3.3.2 Costs (Edexcel)

This Edexcel study note covers short run costs.

a) Formulas and Relationships:

1. Total Cost (TC): TC = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
2. Total Fixed Cost (TFC): TFC remains constant regardless of the level of production.
3. Total Variable Cost (TVC): TVC varies with the level of production.
4. Average Total Cost (ATC): ATC = TC / Quantity of Output ATC = (TFC + TVC) / Quantity of Output
5. Average Fixed Cost (AFC): AFC = TFC / Quantity of Output
6. Average Variable Cost (AVC): AVC = TVC / Quantity of Output
7. Marginal Cost (MC): MC = Change in Total Cost / Change in Quantity of Output

Relationships:

• TC = TFC + TVC
• ATC = AFC + AVC
• MC represents the additional cost incurred when producing one more unit of output.
• When MC is less than ATC, ATC is decreasing.
• When MC is greater than ATC, ATC is increasing.
• When MC is equal to ATC, ATC is at its minimum point.

b) Derivation of Short-Run Cost Curves from Diminishing Marginal Productivity:

The short-run cost curves are derived from the assumption of diminishing marginal productivity. This assumption implies that as a firm increases its variable inputs (like labor or raw materials) while keeping some inputs fixed (like machinery or factory space), the additional output generated by each additional unit of the variable input will decrease.

1. Total Product (TP): Total quantity of output produced as a function of variable inputs.
2. Marginal Product (MP): Change in total product resulting from an increase in one unit of the variable input.
3. Total Cost (TC): The cost incurred in the short run, which includes both fixed and variable costs.
4. Average Variable Cost (AVC): Variable cost per unit of output.

The derivation of short-run cost curves involves these steps:

i. Calculate Marginal Product (MP) by observing the change in output when one more unit of variable input is added.

ii. Calculate Average Variable Cost (AVC) by dividing the total variable cost by the quantity of output.

iii. Calculate Total Cost (TC) as the sum of Total Fixed Cost (TFC) and Total Variable Cost (TVC).

iv. Derive Marginal Cost (MC) by calculating the change in Total Cost (TC) when producing one more unit of output.

v. Plot the short-run cost curves:

• AVC curve typically U-shaped due to diminishing marginal productivity. Initially, AVC falls as MP rises, then it rises as MP declines significantly.
• MC curve intersects the AVC curve at its minimum point, representing the point of efficient production.

c) Relationship between Short-Run and Long-Run Average Cost Curves:

In the short run, firms have fixed inputs (like factory size), and they can only vary their variable inputs (like labor and raw materials). As a result, short-run average cost curves (SAC) show the cost of production under these fixed and variable constraints.

In the long run, firms have the flexibility to adjust all inputs, including fixed inputs. Therefore, long-run average cost curves (LAC) represent the cost of production when firms can choose the optimal combination of inputs and production techniques.

The relationship between short-run and long-run average cost curves can be summarized as follows:

1. In the long run, a firm aims to produce at the lowest possible average cost, so LAC represents the envelope of all possible SAC curves.
2. The LAC curve is tangent to the lowest point of the SAC curves at each level of output.
3. As a result, the long-run average cost curve is typically flatter and more efficient than any of the short-run average cost curves. This reflects the firm's ability to adapt and make optimal choices regarding input combinations and scale of production in the long run.