III. Theory of the firm: production and costs

    B. Costs for the firm

    Introduction

    Any firm which maxes profits must minimize costs

    Economic cost of an input: the value of the input in its best alternative use (i.e., its opportunity cost)
    Most problematic: capital
    Generally, if you borrow, you pay interest--this is a cost, both to accountants and to economists
    If you use equity capital, direct investment, accountants call the return profit. But invested funds have an O/C very similar to borrowed funds--those funds could have earned some return by being loaned out instead. This foregone income is an O/C and is considered as a cost in econ.

    Basic cost equation:

    TC = pL^.L + pK^.K + p3^.F3 + p4^.F4 +...

    PK includes the normal return to K.

    1. Short-run costs

    Recall, in SR, some inputs are in fixed supply. This results in fixed costs.

    a. Total costs and unit costs

    Total fixed costs (TFC): Costs which do not change with output and which the firm must pay even if Q=0.
    Recoverable only if the firm exits from the industry vs "sunk costs"; must be paid even with exit.

    Total variable costs (TVC): Costs which change with the level of output.

    TC = TVC + TFC

    Ex. Here: pK^.K is fixed / pL^.L is variable

    So: TC = PL^.L + PK^.K
               = TVC + TFC

Example: IBM Pisces 370/68 series computer:     TFC = $30M     TC, Q= 500=$250M     ? How does TFC look?     ? What is TVC when Q=0     ? What is TVC at Q=500?     ? What does slope of TC tell you?     ?What does slope of TVC tell you?

    Unit costs

    2 main types:

    (1) marginal cost (MC): the change in total costs associated with a change in output.
        Basic def.: MC = DTC/DQ (true in SR and LR)

    In the SR, DTFC/DQ = 0, so

DTC/DQ = DTVC/DQ+DTFC/DQ =	DTVC/DQ in SR = SRMC
slope of TC	slope of TVC

    In SR, MC does not change with a change in TFC.

    (2) Average costs: costs per unit of q.

    TC/Q = TVC/Q + TFC/Q

    ATC = AVC + AFC

    note: AFC falls continuously as Q rises (it's a rectangular hyperbola)

Complete worksheet on unit costs

    b. Relating costs and resource productivity--the short run

    Issue now: Why do a firm's SR costs rise as output rises?

    Recall: We started SR production theory by looking at resource productivity
        MPL, APL, diminishing returns
    So what? We'll see so what now.
    These resource productivity considerations determine the behavior of firm costs.

    Intro. econ: costs rise because as you hire more, hire less well suited resources, pay higher prices for inputs, etc.--all false in general.
    The truth: for most firms, as Q rises in SR, input prices are constant.
    Quality of inputs is constant.
    Unit costs rise in SR because of diminishing returns

    (1) MC and MPL

    Suppose a firm wants to increase Q

    ? In the SR, what will the firm have to do?

    ? What measures how much their costs will rise?

    ? What do we call the extra output we get?

    We combine this information to calculate MC:

    MC = DTC/DQ = DTVC/DQ = D(PL^.L)/DQ

        = PL^.(DL)/DQ = PL / (DQ/DL) = PL/MPL

    End result:

    MC = PL/MPL
    Notes: PL is constant
MPL rises => MC falls
        MPL falls (because of DMR) => MC rises

    Ex:
    PL = $60
    MPL = 40
    ? MC of the 40 extra units =?

    Recap: 2 ways to measure MC:
    Method 1: given total cost and output data: DTC/DQ
    Method 2: given input cost and productivity data: PL/MPL

    In general, the information is about the same.
    Choose the method which gives you the more precise estimate

    (2) AVC and APL

    Works the same way:

    AVC = TVC/Q = PLL/Q = PL/(Q/L) = PL/APL

    Again, APL rises => AVC falls,
    APL falls (diminishing average returns) => AVC rises

See worksheet on resource productivity and SR costs:

    Summary:
        MC = PL/MPL: MPL falls => MC rises
        AVC = PL/APL: APL falls => AVC rises

    2. Long-run costs

    Now: all inputs are variable
    SR productivity concepts aren't meaningful now.

    The isocost line (Co)

    Recall: TC = PL^.L + PK^.K

    If we fix TC at TCo, TC becomes a constraint just like BL constrained consumers

    Helpful to be able to depict this in input space, to combine it with isoquants

    When we do this, we get an isocost line: an isocost line tells us the combinations of inputs which can be purchased for the same total cost.

    TCo = PL^.L + PK^.K =>
    PK^.K = TCo - PL^.L =>
    K = TCo/PK - (PL/PK)^.L

    Intercept = affordable K w/L=0
    Slope = PL relative to PK

Example:     TC = 300     PL = 60; PK = 20     300 = 60L + 20K     K = 300/20 - (60/20)L     K = 15 - 3L     Opp.cost of 1L = 3K     ? +PL => steeper or flatter Co?

    The logic:

	General case:	|	Example here:
	PL = $ needed for an extra L	|	PL = $60
	PK = rate $ accumulated by giving up K	|	PK = $20
		|
	=> PL/PK	|	$60/($20 per K)
	= total K you must give up to afford 1L	|	3K for 1L
	= |-DK/DL| (the size of the slope of Co)	|

    The math:
    Along Co, DTC = 0 =>
    vary L&K to keep TC the same =>
    PKDK = PLDL =>
    |-DK/DL| = PL/PK
    size of slope = PL relative to PK

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