Intermediate Microeconomic Theory

1
Intermediate Microeconomic Theory

• Technology

2
Inputs

• In order to produce output, firms must employ
  inputs (or factors of production)
• Sometimes divided up into categories
• Labor
• Capital
• Land

3
The Production Function

• To produce any given amount of a good a firm can
  only use certain combinations of inputs.
• Production Function a function that
  characterizes how output depends on how many of
  each input are used.
• q f(x1, x2, , xn)
• units of output units of input 1 units of
  input 2units of input n

4
Examples of Production Functions

• What might be candidate production functions for
  the following?
• Vodka Distillary can be made from either
  potatoes or corn.
• Axe Factory each axe requires exactly one blade
  one handle.
• Car Wash requires both Labor and Capital,
  though not necessarily in fixed proportions.
• So what are Production functions analogous to?
  How are they different?

5
Production Functions vs. Utility Functions

• Unlike in utility theory, the output that gets
  produced has cardinal properties, not just
  ordinal properties.
• For example, consider the following two
  production functions
• f(x1,x2) x10.5x20.5
• f(x1,x2) x12x22

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Isoquants

• Isoquant set of all possible input bundles that
  are sufficient to produce a given amount of
  output.
• Isoquants for Vodka?
• Isoquants for Axes?
• Isoquants for Cars Washed?
• So what are Isoquants somewhat analogous to? How
  do they differ?

7
Isoquants

• Again, like with demand theory, we are most
  interested in understanding trade-offs.
• What aspect of Isoquants tells us about
  trade-offs in the production process?

8
Marginal Product of an Input

• Consider how much output changes due to a small
  change in one input (holding all other inputs
  constant), or
• Now consider the change in output associated with
  a very small change in the input.
• Marginal Product (of an input) the
  rate-of-change in output associated with
  increasing one input (holding all other inputs
  constant), or

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Marginal Product of an Input

• Example
• Suppose you run a car wash business governed by
  the production function
• q f(L, K) L0.5K0.5
• (q cars washed, L Labor hrs, K machine
  hrs.)
• What will Isoquants look like?
• What will be the Marginal Product of Labor at the
  input bundle L4, K 9?
• What will be the Marginal Product of Labor at the
  input bundle L9, K 9?

10
Substitution between Inputs

• Marginal Product is interesting on its own
  (unlike marginal utility)
• MP also helpful for considering how to evaluate
  trade-offs in the production process.
• Consider again the following thought exercise
• Suppose firm produces using some input
  combination (x1,x2).
• If it used a little bit more x1, how much less of
  x2 would it have to use to keep output constant?

x2
?x1
x2 x2
?x2
f(x1,x2)
f(x1,x2)
x1 x1
x1
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Technical Rate of Substitution (TRS)

• Technical Rate of Substitution (TRS)
• TRS Slope of Isoquant
• Also referred to as Marginal Rate of Technical
  Substitution (MRTS) or Marginal Rate of
  Transformation (MRT)
• So what would be the expression for the TRS for a
  generalized Cobb-Douglas Production function
  F(x1,x2) x1ax2b?

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Substitution between Inputs (cont.)

• We are often interested in production
  technologies that exhibit
• Diminishing Marginal Product (MP) in each input.
• Diminishing Technical Rate of Substitution (TRS).
  

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Diminishing MP
machine hrs (K) 9
9.5 9
6.7 cars
6 cars
4 5
9 10 worker hrs (L)
14
Diminishing TRS
machine hrs (K) 16 4

4 cars
1 4
worker hrs (L)