B. Costs for the firm
    1. Short-run costs
    b. Resource productivity and short-run costs

See worksheet on resource productivity and SR costs: (Key)

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

Application: IBM Pisces 370/68 series computer:     TFC = $30M     TC when Q=500=$250M     ? AFC = $60K     ? ATC = $500K     ? AVC = $440K? = constant     ? MC = $440K     Graph MC, AVC, ATC

2. Long-run costs

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

    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?

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

III. Theory of the firm: production and costs
C. The producer's optimum

Learning objectives: Use productivity-cost relationships to recommend cost-reducing input adjustments. Diagram and interpret the tangency condition for a cost-minimizing optimum. Solve cost-minimization problems.

    We can look at a firm's decisionmaking from 2 directions:
    Given Co: How much can the firm produce with that budget--strictly analogous to consumer theory
        --Max Q given Co, PL, PK
    Not really the typical situation

    Alternatively and more common:
    Given an output level to produce: What is the minimum cost of producing that output
    --this is the problem we'll work on. It's a problem which must be solved for any Q which the firm produces.
    --rather than start with some BL and move Uo's around to reach max., start with some Qo and move TCo around to find min. TC.
    --but equil. will look the same
    --we'll want to then figure out just how much the final TC is.

    Comparing productivity (value) and cost

c PL $5 PK $10 L 60 K 45 Q 300 MPL 9 MPK 4 MRTS 2.25 TC $750     ? is this firm at a production optimum?     MRTS = MPL/MPK = 9/4 = 2.25     PL/PK = $5/$10 = 1/2

    MRTS > PL/PK
    => relative prod'y of another L exceeds its relative cost
    => hire L, fire K.

    Substitution process: +L, -K --> MRTS falls.
    Continue until MRTS = PL/PK

    Note the tangency condition:
    Relative productivity of labor = its relative cost
 

    Consider Least-cost condition worksheet