1. Modelling the producer: Costs and supply decisions
Production function
Production technology
The supply curve

2. 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

3. Modelling the producer
The production function
Isoquants and Isocosts
Costs and supply

4. 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

5. The production function of a farm
employees 1 2 3 4 5 6 7 8
Output 3 10 24 36 40 42
Tons of wheat per year
Number of employees

6. The production function of a farmY
Impossible
Production frontier
Tons of wheat per year
Feasible
Number of employees

7. The production function of a farmY
Decreasing returns
starting from b
Tons of wheat per year b
Number of employees

8. The production function of a farmY
Maximum Output
Tons of wheat per year b
Number of employees

9. The production function
Total output (TP):
The average output (AP):
The marginal product (mP):

10. The production function of a farmTP
Tons of wheat per year
DY = 14
DL = 1
Number of employees
mP = DY / DL = 14
mP, AP
Number of employees

11. The production function of a farmTP
Tons of wheat per year
DY = 14
DL = 1
Number of employees
mP, AP mP
Number of employees

12. The production function of a farmTP
Tons of wheat per year
Number of employees
mP, AP
AP = TP / L mP
Number of employees

13. The production function of a farmTP
Tons of wheat per year
Decreasing returns
(inflexion point)
Number of employees
mP, AP
AP = TP / L mP
Number of employees

14. The production function of a farmTP
Tons of wheat per year
Maximumoutput
Number of employees
mP, AP
AP = TP / L mP
Number of employees

15. 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

16. Modelling the producer
The production function
Isoquants and Isocosts
Costs and supply

17. 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

18. Isoquants and Isocosts
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 Z
Units of capital (K) Y X
Y= 150 A B
Y= 100
Y= 50
Units of labour (L)

19. Isoquants and Isocosts
The technical rate of substitution 7
Units of capital (K) 6 5 X
TRS = - (Slope of the Isoquant) 4
 K 3 2 1 2 3 4 5 6 7 8 9 10
Units of labour (L)
 L

20. 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

21. 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

22. Isoquants and Isocosts
Imagine 5 combinations A, B, C, D, E
Cost = (L x PL)+ (K x PK)
Units
of capital (K)
Units
of labour (L)
If PL = 1€
& PK = 1€
If PL = 5€
& PK = 1€
Combination A 2 10 B 3 6 C 4 D E
12 €
52 €
9 €
33 €
8 €
24 €
21 €
20 €
The best combination depends on the price of the inputs

23. 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 capital (K)
Units of labour (L)

24. Isoquants and Isocosts
The optimal combination of inputs minimises the production cost for a given level of output
The isocost curve is tangent to the isoquant
Units of capital (K)
Definition of the technical rate of substitution at C !!! C 
Optimal combination
Units of labour (L)

25. 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 ...

26. Modelling the producer
The production function
Isoquants and Isocosts
Costs and supply

27. 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

28. 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 € !!

29. Costs and supply Fixed and variable costs
Fixed 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.

30. 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.

31. 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.

32. Costs and supply
Output
(Y) 1 2 3 4 5 6 7
TFC
(€) 12
The total cost of a firm is obtained by adding the total fixed cost …
TFC

33. Costs and supply … and total variable cost TVC Output TVC (Y) (€) 1 101 2 3 4 5 6 7
TVC
(€) 10 16 21 28 40 60 91
TVC
… and total variable cost

34. Costs and supply TC TVC TFC Output (Y) 1 2 3 4 5 6 7 TFC (€) 12 TVC1 2 3 4 5 6 7
TFC
(€) 12
TVC
(€) 10 16 21 28 40 60 91 TC
TVC
TFC

35. 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

36. 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

37. Costs and supply TC
Working out the marginal cost
DTC=5 mC
DY=1

38. Costs and supply General form of the marginal cost mC Costs(€)
Output (Y )

39. Costs and supply Average and marginal costs mC AC AVC Costs(€) z y x
AFC
Output (Y )

40. 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

41. 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

42. 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)

43. 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)

44. Costs and supply Supply curve mC AC Price AVC z s Output (Y ) pz ps qsqz
Output (Y )