III. Theory of the firm: production and costs
    A. Production theory
    2. Production in the long run

    c. Interpreting isoquants

    Note: Inputs = factors of production

    (1) factor intensities

    Pertains to factor combinations in production

    Example: capital per worker (K/L)

Consider 2 points on Q1 (b with more L and less K than a):     ? which is more k-intensive?     Production technique a is capital-intensive relative to b. Useful in    --comparing industries and    -considering how production techniques respond changes in resource prices     Examples of US industries Industry L-cost share K-cost share crude oil 32% 68% appliances 61% 39% apparel 83% 17%

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    (2) Returns to scale (RTS)

    Pertains to movements between isoquants, holding factor intensity constant.
      %DScale => the same %D for every input.

3 RTS possibilities:     (1) %DQ = %DScale => CRTS (pumpkin pies / wheat: 1/2/3)     (2) %DQ > %DScale => IRTS (costumes / water: 1/3/6)     (3) %DQ < %DScale => DRTS (Jack-O-Lanterns / bonsai trees: 1/1.5/1.8)     Why do RTS matter?     --optimal firm size: feasibility of competition depends on returns to scale     --resource productivity: higher labor productivity => higher real wage         2 sources of higher labor productivity:             (1) more K per L             (2) output rises faster than inputs (ex: IRTS)

Example: Cobb-Douglas:

See worksheet

    1. Q = BoL^BLK^BK  
        exponents = elasticities:
            BL = eQ,L; BK = eQ,K

    2. %DQ =(approximately) (BL+BK)·%DScale

    B. Costs for the firm

Learning objectives: Calculate and diagram short-run costs. Explain and illustrate how diminishing returns accounts for the way short-run costs behave. Calculate, diagram, and interpret isocost lines for long-run costs.

    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

    Unit costs

    2 main types:

    (1) marginal cost (MC) = DTC/DQ the change in total costs associated with a change in output.

    In the SR, DTFC/DQ = 0, so

    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)

    b. Resource productivity and short-run costs

    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 the 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

    End result:

    AVC = PL/APL

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