Theory of Firms
V. Hajko
2014
V. Hajko (FSS MU) Introduction to Economics 1 / 24
1 Firm behavior
2 Production function
3 Costs
4 Revenues and demand
5 Profit maximization problem
V. Hajko (FSS MU) Introduction to Economics 2 / 24
Firm behavior
The principal interests of this lecture
What is the goal of the firm?
How do firms make decisions?
What is a production function, marginal product, fixed and variable
costs, marginal costs and marginal revenue?
What is a perfectly competitive market and what is imperfet
competition?
What is the link to the demand function?
How the firm determines its supply function?
V. Hajko (FSS MU) Introduction to Economics 3 / 24
Firm behavior
The goal of the firm
The producers of the goods and services are called firms (to
distinguish the specific production units and their behavior)
The business operation of the firm is the transformation of (typically
multiple) inputs into (one or more) outputs.
The formal description of this transformation is called the production
function
This transformation faces economic constraints - there are costs of
production
The firm sells its production - it has to be aware of the demand in
order to calculate its revenues
The goal of the firm is to maximize profits (profit = total revenues total
costs, Π = TR − TC)
Can you provide the reason why?
V. Hajko (FSS MU) Introduction to Economics 4 / 24
Firm behavior
Firm’s profit maximization problem
In general, the firm aims to maximize profits Π = TR − TC
the solution to the problem is found by setting the optimal Q (since
Π (Q) = TR (Q) − TC (Q)
the optimal Q can be produced using various combinations of inputs
(typically, K and L) (i.e. Q (K, L)), hence the firm can find the
solution by setting optimal K and L (i.e.
Π (Q (K, L)) = TR (Q (K, L)) − TC (Q (K, L)))
alternative method is to formulate the cost minimization problem to
produce a given quantity ¯Q
V. Hajko (FSS MU) Introduction to Economics 5 / 24
Production function
The production function
The production function (Q = f (F1, F2, . . . FN )) describes the
technological process of the transformation of inputs to outputs.
The typical production factors (F) considered in the production of the
firm are: capital (K) and labor (L).
Q = f (K, L)
V. Hajko (FSS MU) Introduction to Economics 6 / 24
Production function
Short run and long run
Due to the technological limitations, it is usually time consuming to
change the amount of capital used in production.
This assumption is reflected in the distinction between the the short
run and the long run
in the short run, we consider some of the production factors (typically
capital (K)) as fixed and only some as variable (typically labor (L))
i.e. Q = f ( ¯K, L), or for the sake of simple notation Q = f (L)
in the long run, we consider all the production factors as variable
V. Hajko (FSS MU) Introduction to Economics 7 / 24
Production function
Marginal product
The marginal product of factor Fi (MPFi = ∂Q
∂F ; note it also shows
the slope of the production function!) is the increase in output caused
by the additional unit of the input (while other inputs remain
constant)
The marginal product is not constant, but is (typically) diminishing
In contrast, if you hire additional worker, or buy additional machine, the
costs of the aditional unit are often the same as with the previous unit
You can compare the marginal benefit (the increase in production) with
the marginal costs (the increase in costs) to determine whether or not
you want to add the additional unit of the input.
Try to provide an example.
V. Hajko (FSS MU) Introduction to Economics 8 / 24
Figure : Production function in the long run
4 6 8 10 12 14 16 1820
40
60
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
x 10
6
Figure : Production function in the short run
1 2 3 4 5 6 7 8 9
−5000
−4000
−3000
−2000
−1000
0
1000
2000
3000
4000
Figure : Production function in the long run, no diminishing returns
(non-decreasing function)
0
5
10
15
20
0
20
40
60
0
1000
2000
3000
4000
5000
Production function
Isoquants
Isoquants are the contour lines of the production function.
Isoquants represent all points, where the various combinations of
amounts of inputs (K and L) lead to the same values of the
production function.
they show the one given level of output that can be produced using
various combinations of inputs
In a similar fashion as the indifference curves, the isoquants are the 2-D
representation of the 3-D figure
the slope of an isoquant is called the marginal rate of technical
substitution - it shows the ratio in which we can substitute the
production factors while keeping the output constant
V. Hajko (FSS MU) Introduction to Economics 12 / 24
Figure : Isoquants of the production function in the long run, no diminishing
returns (non-decreasing function)
2 4 6 8 10 12 14 16
5
10
15
20
25
30
35
40
45
Costs
Costs
In order to produce something, the firm has to pay for the inputs.
We need to consider both implicit and explicit costs
Explicit costs: everything that will show up in the accounting (e.g.
the electricity bill, the wages of hired workers)
Implicit costs: the opportunity costs (the value of foregone alternative
use of resources)
Illustration:
you want to buy a machine, the price of the machine is $10,000, you can both lend or borrow
money, with the fixed interest rate 3%.
you can take a loan for $10,000 and pay 3% interest to the bank → explicit cost = $300
you can take your own $10,000 and pay 0% interest to the bank → explicit cost = $0
But you could have lent the $10,000 to someone else and collect the 3% interest!
By using your own money your foregone interest is $300 = implicit costs
V. Hajko (FSS MU) Introduction to Economics 14 / 24
Costs
Accounting profit vs. economic profit
Accounting can only record actual events, not the alternate foregone
opportunities.
BUT economic costs are not meaningless → they influence the
decisions! (it would not be rational / economical to pursue a certain
activity, if there exists a more profitable alternative)
Accounting profit = total revenue minus total explicit costs
Economic profit = total revenue minus (total explicit and total
implicit costs)
V. Hajko (FSS MU) Introduction to Economics 15 / 24
Costs
Fixed costs vs. variable costs
We have already differentiated between the short run and the long
run.
This distinction implies that in the short run, we can not change the
quantity of some production factors
BUT we still have to pay for them
these costs are fixed by the inability to change the amount of certain
production factors in the short run
If we can change the quantity of the inputs we include into the
production, we are dealing with the variable costs
In the short run, there are fixed costs (typically the cost of capital)
and variable costs (cost of labor)
In the long run, all inputs and hence all costs are variable
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Costs
Marginal costs
The marginal costs (MC = ∂TC
∂Q ; note it also shows the slope of the
function of total costs!): the change in total costs caused by
producing the additional unit of the output
The marginal costs are not constant, but are (typically) increasing
(due to the diminishing returns of the production function!).
V. Hajko (FSS MU) Introduction to Economics 17 / 24
Figure : Total and marginal costs
ATC
AVC
AFC
MC
Q
FC
VC
TCTC
VC
FC
Q
MC
ATC
AVC
AFC
Revenues and demand
Revenues
Firms generate revenues by selling their output, i.e. TR = p.Q (K, L)
we have seen the firm is able to influence the quantity of the product it
produces by using various amounts of inputs
Depending on the market structure (influencing the demand for their
products), they either take the price from the market (p is constant),
or they are able to influence the market price by changing the
quantity produced (p is a function of Q)
perfect competition: TR = p.Q (K, L)
imperfect competition: TR = p (Q (K, L)) .Q (K, L)
V. Hajko (FSS MU) Introduction to Economics 19 / 24
Figure : Total, marginal and average revenue
TR
TR
Q
TR
Q
TR
Q
MR
Q
MR
MR=AR
MR
AR
Revenues and demand
Marginal revenue
The marginal revenue (MR = ∂TR
∂Q ; note it also shows the slope of the
function of total revenues) is the change in the total revenue caused
by producing the additional unit of the output.
The demand function is different in perfect competition and in
imperfect competition: the demand function shows the quantity
demanded for the given price
The perfectly competetive firm can sell as many units as it can
produce for the market price
The demand function is a horizontal line, AR=MR
The imperfect competitive firm: in order to sell more units of Q, it has
to lower the price on all units → it faces downward sloping demand
It has downward sloping marginal revenues
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Profit maximization problem
Profit maximization problem
To maximize the profits Π = TR − TC, the firm will set the quantity
produced so that
∂Π
∂Q = ∂TR
∂Q − ∂TC
∂Q = 0 → MR − MC = 0 → MR = MC
In other words, the firm will produce additional unit of production, as
long as the marginal revenue of this additional unit is larger or equal
to what this additional unit costs.
Holds true for both perfectly and imperfectly competitive firms.
V. Hajko (FSS MU) Introduction to Economics 22 / 24
Figure : Total and marginal revenues
MC
ATC
π
π
TR
ATC
AVC
AFC
MC
Q
TCTC
VC
FC
Q
MR=AR
Profit maximization problem
Supply function
The supply function of the firm is the upward sloping part of the MC
curve above the AVC (or ATC in the long run)
The profit maximization problem explains the supply of the firm - a firm
will supply as long as the last unit of the product that is still profitable
In the short run (with existence of fixed costs), a firm might choose to
produce, even if the production ends in red numbers (in loss)
The alternative option is to produce nothing, yet still pay fixed costs
If a firm covers at least variable costs for producing given amount of
product, it will engage in production
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