Mr Sydney Armstrong
ECN 1100 Introduction to Microeconomics
Lecture Note (7)
Production with two variable inputs: Isoquant
We now turn to the case where the firm has only two factors of production, labour and capital,
both of which are variable. Since all factors are variable, we are dealing with the long run.
An isoquant shows the different combinations of labour (L) and capital (K) with which a firm can
produce a specific quantity of output. A higher isoquant refers to a greater quantity of output
and a lower one, to a smaller quantity of output.
Isoquant
I q =10
L
K
2
11
1
8
2
5
3
3
4
2.3
5
1.8
6
1.6
7
1.8
Isoquant
II q =20
L
K
4
13
3
10
4
7
5
5
6
4.2
7
3.5
8
3.2
9
3.5
Isoquant
III q = 30
L
K
6
15
5
12
6
9
7
7
8
6.2
9
5.5
10
5.3
11
5.5
This information can be shown graphically.
The Marginal Rate of Technical Substitution
The marginal rate of technical substitution of L for K (MRTS LK) refers to the amount of capital (K)
that a firm can give up so as to increase the amount of labour (L) used by one unit and still
remain on the same isoquant. The MRTS LK is also equal to the marginal product of labour divide
by the marginal product of capital that is MP L / MPK. As the firm moves down an isoquant, the
MRTSLK diminishes.
Characteristics of Isoquants
Isoquants have the same characteristics as indifference curves: (1) in the relevant range
isoquant are negatively sloped, (2) Isoquants are convex to the origin and (3) isoquants can
never cross.
Special cases
Perfect Complements
If the two inputs are perfect complements, the isoquant map takes the form of the figure below
with a level of production Q3, input X and input Y can only be combined efficiently in the
certain ratio occurring at the kink in the isoquant. The firm will combine the two inputs in the
required ratio to maximize profit.
Perfect Substitutes
If the two inputs are perfect substitutes, the resulting isoquant map generated is represented in
fig. A; with a given level of production Q3, input X can be replaced by input Y at an unchanging
rate. The perfect substitute inputs do not experience decreasing marginal rates of return when
they are substituted for each other in the production function.
Isocosts
An isocosts shows all the different combinations of labour and capital that a firm can purchase,
given total outlay (TO) of the firm and factor prices. The slope of an isocost is given by – PL /PK,
where PL refers to the price of labour and PK to the price of capital.
TO = PL * QL + PK * QK
For example if PL=PK= 1 and TO = $ 10 (the intercept for both axes would 10)
Producer Equilibrium
A producer is in equilibrium when he or she maximizes output for the give total outlay. Another
way of saying this is that a producer is in equilibrium when the highest isoquant is reached,
given the particular isocost. This occurs where an isoquant is tangent to the isocost. At the
point of tangency, the absolute slope of the isoquant is equal to the absolute slope of the
isocosts. That is at producer equilibrium MRTSLK = PL /PK. This is completely analogous to the
concept of consumer equilibrium discussed in lecture note 5. Since MRTSLK = MPL / MPK, at
equilibrium MPL / MPK = PL / PK or MPL /PL = MPK /PK.
This means that at equilibrium the MP of the last dollar spent on labour is the same as the MP
of the last dollar spent on capital.
Returns to Scale
The term returns to scale arises in the context of a firm's production function. It explains the
behavior of the rate of increase in output (production) relative to the associated increase in the
inputs (the factors of production) in the long run. In the long run all factors of production are
variable and subject to change due to a given increase in size (scale).
If output increases by that same proportional change as all inputs change then there
are constant returns to scale (CRS). If output increases by less than that proportional change in
inputs, there are decreasing returns to scale (DRS). If output increases by more than that
proportional change in inputs, there are increasing returns to scale (IRS). A firm's production
function could exhibit different types of returns to scale in different ranges of output. Typically,
there could be increasing returns at relatively low output levels, decreasing returns at relatively
high output levels, and constant returns at one output level between those ranges
Constant Returns to Scale
Decreasing Returns to Scale
Increasing Returns to Scale
Long Run Cost Analysis
In the long run, no cost is fixed. We can determine our production level and adjust plant sizes,
investment in capital and labour accordingly. As we can see in the diagrams below, this gives us
unlimited options. Depending on the scale we choose to implement, each level of production
will be associated to new, short run cost curves. When we exhaust the infrastructure these
provide us, we can upgrade to a new production level and so forth. The actual long run cost
curve is made up of all of these individual scenarios, built up year after year.
Long run cost analysis. If we look at average costs, we can see that the long run average cost
curve is also the buildup of the individual short run curves. These form a U shape, as we can see
in the diagram. When average cost is decreasing with each additional investment, we are
enjoying economies of scale. Economies of scale therefore refer to the reduction in the long run
average cost curve as output is expanded. The average cost curve then reaches a minimum and
begin to rise again. At this point when it is increasing with additional investment we are
experiencing diseconomies of scale. Diseconomies of scale are therefore increases in the long
run average cost cure as output is expanded.
Graph 2
Market Structure – A market is a set of buyers and sellers, commonly referred to as agents,
who through their interaction, both real and potential, determine the price of a good, or a set
of goods. The concept of a market structure is therefore understood as those characteristics of
a market that influence the behaviour and results of the firms working in that market. Market
structure ranges from no competition to intense competition. There are many types of market
structure that exist but for our course we would only focus on the 4 main types, that is
Monopoly, Monopolistic competition, Oligopoly and perfect competition. The table below gives
us a fair understanding of these types of market structures. It is also important for us to
distinguish between the firm and the industry. The Industry is the collection of firms selling
similar products where as a firm is an individual seller of the product.
Characteristics
Perfect
Competition
Monopolistic
Competition
Oligopoly
Monopoly
# of Buyers
# of Sellers
Control over
price
Many
Many (1000)
None
Price Takers
Barriers to
Entry and Exit
Type of Product
None
Many
Many (100)
Some but
limited
Price Makers
None
Homogenous
Perfect Substitutes
Similar but
Differentiated
Many
one
Significant
control
Price Makers
Heavy
Restriction
Unique
Profit
Maximizing
Output
Profit in the
short run
Profit in the
long run
P = MC
P = MR
Many
Few
Significant
control
Price Makers
Heavy
Restriction
Homogenous
or
Differentiated
P = MR
+ or -
+ or -
+ or -
+ or -
0 Economic Profit/
Normal profit
+
+
Efficiency
Both Productive
and Allocative
The Markets for
Agriculture
Products
0 Economic
Profit/ Normal
Profit
Not Efficient
Not Efficient
Not Efficient
The Fast-food
Industry
Cell Phone
Service
GTT Landline
Service
Example
P = MR
Perfect Competition
In economic theory, perfect competition (sometimes called pure competition) describes
markets such that no participants are large enough to have the market power to set the price of
a homogeneous product. Because the conditions for perfect competition are strict, there are
few if any perfectly competitive markets.
The behaviour of a single firm
Let us first examine the incentives of a typical firm. Suppose a firm has the short run cost in
figure….and faces a market price of p0.
How much should it produce? Or should it produce anything at all?
Profit Maximization. The objective of any firm, including a competitive firm, is to maximize its
profits (or equivalently, minimize its losses). The competitive firm’s profits are:
Π = pq- C(q). Where p is price, q is quantity and C(q) is total costs.
The firm is too small a part of the market to influence the market price and therefore it faces a
horizontal demand curve at price p.
It is profitable for a firm to expand output as long as the extra revenue from selling an
additional unit exceeds the extra cost of producing that unit.
Extra revenue = MR and in this case = p
Extra cost = MC
Hence profit is maximize when P= MC for a competitive firm.
Given the behaviour of individual competitive firms, we can derive a market supply (the
Horizontal summation of each individual supplier).
The intersection of the market supply and demand curve determines the competitive
equilibrium.
Perfect Competition in the Short run
In the short run firms under perfect competition can make either positive or negative economic
profit.
Positive Economic Profit (profit maximization)
Negative Economic Profit (loss minimization)
Perfect Competition in the long run
Zero Economic Profit
The explanation for these graphs would be done in class. You are advise however to
supplement this with additional reading.