Appunti Industrial Organization + schemi risoluzione esercizi (a mano)

Industrial Organization

De Francesco Massimo Alfiero

Lezione 1 – Recap of Micro and Macro (con slide)

The Firm

An economic organization which produces (material) goods and/or services using inputs.

We shall mainly be concerned with the private firm but we will also deal with public firms, especially in connection

with natural monopoly.

The private firm as aiming at maximal profits -> the behavioural assumption usually made with regards to the

private firm is that it aims at maximising profits, namely, the difference between revenues and costs:

Profits = Revenues – Costs

Some Underlying assumptions

- The level of profits arising out of some decisions made by the firm is not constant over time

- Based on the above observation, it would perhaps be more accurate to say that the firm aims at maximizing the

“value” it creates for its owners (its shareholders, in case of a corporation).

- The last criterion is what is know as the maximization of Net present value (NPV): namely, maximization of the

present value of its cash flows.

The firm’s costs include, besides what is spend out for the inputs it must purchase, the so called “opportunity costs”.

An opportunity costs relates to factors of production which are conferred to the firm by the owner(s): by so doing,

the owner renounce to selling these factors to other. The proceeds he would have otherwise earned is an

“opportunity costs” that must be considered in order to evaluate whether the firm is rewarding for its owner(s).

Some examples of “opportunity costs”:

- The owner of the firm might work in it. By so doing he is renouncing to the wage he would earn if working as an

employee at some other firm: that wage must be considered as a cost

- The owner of the firm might invest part of his monetary wealth in the purchase of equipment to be employed in

the firm. By so doing, he renouncing to the opportunity to an alternative investment of his wealth, for instance the

purchase of bonds of the government of Japan: the missed interest on this alternative investment is an opportunity

cost.

- Suppose that the building where the firm operates is owned by the owner of the firm. Clearly, by using that

building in such a way, the firm owner is renouncing to obtaining a rent on his building. The foregone rent is an

opportunity cost.

Based on all above, what is the meaning of “zero profits”?

If the firm is obtaining zero profits, this means that firm’s proceeds cover all the firm’s costs, including its

opportunity costs. This in its turn means that the owner of the firm obtain a “normal remuneration” on the factor of

production he confers to the firm: in working in the firm, he obtains no less than what he would obtain if he was

instead an employee of another firm; the capital he invests in his firm obtains the same remuneration it would

obtain if invested in the best alternative way, and so on and so forth.

Cost Function C(q)

Consider a firm that produce a single commodity

- For any quantity q, the cost function C=C(q) shows what is the minimum cost at which the firm can produce that

level of output.

- This suggests that, behind the cost function, there is an underlying optimization problem that the firm has already

solved: each level of output is being produced by the firm by combining its inputs in such a way as to minimize costs

for that output level.

- Indeed, minimizing total cost for any level of output is one necessary condition to be meet in order for the firm to

maximize its profits. ()

= −

Short-run cost function vs Long-run cost function

- In the short-run there are constraints on the set of alternatives available to the firms as far as the quantities of

inputs to be employed. (there are some factors that are fixed in the short-run, whereas the quantity of these factors

can be changed in the long-run)

In particular, but not only:

- Moving to a larger plant or enlarging the existing plant might be unfeasible or too costly in the short-run and the

same might be the case for changing the machinery in use.

The short-run cost function: () ()

= +

()

=

Where: = variable cost, fixed cost.

Short-run average cost: ()

()

= +

()

() ()

= =

Where: Average Variable Cost = , Average Fixed Cost =

Marginal Cost (MC)

Three slightly different ways to defining MC: =

1) The increase in cost when the firm output is raised by one unit: =1

(+)−() (+)−()

′ ()

= =

2) The “rate of change” of cost, namely: or

→0

There is a close relationship between these definitions, indeed:

′ ′

() ()

≅ ≅

and hence

| |=1

′ ()

=

We will always use

A typical representation of average and marginal cost curves in the short run is the following page: these curves have

been derived from the following short-run cost function: 2 3

()

= 18 − 4 + + 16

Short-run AC, AVC (short-run average variable cost) , MC (Marginal cost) Curves

- The interception between marginal cost and

average cost is at the minimum of average cost, and the

same is true for the interception between the marginal

cost and the average marginal cost.

A few important properties (saltata)

() ()

=

() ()

=

Proof of (b)

It is normally assumed that in the short-run average cost is first decreasing in output and next increasing. Why?

The decreasing part of AVC(q) curve:

There are economies in the use of the labour input.

Notice: labour is to some extent an “indivisible” factor. Consequently, when the firm produces very small quantities

it employs very few workers.

When q increases, the workforce consequently increases and each employee specializes himself in a restricted

number of tasks. This increases labour productivity, which in turn reduced labour cost per unit of output.

Thus AVC (q) decreases as q increases and, for the same reason, AC(q) decreases too as q increases.

Another reason for the fall in the AC curve is that, of course AFC(q) = decreases as q increases.

In analytical terms:

Let L= L(q), the quantity of labour employed.

() =

Then labour productivity q/L can be written as ()

Total labour costs W:

()

()

= = = =

( ) ()

Then “Unit Labour cost”, ULC = W/q, can be written as a function of q:

()

= =

()

()

Therefore, ULC decreases as q increases since increases as q increases.

Thus AVC (q) decreases as q increases and, for the same reason, AC(q) decreases too as q increases.

Another reason for the fall in the AC curve is that, of course, AFC(q) = decreases as q increases.

Notice: The rate of fall of ULC (q), and hence of AVC(q) is higher the lower the level of output; it becomes weaker

and weaker as the total output … , and hence the firm’s workforce is becoming larger and larger.

From some level of q onwards, the AVC and AC curves are increasing in q

In the short-run, the plant, the number and types of machines and the quantities of some other inputs are fixed: to

increase its output q the firm can only increase the quantities of the variable inputs, but they must be combined with

fixed quantities of the fixed inputs.

As a consequence, machines are utilized more intensively, the workers must often work overtime and night shifts

must be introduced. All this tends to increase cost per unit of output: machines need to be repaired more frequently

and must be reset more frequently; overtime wage is higher than the ordinary wage, congestion at the fixed

equipment occurs which increases waiting time on the production lines.

At any rate, I represent below what appears to be a more realistic behaviour of the AVC and MC curves in the short

run:

Long-run cost function

In the long-run, several costs that in the short-run are fixed

become variable: in particular the firm can equip itself with

new machines as its old ones become obsolete.

Similar to the short-run cost function, the long-run cost

function LRC(q) shows, for any quantity q, the minimum cost

at which that level of output can be produced in the long-run.

LRAC: The lowest envelope of the SRAC curves

Lezione 2 – (continua) (con slide) -> smooth version:

The U-shaped LRAC of microeconomics textbooks

There is a first range of output levels over which there are «economies of scale»: LRAC decreases as q increases;

Then there is a subsequent range of output levels over which there are «diseconomies of scale»: LRAC decreases as

q increases.

Whatever quantity it wants to produce, the firm chooses the plant which minimize its costs for that level of output.

the cost the firm faces to produce a certain output:

()

() ()

= = -> in order to minimize the total cost, the firm has to minimize the Average Cost for that

output. How? By choosing this plant

Standard assumption: the average cost in the long run is first decreasing

as output increases, then from a certain quantity it starts increasing. An

alternative way of saying this is the following: at first total cost

increases, but in a lower proportion than output:

() ()

= ⋅ → = -> this situation is called

economies of scale

Then we have the diseconomies of scale.

According to empirical analysis

• There is a first range of output levels over which LRAC is decreasing as q increses.

• After that range of output, there is a range of output levels over which LRAC remains more or less constant as q

changes.

• It is not clear whether LRAC becomes increasing in q at high levels of output.

Now, applying the “lenses” of applied industrial organization, we have a glance of reality (according to empirical

studies), knowing that the situation it’s a bit different: AC is first decreasing, then it reaches a minimum and then it

stays more or less constant. What is a bit controversial is whether for outputs level large enough, AC becomes

increasing (it is still not clear this part). However, our concern will be to understand reasons underlying economies of

scale, so why LRAC is decreasing in output as the firm becomes larger. There are number of reasons:

What lies behind economies of scale

• Again, the benefits of increased specialization.

• «indivisibilities of inputs», in particular of machines.

• For some capital goods, costs often mainly depend on their area, S (think of tanks or pipelines); by contrast their

«capacity» depends from the volume, V. As the firm increases output, it must resort to a larger tank or pipeline,

hence V and S increase. But V/S increases as S increases. This means a reduction in the cost per unit of output.

1) Indivisibility of capital equipment: due to the

indivisibility of the Labour factor of production,

when the firm becomes larger, it increases its

workforce, and the member of this workforce (the

workers) becomes more specialized. This increase

labour productivity and, on the reverse side, AC

decreases.

An example of Indivisibilities Railway trasport

requires railwaty carriage, locomotive, travelling

personnel, railway station. Some of these costs do

not change as the volume of daily traffic increases: as a consequence the LRAC(q) decreases as q increases.

A numerical example for capital indivisibilities

K: quantity of capital (a specified machine or bundle of machines)

r=200: cost per unit of capital 1 unit of K produces up to 100 units of output.

Then:

∈ 1,100 requires 1 unit of K.

∈ 101,200 requires 2 units of K.

∈ 201,300 requires 3 units of K; etc. ()

In each of the above intervals of output, is decreasing – there are economies of scale - and

reaches its minimum at interval extreme, where productive capacity is fully utilized: = 2

Notice that these economies of scale are mostly significant at the initial intervals of output :

∈ (100)=2;

For 1,100 , = 1, = 200 1 = 200,

∈ (200)=2;

101,200 , = 2, = 400: 101 = 3,96,

∈ (300)=2;

For 201,300 , = 3, = 600: 201 = 2,98,

2) The need of inventories doesn’t increase as the same proportion as output. Them (that for the firms are

costs) increase in a lower proportion than output, and this tells that average costs tends to decrease.

3) Physical reason: let’s think for example of a tank, usually the cost of this type of equipment mostly depends

on the material which make the surface, whereas the capacity (the quantity of output I can put inside it)

depends on the volume. The ratio between the surface and the volume is a proxy of the ratio between costs

(depending on the surface) and output (depending on the volume). Bigger firms needs more capacity, and as

long as in increases the average cost decreases.

Areas and volumes: For some capital goods, costs often mainly depend on their area, S (think of tanks or

pipelines); by contrast their «productive capacity» depends on the volume, V. As the firm increases output, it

must resort to a larger tank or pipeline, hence V and S increase. But V/S increases as S increases. This means

a reduction in the cost per unit of output.

Example: In a cube, let be the side. Then: Now, suppose that cost is proportional to the surface,

= whereas the quantity that can be produced is

ℎ

proportional to the volume of the container, q= :

6

=

Then we have = ℎ ℎ

average cost is decreasing in (the dimension of the cube).

4) “Learning-by-doing”

Experience in carrying out the production process enhances the knowledge in a number of ways and this in

turn tends to increase productivity («learning by doing»).

A proxy of the accumulated experience up to some date is the cumulative production Q made by the firm

over the (more or less recent):

the current cost function can then be written as

The cost functions show the relationship between output and costs. This means that we put into relation the

quantity of output that the firm produces in a certain unit of time, with the costs incurred for producing that

quantity. But it turns out that the effectiveness and efficiency of the firm in production depend on the

experience (as accumulated knowledge), which, by learning of “routines”, decreases costs as time pass.

-> C(q, Q) -> Cost as a function of quantity and accumulated experience over the last x years.

What are the reasons behind the hypothetical “diseconomies of scale”?

1) According to someone, if the firms becomes a giant firm, then LRAC starts increasing. This happens because there

are “managerial diseconomies of scale”: among the factors of production, there is also the managerial factor,

persons who are involved and in charge of coordinating and supervising the activities within the firm. Managers

need information, which is costly even withing one single organization, from people who have those info -> as org.

become larger, the amount of information decreases (since not shared by everyone in the org.).

There are economies of scale in the management of inventories of final output, components and semi-finished

goods: the quantity of inventories per unit of finished output tend to decrease as output increases. When the firm

produces more it makes larger orders of raw materials, components, and semifinished products, which in turn allows

lower purchasing prices.

Possible cause of diseconomies of scale: «managerial diseconomies»

As output increases and the firm becomes larger and larger, coordination among its various parts becomes more

complex and costly. Issues of «asymmetric information» arise since information is not immediately available to every

part of the firm. This asymmetry might even induce opportunistic behaviour in some members of the organization.

Economies of scope 1 2 1 2

The joint production by a single firm of quantities and of goods 1 and 2 entails a lower cost than if and

were separately produced by two distinct firms.

1 1 2 2

More formally: Let and be the cost functions of goods 1 and 2, respectively, when separately produced;

2)

And let C (1 + be the cost function if goods 1 and 2 are produced jointly by one firm.

2) 1(1) 2(2)

Then, «scope economies» means that C(1 + < + .

Two main reasons for economies of scope

• The production process of good 1 and the production process of good 2 may require some common input X.

If 1 and 2 are produced independently by two different firms, it might happen that X can be only partially utilized in

each production process; by contrast, if goods 1 and 2 are produced jointly, that input X may be more fully utilized.

• Producing good 1 along with good 2 may increase the productivity of some input necessary to produce good 1. This

sometimes happen in agriculture.

Elasticity of Demand (with respect to the price)

• Demand function: q=q(p)

• The elasticity of the demand is the ratio between the proportional change in the quantity demanded and the

=

proportional change of the price.

Re-rewrite as: . In the economic analysis it is often employed the