modelling the producer: costs and supply decisions production function production technology the...

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


The production function

Isoquants and Isocosts

Costs and supply


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


Y

Feasible

Impossible

Production frontier

Number of employees

Ton

s of

wh

eat

per

year


Y

b

Decreasing returns starting from b

Ton

s of

wh

eat

per

year

Number of employees


Y

b

Maximum Output

Ton

s of

wh

eat

per

year

Number of employees


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


Tons

of

wheat

per

year

mP, A

P

Y = 14

L = 1

mP = Y / L = 14

TP

Number of employees

Number of employees


Y = 14

L = 1

mP

TPTons

of

wheat

per

year

mP, A

P

Number of employees

Number of employees


TP

mP

AP = TP / L

Tons

of

wheat

per

year

mP, A

P

Number of employees

Number of employees


Decreasing returns(inflexion point)

TP

mP

AP = TP / L

Tons

of

wheat

per

year

mP, A

P

Number of employees

Number of employees


Maximumoutput

TP

mP

AP = TP / L

Tons

of

wheat

per

year

mP, A

P

Number of employees

Number of employees


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




Costs and supply


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


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


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

)


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


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


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


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 !!!


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




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

modelling the producer: costs and supply decisions production function production technology the...

Documents

wheatthe production

tp ltons of wheat

farmtons of wheat

btons of wheat

mptptons of wheat

apnumber of employeesnumber

average output ap

tpnumber of employeesnumber