III. THEORY OF THE FIRM: PRODUCTION AND COSTS

    INTRODUCTION

    So far: looked at households as consumers
    --demand side of product markets
    --will appear again on supply side of resource markets

    Focus now: firms:
    --supply side of product markets
    --will appear again on demand side of resource markets (implicitly there now)

    The better you learned consumer theory, the easier producer theory will be.
    Else, get a 2d chance to learn it now.

Basic assumptions: goal: firms try to maximize profits
    Profits = TR - TC

    Constraints:
    Technology
    Input prices
    Demand for output

    In practice: firms maximize "discounted value of expected future profits"
    --intertemporal
    --expected

    A. PRODUCTION THEORY

    One of the constraints faced by firms is the technology they have to work with. A production function is intended to reflect this technology constraint

    A production function tells us the maximum amount of output which can be obtained from any specified set of inputs.

    Q = f(L,K,F3,F4,...)

    Q = output
    L = Labor
    K = Capital
    F3, F4,... = other inputs

    Note: must use inputs efficiently most unrealistic assumption here: only one output

    Ex: Q = 18 K^1/2L^1/2 (a Cobb-Douglas production function)

    L = 4 / K = 16 / Q = 18 x 2 x 4 = 144

    1. PRODUCTION IN THE SHORT RUN

    a. BASIC SITUATION

    Distinguishing characteristic:
    Short run => one or more inputs is fixed.
        Ex here: fixed input: K variable input: L

    No decision is ever really SR or LR.
    Every benefit-cost decision should take all future B's and C's into account, properly adjusted to recognize that $now>$later.
    The key is: + time => + # of costs you have control over.
    The only costs which matter = those you can control

    Geometry

    We can depict the behavior of total output of the firm as one input is allowed to vary, all others held constant.
    Here: L varies, K constant, typical of SR.

    Exercise: Q=widgets L=labor

Resume day 14

K  L   Q a  1  0  ___ b  1  1  ___ c  1  2  ___ d  1  3  ___ e  1  4  ___

    Note: it's possible to add so much L that tp falls--firms would never do so voluntarily.

    ? What's the meaning of the convex stretch of Q?

    Suppose we raise this firm's capital: k = 2.

    ? What happens in our diagram?

    For each combination of the fixed inputs we can and must draw a total product curve for the variable input.

    b. RESOURCE PRODUCTIVITY CONCEPTS

    Our ultimate concern: how to choose inputs to produce our output as inexpensively as possible.

    For decisionmaking, it turns out to be very useful to make use of some per unit resource productivity concepts instead of just total output
    Input productivity concepts are meaningful only when the amounts of the other inputs are held fixed

    Ex: given Ko, a fixed amount of k:

    Average Product of Labor (APL):
        APL = Q/L

    Marginal product of labor (MPL): Change in total output associated with a change in labor input:          MPL = DQ/DL

   Ex. from widgets:
      K   L    Q   APL   MPL
    a 1  ___  ___  ___
    b 1  ___  ___  ___  ^___

    ? Does APL rise or fall?

    ? How does MPL account for that?

Universal relationship between MPL and APL:    As L rises: MPL > APL => __________ MPL = APL => __________ MPL < APL => __________

    Notes:
    (1) MPL rises at first--maybe, maybe not (sports)
    (2) When MPL 1st falls, APL still rises.
    (3) MPL can turn negative, but => Q falls => never worth hiring such workers.

Diminishing returns

    Behavior of productivity curves depicted above is thought to be quite general:
    Law of dinimishing returns: if one input is increased while the others are held constant, the marginal and average products of the variable input will eventually decline.
    DMR = diminishing marginal returns
    DAR = diminishing average returns

    Assumes
    (1) a given technology
    (2) other inputs fixed.

    Ex: Cobb-Douglas production function:

    Ex:
    Q = 18 K^1/2L^1/2
    K = 4 => Q = 36L^1/2

    APL = 36L^1/2/L = 36/L^1/2

    MPL = dQ/dL = 1/2(36L^-1/2) = 18/L^1/2

    Note from formulas:
    --L in denominator: APL and MPL fall as L rises.
    --Therefore, for all L, this C-D production function has DMR and DAR.
    (Verify that it will not have DMR and DAR if exponent on L exceeds 1.)

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