Modelling the producer: Costs and supply decisions
-
Upload
euridice-cerelia -
Category
Documents
-
view
23 -
download
0
description
Transcript of Modelling the producer: Costs and supply decisions
Modelling the producer: Costs and supply
decisions
Production functionProduction technology
The supply curve
Modelling the producer
Up until now, we have focused on how consumers choose bundles of good But we have not examined how these goods are
produced We have implicitly assumed that they just “exist”
But, clearly, a theory of decision should also explain the decision to produce goods. We shall see that the framework of consumer
choice can also be used to understand producer choices
Modelling the producer
The production function
Isoquants and Isocosts
Costs and supply
The production function
The production function is the relation between inputs to production and the amount of output produced for a given technology
For the moment, let us assume that there is a single input to production (simplification)A farm using labour to produce wheat
1 2, ,..., nY f I I I
The production function of a farm
Number of employees
Ton
s of
wh
eat
per
year
N˚ of employees
012345678
Output 0 310243640424240
The production function of a farm
Y
Feasible
Impossible
Production frontier
Number of employees
Ton
s of
wh
eat
per
year
The production function of a farm
Y
b
Decreasing returns starting from b
Ton
s of
wh
eat
per
year
Number of employees
The production function of a farm
Y
b
Maximum Output
Ton
s of
wh
eat
per
year
Number of employees
The production function
Total output (TP):
The average output (AP):
The marginal product (mP):
1 2, ,..., nY f I I I
for 1, 2,...,i
Yi n
I
for 1, 2,...,i
Yi n
I
The production function of a farm
Tons
of
wheat
per
year
mP, A
P
Y = 14
L = 1
mP = Y / L = 14
TP
Number of employees
Number of employees
The production function of a farm
Y = 14
L = 1
mP
TPTons
of
wheat
per
year
mP, A
P
Number of employees
Number of employees
The production function of a farm
TP
mP
AP = TP / L
Tons
of
wheat
per
year
mP, A
P
Number of employees
Number of employees
The production function of a farm
Decreasing returns(inflexion point)
TP
mP
AP = TP / L
Tons
of
wheat
per
year
mP, A
P
Number of employees
Number of employees
The production function of a farm
Maximumoutput
TP
mP
AP = TP / L
Tons
of
wheat
per
year
mP, A
P
Number of employees
Number of employees
The production function
Relation between the average and marginal products
The average product is maximal when it is equal to the marginal product
If mP>AP , then the average product must be increasing
If mP<AP , then the average product must be decreasing
Modelling the producer
The production function
Isoquants and Isocosts
Costs and supply
Isoquants and Isocosts
Lets go back to the case with several inputs to production. Imagine a case with 2 inputs
…which are labour (L) and capital (K)…
We define an isoquant as the set of combinations of inputs that are just sufficient to produce the same level of output. This is where the analogy with consumer choice
will become obvious
,Y f L K
Isoquants and Isocosts
Units of labour (L)
Un
its
of
cap
ital (K
)
Y= 150
Y= 100
Y= 50
X
Y
Z
A B
Isoquants are a 2-D mapping of the 3-D production function
Just like:
Indifference curves are a 2-D mapping of the 3-D utility function
Isoquants and Isocosts
Units of labour (L)
0
1
2
3
4
5
6
7
2 3 4 5 6 7 8 9 10
X
K
L
TRS = - (Slope of the Isoquant)
The technical rate of substitution
Rate of substitution of factorsK
L
Un
its
of
cap
ital (K
)
Isoquants and Isocosts
Reminder : The marginal product of a factor is the increase in total output (TP) following a marginal increase in that factor (∂L or ∂ K)
On any given Isoquant :
Note the similarity with the marginal rate of substitution
L
K
mPKTRS
L mP
2
1
1
2
x
x
mUxMRS
x mU
K LK mP L mP
Isoquants and Isocosts
The overall aim of the firm is to maximise profits, i.e. the difference between revenue and production costs However, for a given price of output, the
combination of inputs that maximises profits is also the one that minimises costs
Therefore, when choosing the best combination of inputs, the aim of the firm is to minimise the cost of production for any level of output
Isoquants and Isocosts
A 2 10
B 3 6
C 4 4
D 6 3
E 10 2
CombinationUnits
of capital (K)Units
of labour (L)
12 € 52 €
9 € 33 €
8 € 24 €
9 € 21 €
12 € 20 €
Cost = (L x pL)+ (K x pK)
If pL = 1€& pK = 1€
If pL = 5€& pK = 1€
Imagine 5 combinations A, B, C, D, E
The best combination depends on the price of the inputs
Isoquants and Isocosts
Isocost: Set of combination of inputs available for a given cost of production
All the spending on a single input
Units of labour (L)
Un
its
of
cap
ital (K
)
K LC Kp Lp
L
K K
pCK L
p p
Isoquants and IsocostsU
nit
s of
cap
ital (K
)
Units of labour (L)
The optimal combination of inputs minimises the production cost for a given level of output
C
Optimal combination
The isocost curve is tangent to the isoquant
Definition of the technical rate of
substitution at C !!!
Isoquants and Isocosts
The optimal combination is at the tangency of the isoquant and the isocost
Therefore :
The ratio between the marginal output of an input and its price (marginal cost of the input) is the same for all inputs ...
L L
k K
mP pTRS
mP p
kL
L K
mPmP
p p
Modelling the producer
The production function
Isoquants and Isocosts
Costs and supply
Costs and supply
There are different types of costs to consider
Depending on the type of input Fixed / Variable costs
Depending on the time horizon Short / Long term
Costs and supply
Important note: Economic costs take into account the existence of an opportunity cost The opportunity cost is the cost of giving up the
next-best alternative.
What is the cost of a year at university ? Objective costs: fees, books, laptop, food, rent,
etc. Opportunity cost: The year’s worth of
(minimum) wages you are forgoing whilst you are at university. In France, that’s 12,000 € !!
Costs and supply
Fixed and variable costsFixed costs are the incompressible costs
that the firm incurs regardless of the level of production. Example: lighting of a factory floor, setup
cost of a new production line, etc.
Any other production cost is part of the variable cost, because their size increases with the level of production.
Costs and supply
The time horizon is important in determining the fixed/variable nature of production costs.
In the short run, the firm cannot change the production technology (the method of production) or the combination of inputs (the size of the production plant is fixed)
In the long run, all the inputs are theoretically adjustable. Most of the inputs that are fixed in the short run become variable in the long run.
Costs and supply
The total cost curve gives the total expenditure on inputs required for any given level of output. It is the minimal cost of production for that level
It is obtained through the cost-minimisation process described in the previous section For each level of output (isoquant), the firm
chooses the combination on the lowest (tangent) isocost curve.
Costs and supply
TFC
Output(Y)
01234567
TFC(€)
1212121212121212
The total cost of a firm is obtained by adding the total fixed cost …
Costs and supply
TVC
… and total variable cost
Output(Y)01234567
TVC(€) 010162128406091
Costs and supply
TVCOutput
(Y)01234567
TVC(€) 010162128406091
TFC
TFC(€)1212121212121212
TC
Costs and supply
The average cost curve gives the unit cost of production for each level of output. It obtained by dividing total cost (TC) by the
level of output (Y)
The average fixed cost falls with the level of output An increasing production means that the total
fixed cost can be spread over more units
TCAC
Y
Costs and supply
The marginal cost curve gives the increase in total cost for a one-unit increase in output.
The marginal cost curve at a given level of output gives the slope of the total cost curve for that level of output
TCmC
Y
Costs and supply
mC
TC
Y=1
TC=5
Working out the marginal cost
Costs and supply
Output (Y )
Cost
s(€)
mCGeneral form of the marginal cost
Costs and supplyC
ost
s(€)
AFC
AVC
mC
x
AC
z
y
Output (Y )
Average and marginal costs
Costs and supply
The marginal cost curve cuts the average cost curve at its minimum point If the marginal cost is lower than the average
cost, the average cost is decreasing
If the marginal cost is higher than the average cost, the average cost is increasing
If the marginal cost is equal to the average cost, the average cost does not change
Costs and supply
This is important as it tells us about the level of returns to scale
If the average cost is decreasing, then total costs are increasing more slowly than output ⇒increasing returns to scale
If the average cost is increasing, then total costs are increasing faster than output ⇒ decreasing returns to scale
Costs and supply
The profit maximising condition A firm’s profit is given by total revenue minus
total cost :
The firm chooses its output such that profit is maximised (marginal profit is zero)
0 0TR TC
q q q
TR TC
0m
m m
C
C
R m
R
Costs and supply
On a perfectly competitive market, the price p is given by the market. We will see next week that in order to maximise
its profits, the firm will choose its output q such that the marginal cost of production equals the price ⇒ p = mC
This condition gives the supply curve of the firm
Note: if the market price is less than the average variable cost, the firm will prefer to produce nothing (shutdown condition)
Costs and supplyPri
ce AVC
mC AC
z
Output (Y )
s
pz
ps
qzqs
Supply curve