Lecture 1 FirmBasics edited version .pdf - Frank Cowell:...

Frank Cowell:
Microeconomics
The Firm: Basics
Lecture 1
29 - 07 - 2022

Frank Cowell:
Microeconomics
The Firm: Basics
◼
Disclaimer: This lecture is partly based on lecture
slides of Prof Frank Cowell posted at

Frank Cowell:
Microeconomics
Technology
◼
In the first part of the course we will be interested in studying
the behavior of firms .
◼
The amount of output firms produce depends on the
characteristics of the available technology .
◼
In this first lecture we introduce important concepts regarding
technology that will help us in order to study profit
maximization (ch . 2 - 3 ) and cost minimization (ch . 4 - 5 ) of
Varian (chap - 3 ) of Cowell
◼
We are aiming at introducing some definitions about technology
and a few results that will be useful later .

Frank Cowell:
Microeconomics
Roadmap
◼
Assume profit maximising firms that operate in a
competitive environment
◆
Basics of the production function
◆
Input requirement set
◆
Convex and Non - convex technologies
◆
Marginal rate of technical substitution
◆
Elasticity of Substitution
◆
Returns to scale

Frank Cowell:
Microeconomics
The basics of production...
◼
Some of the elements needed for an analysis of the
firm
◆
Technical efficiency
◆
Returns to scale
◆
Convexity
◆
Substitutability
◆
Marginal products
◼
This is in the context of a single - output firm...
◼
...and assuming a competitive environment .
◼
First we need the building blocks of a model...

Frank Cowell:
Microeconomics
Some definitions
◼
Imagine of 𝑛 available goods that can be either inputs
or outputs, where ?
??
and ?
? ?
are the quantities of the
good j used as an input and output respectively . The net
output of good j is given by ?
?
= ?
? ?
- ?
? ?
.
◼
A production plan is a list of net outputs for the 𝑛
goods ; ? = ( ?
1
, ?
2
… . ?
?
) ∈ ℝ
?
◼
Convention ; If ?
?
>(<) 0 then the good is a net
output(input ) .
◼
The set of all technologically feasible production plans
is the production possibility set , 𝑌 ∈ ℝ
?
.
◼
For ease of exposition let us denote inputs by ? and
output by ?

Frank Cowell:
Microeconomics
Notation

Quantities
x
i
• amount of input i
x = ( x
1
, x
2
, ..., x
m
)
• input vector
• amount of output
y

Prices
• price of input i
w = ( w
1
, w
2
, ..., w
m
)
• Input-price vector
• price of output
p
For next
presentation
w
i

Frank Cowell:
Microeconomics
Feasible production

The basic relationship between
output and inputs:
y 
f
( x
1
, x
2
, .... , x
m
)

This can be written more compactly
as:
y 
f
( x )
• single-output, multiple-input
production relation

f gives the maximum amount of
output that can be produced from a
given list of inputs
•Note that we use “  ” and not
“=” in the relation. Why?
• Consider the meaning of f
Vector of inputs
The production
function
distinguish two
important cases...

Frank Cowell:
Microeconomics
Technical efficiency
• The case where
production is technically
efficient
• The case where
production is
(technically) inefficient

Case 1:
y = f ( x )

Case 2:
y < f ( x )
Intuition: if the combination ( x ,y ) is inefficient you can
throw away some inputs and still produce the same output