-run, all input factors are variable.

Short-run Marginal Cost Curve

The short-run marginal cost curve represents the costs associated with producing additional units of output in the short-run, given the fixed inputs. It is typically upward sloping due to the law of diminishing returns, which states that as more units of output are produced, the additional cost of producing each unit increases.

Long-run Marginal Cost Curve

The long-run marginal cost curve, on the other hand, represents the costs associated with producing additional units of output in the long-run, where all inputs are variable. It is downward sloping at first, indicative of economies of scale, and eventually becomes upward sloping, illustrating diseconomies of scale.

Deriving the Long-run Marginal Cost Curve from Short-run Marginal Cost Curves

To derive the long-run marginal cost curve from a set of short-run marginal cost curves, follow these steps: 1. Identify a range of short-run marginal cost curves, each representing different levels of fixed inputs. 2. For each level of output, determine the lowest short-run marginal cost among the different short-run marginal cost curves. 3. Plot these lowest marginal costs for each level of output to form the long-run marginal cost curve. The derived long-run marginal cost curve will represent the lowest possible marginal costs for producing different levels of output in the long-run, taking into account the variable nature of all input factors.