Cost Concepts Notes

  • COST CONCEPTS

    • Total Cost (TC): the amount that the firm pays to buy inputs.

    • Explicit Cost: input costs that require an outlay of money by the firm.

    • Implicit Cost: input costs that do not require an outlay of money by the firm (e.g., use of own buildings, land, etc.).

    • Total Cost relationship:

    • TC=extExplicitCost+extImplicitCostTC = ext{Explicit Cost} + ext{Implicit Cost}

  • Sunk, Historical, and Opportunity Costs

    • Sunk Cost: expenditure that has already been made and cannot be recovered.

    • Historical Cost: the price at which capital goods were originally purchased; a portion of the original price is taken as depreciation charged to current costs of production per year.

    • Opportunity Cost: the cost associated with opportunities forgone by not using resources in their best alternative use.

  • FIXED COSTS vs VARIABLE COSTS

    • Fixed Costs (FC): costs that do not vary with the quantity of output produced. Incurred even if output is zero. Also described as overhead or sunk costs in some contexts. Examples: rent for factory/office space, interest on debts, salaries of tenured faculty, etc.

    • Variable Costs (VC): costs that vary with the quantity of output produced.

    • Total Costs (TC): sum of fixed and variable costs.

    • Mathematical relationships:

    • TC=FC+VCTC = FC + VC

  • AVERAGE AND MARGINAL COST COMPONENTS

    • Average Cost (AC) or Average Total Cost (ATC):

    • ATC=racTCQATC = rac{TC}{Q}

    • where Q  is the unit of outputQ\;\text{is the unit of output}.

    • Average Fixed Cost (AFC):

    • AFC=FCQAFC = \frac{FC}{Q}

    • Average Variable Cost (AVC):

    • AVC=VCQAVC = \frac{VC}{Q}

    • Marginal Cost (MC): the increase in cost from producing one additional unit of output. Since fixed cost does not change with output,

    • MC=ΔTC/ΔQ=ΔVC/ΔQMC = \Delta TC / \Delta Q = \Delta VC / \Delta Q

    • In discrete terms, MC is the change in TC (or VC) when output changes from one level to the next.

  • DETAILED COST TABLE ILLUSTRATION (q = output levels 0 to 11)

    • The following data illustrate how FC, VC, TC, MC, AFC, AVC, and ATC change with output. FC is constant at 50 across all levels.

    • For each output level q, the values are:

    • q = 0: FC = 50, VC = 0, TC = 50, MC = 0, AFC = 50, AVC = undefined, ATC = 50

    • q = 1: FC = 50, VC = 50, TC = 100, MC = 50, AFC = 50, AVC = 50, ATC = 100

    • q = 2: FC = 50, VC = 78, TC = 128, MC = 28, AFC = 25, AVC = 39, ATC = 64

    • q = 3: FC = 50, VC = 98, TC = 148, MC = 20, AFC = 16.7, AVC = 32.7, ATC = 49.3

    • q = 4: FC = 50, VC = 112, TC = 162, MC = 14, AFC = 12.5, AVC = 28, ATC = 40.5

    • q = 5: FC = 50, VC = 130, TC = 180, MC = 18, AFC = 10, AVC = 26, ATC = 36

    • q = 6: FC = 50, VC = 150, TC = 200, MC = 20, AFC = 8.3, AVC = 25, ATC = 33.3

    • q = 7: FC = 50, VC = 175, TC = 225, MC = 25, AFC = 7.1, AVC = 25, ATC = 32.1

    • q = 8: FC = 50, VC = 204, TC = 254, MC = 29, AFC = 6.3, AVC = 25.5, ATC = 31.8

    • q = 9: FC = 50, VC = 242, TC = 292, MC = 38, AFC = 5.6, AVC = 26.9, ATC = 32.4

    • q = 10: FC = 50, VC = 300, TC = 350, MC = 58, AFC = 5, AVC = 30, ATC = 35

    • q = 11: FC = 50, VC = 385, TC = 435, MC = 85, AFC = 4.5, AVC = 35, ATC = 39.5

    • Observations from the table:

    • FC constant at 50 for all q

    • VC increases with q; TC increases correspondingly

    • MC rises as output increases, with positive increments

    • AFC decreases with higher q (as FC is spread over more units)

    • AVC varies with VC/q and ATC = TC/q

  • THE COST IN THE SHORT RUN: AC AND MC RELATIONSHIP

    • Key relationship:

    • When MC < AC, AC falls as output increases

    • When MC > AC, AC rises as output increases

    • At the minimum point of AC, MC = AC

    • Practical takeaway: MC pulls the AC curve toward its direction; the AC curve has its minimum where MC intersects it.

  • COSTS: SUMMARY (TERMS AND DEFINITIONS)

    • Explicit costs:

    • Definition: Costs that require an outlay of money by the firm

    • Mathematical/Conceptual: part of the monetary payments the firm makes to others (e.g., wages, rent, materials)

    • Implicit costs:

    • Definition: Costs that do not require an outlay of money by the firm

    • Examples: using owner-provided resources (e.g., own buildings or land, owner’s time)

    • Fixed costs:

    • Definition: Costs that do not vary with the quantity of output produced

    • Characteristics: incur even if output is zero; often considered overhead or sunk in the short run

    • Variable costs:

    • Definition: Costs that vary with the quantity of output produced

    • Total cost:

    • Definition: The market value of all inputs used in production

    • Formula: TC=FC+VCTC = FC + VC

    • Average fixed cost (AFC):

    • Definition: Fixed cost per unit of output

    • Formula: AFC=FCQAFC = \frac{FC}{Q}

    • Average variable cost (AVC):

    • Definition: Variable cost per unit of output

    • Formula: AVC=VCQAVC = \frac{VC}{Q}

    • Average total cost (ATC) / Average cost (AC):

    • Definition: Total cost per unit of output

    • Formula: ATC=TCQATC = \frac{TC}{Q}

    • Marginal cost (MC):

    • Definition: The increase in total cost arising from producing an extra unit of output

    • Formula (discrete): MC=ΔTCΔQ=ΔVCΔQMC = \frac{\Delta TC}{\Delta Q} = \frac{\Delta VC}{\Delta Q}

  • ADDITIONAL NOTES

    • In practice, when analyzing production decisions, MC is crucial for determining the optimal scale of production because it dictates how costs change with additional output.

    • The relationship between MC and AC is a central concept in short-run cost theory, often used to derive supply decisions in perfectly competitive markets.