HSS-01: Economics Lesson: 04

Production
Production Decisions, Variable Inputs, Returns to Scale, Costs
in Short & Long Run, Economies of Scope
6.1. PRODUCTION DECISIONS
 The Real Role of a Firm
You and me, if we have enough time, can also build a house, isn’t it? At least a very small one…
We can convert inputs into output, isn’t it? Why do we need a firm/company?

• Benefits of a firm

 Organizational efficiency – machines, workers, managers

 Large scale process automation – factories (More than sum of the parts.)

A natural extension of you and me working together… As we grow, we become a small scale firm, then a
medium scale firm, and finally a large enterprise.
 Factors of production • Land
• Capital
Production (in a firm) is done in a way to minimize
the costs of production.
• Labour
• Inputs (e.g., natural resources)

• Technology – efficiency of transforming inputs to output

Since a firm wants to minimize the costs of production,
why do you think they would pay you more for your job?

You would ideally expect that, isn’t it?

 Production Function of a Firm
The highest output q that a firm can produce for every specified combination of inputs.

q = F (K, L)

 K = capital
 L = labour

Imagine that the function F() is applied on a given set of inputs/materials to produce output.
In above equation, technology is assumed to be a constant.
 Short Run vs. Long Run
You take time to learn how to write an essay. A firm takes time to learn to minimize costs.

• Short run: Period of time in which quantities of one or more production factors cannot be
changed. At least one factor (fixed input) that cannot be varied.
• Long run: Amount of time needed to make all production inputs variable.

In the short run, firms vary the intensity with which they utilize a given plant and machinery; in the long run, they vary
the size of the plant.
All fixed inputs in the short run represent the outcomes of previous long-run decisions based on estimates of what a
firm could profitably produce and sell.
6.2. PRODUCTION WITH ONE
VARIABLE INPUT (LABOR)
 One Variable
Input -- Labor
Average output = q/L
Marginal output = Δq/ΔL

Once the labor input exceeds 9

units (point C), the marginal
product becomes negative, so that
total output falls as more labor is
added.

But why?
 Law of Diminishing
Marginal Returns

As the use of an input increases

with other inputs fixed, the
resulting additions to output
will eventually decrease.

This holds irrespective of the

quality/productivity of labor.
 Labor Productivity
Average product of labor for an entire industry or for the economy as a whole.

• Determines the real standard of living in an economy (e.g., a country).

• Income as a producer is spent to purchase items, as a consumer.
• Consumers, in aggregate economy, can increase consumption by increasing production.
• Sources of growth in labor productivity
• Stock of capital – amount of capital available for use in production.
• Technological change -- development of new technologies that allow labor (and other factors of
production) to be used more effectively
What about AI?
6.3. PRODUCTION WITH TWO
VARIABLE INPUTS (LABOR)
 Production
Isoquants
Diminishing
Marginal Returns
Production isoquants show the
various combinations of inputs
necessary for the firm to produce a
given output. A set of isoquants, or
isoquant map, describes the firm’s
production function. Output
increases as we move from
isoquant q1 (at which 55 units per
year are produced at points such as
A and D), to isoquant q2 (75 units
per year at points such as B), and to
isoquant q3 (90 units per year).
 Marginal Rate of
- ΔK /ΔL
Technical Substitution

Isoquants are downward sloping

and convex.
The slope of the isoquant at any
point measures the marginal rate of
technical substitution (MTRS)—the
ability of the firm to replace capital
with labor while keeping the same
level of output.
On isoquant q2, the MRTS falls
from 2 to 1 to 2/3 to 1/3.
 Substitution among Inputs
The marginal rate of technical substitution between two inputs is equal to the ratio of the marginal
products of the inputs.

• Along an isoquant, we have:

(MPL)(ΔL) + (MPK)(ΔK) = 0
gain in labour=reduction in capital

• and on rearranging, we get:

MRTS = MPL / MPK
Special Cases of Production Functions
PERFECT FIXED
SUBSTITUTES PROPORTIONS

PROPORTIONS REDUCES
6.4. RETURNS TO SCALE
 Returns to Scale –
Increasing/Decreasing/Constant
Rate at which output increases as inputs are increased proportionately.
increasing returns to scale: kam units of
labour aur capital lagana pada taki utne output aa paye

CONSTANT INCREASING

CONSTANT:same PROPORTION me badh raha

7.1. MEASURING COST
 Various Types of Costs
• Accounting cost = just note down the transactions of assets and liabilities (upto now)
• Economic cost = overall costs (upto now + future)
• Opportunity cost = cost of best alternative opportunity
• Sunk cost = cost/expenditure that can not be recovered in future (no alternative use)
• Fixed cost FC = cost that does not vary with the level of production output
• Variable cost VC = cost that varies with level of output
• Total cost TC = fixed cost + variable cost
 Cost Calculations
• Marginal cost MC =
• Increase in cost resulting from the production of one extra unit of output
• ΔTC / Δq = ΔVC / Δq
• Average total cost ATC = TC / q q is quantity of output

• Average fixed cost AFC = FC / q

• Average variable cost AVC = VC / q
afc is always downward sloping.
avc and atc is u shaped.
7.2. COST IN THE SHORT RUN
 Nature of Marginal Cost
• When there are diminishing marginal returns, marginal cost will increase as output increases.

• If the marginal product of labor decreases only slightly as the amount of labor is increased,
costs will not rise so quickly when the rate of output is increased.

• Suppose labor is hired at a fixed wage w (in a competitive market). Then

MC = w ΔL / Δq = w / MPL
MC=change in total cost/change in quantity
or
MC=tc(n)-tc(n-1)
 Cost Curves
for a Firm
In (a) total cost TC is the vertical
sum of fixed cost FC and variable
cost VC.

In (b) average total cost ATC is the

sum of average variable cost AVC
and average fixed cost AFC.

Marginal cost MC crosses the

average variable cost and average
total cost curves at their minimum
points.
afc and avc dec with inc in quantity of production.
avc dec less than afc.
7.3. COST IN THE LONG RUN
 Cost Minimizing Input Choice

 Price of Capital
• Capital expenditure per year (a flow measure), also called user cost of capital
r = Depreciation rate + Interest rate.

 Rental Rate of Capital

• Cost per year of renting one unit of capital
• Capital that is purchased can be treated as though it were rented at a rental rate equal to the user
cost of capital
 Isocost Line
Graph showing all possible combinations of labor and capital that can be purchased for a given total cost

• C = w L + r K => K = C/r - (w/r) L

cost=wages*quantity of labour + rate of interest of kapital * quantity of kapital

Δ K / Δ L = - (w / r )

• If the firm gave up a unit of labor (and recovered w dollars in cost) to buy w/r units of capital at a cost
of r dollars per unit, its total cost of production would remain the same.
isocost=cost is same
 Isocost Line & Production

• Since MRTS = - ΔK / ΔL = MPL / MPK we have :

mrts=mpl/mpk=w/r

MPL / w = MPK / r w/r is the slope of the isocost line that gives mrts.
calculated by slope=(c/r)/(c/w)

• For a a cost-minimizing firm, additional output that results from spending an additional dollar for
labor is the same as that of spending for capital.
 Producing Output
at Minimum Cost
Isocost curve C1 is tangent to
isoquant q1 at A and shows that
output q1 can be produced at
minimum cost with labor input L1 and
capital input K1.
Other input combinations—L2, K2
and L3, K3 — yield the same output
but at higher cost.
Input Substitution as
Input Price Changes
Facing an isocost curve C1, the firm
produces output q1 at point A using
L1 units of labor and K1 units of
capital.
When the price of labor increases, the
isocost curves become steeper.
Output q1 is now produced at point B
on isocost curve C2 by using L2 units
of labor and K2 units of capital.
price of labour inc , but total
cost is same so quantity of
labour must dec as shown in
graph
 Expansion Path
Combinations of labor and capital that the firm will choose to minimize costs at each output level.

 The curve passing through the points of tangency between

 the firm’s isocost lines, and
 its isoquants.

 As long as the use of both labor and capital increases with output, the curve will be upward sloping.
.
 passes through points
of tangency between a
Cost Minimization firm’s isocost lines and
its isoquants

with Varying Output

In (a), the expansion path (from
the origin through points A, B, and
C ) illustrates the lowest-cost
combinations of labor and capital
that can be used to produce each
level of output in the long run— expansion path may also be a curve.

i.e., when both inputs to

production can be varied.
price factor curve comes when
the isocost line does not
In (b), the corresponding long-run shift outward or inward but it gets rotated due
to change in quantity or price of
total cost curve (from the origin one of the two inputs.

through points D, E, and F)

same as expansion curve
only difference is above mentioned one.
measures the least cost of
producing each level of output.
7.4. LONG RUN vs. SHORT RUN
 Inflexibility in
Short Run
When a firm operates in the short run, its
cost of production may not be minimized
because of inflexibility in the use of capital
inputs.
Output is initially at level q1. In the short
run, output q2 can be produced only by
increasing labor from L1 to L3 because
capital is fixed at K1.
In the long run, the same output can be
produced more cheaply by increasing labor
from L1 to L2 and capital from K1 to K2.
 Long Run Costs –
Average, Marginal
When a firm is producing at an output
at which the long-run average cost
LAC is falling, the long-run marginal
cost LMC is less than LAC.
Conversely, when LAC is increasing,
LMC is greater than LAC.
The two curves intersect at A, where
the LAC curve achieves its minimum.
 Economies of Scale
Situation in which output can be doubled for less than a doubling of cost.

 Some cases in which costs decreases:

• If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive.
• The firm may be able to acquire some production inputs at lower cost because it is buying them in large quantities and
can therefore negotiate better prices.

 Some cases in which costs increases:

• At least in the short run, factory space and machinery may make it more difficult for workers to do their jobs
effectively.
• Managing a larger firm may become more complex and inefficient as the number of tasks increases.
 Economies of Scale
Situation in which output can be doubled for less than a doubling of cost.

 vs. Returns to Scale

• Increasing returns to scale => Output more than doubles when the quantities of all inputs are doubled
• Economies of Scale => Output more than doubles even with less than a doubling of cost

• Basically, additional inputs obtained during doubling the total output comes at less cost.
• For e.g., technology can be used only when the input size is large (machines to milk cows).
 Economies of Scale
Measured using cost-output elasticity
EC = (ΔC/C) / (Δq/q) = MC / AC

EC = 1 => Neither economies nor diseconomies of scale

• Costs increase proportionately with output
• Constant returns to scale would apply if input proportions were fixed
EC < 1 => Economies of scale
• Costs increase less than proportionately with output
• Marginal cost is less than average cost (both are declining)
 Relationship btw.
Long & Short Run
Costs

Long-run Cost with Economies

and Diseconomies of Scale

The long-run average cost curve LAC is

the envelope of the short-run average
cost curves SAC1, SAC2, and SAC3.

With economies and diseconomies of

scale, the minimum points of the short-
run average cost curves do not lie on
the long-run average cost curve.
7.5. PRODUCTION WITH TWO
OUTPUTS
 Product Trans-
formation Curves
The product transformation curve
describes the different combinations
of two outputs that can be produced
with a fixed amount of production
inputs.
The product transformation curves
O1 and O2 are bowed out (or
concave) because there are
economies of scope in production.
 Economies of Scope
Situation in which joint output of a single firm is greater than output that could be achieved by two
different firms when each produces a single product.

 Degree of economies of scope

• Percentage of cost savings resulting when two or more products are produced jointly rather than individually.
COBB-DOUGLAS COST AND
PRODUCTION FUNCTIONS
 We have already seen
this. Please recall.

Inputs optimizing condition

MPL / w = MPK / r
 Cobb-Douglas Production Function

• q is the rate of output

q = F(K, L) = A Kα Lβ
• K is the quantity of capital
• L is the quantity of labor

• A, α, β are positive constants

• Assume α < 1, β < 1 so that MPL and MPK are decreasing
• α+β=1 => Firm has constant returns to scale
 Cobb-Douglas Production Function
AP of k= q/K
AP of L =q/L

• MPL = β A Kα Lβ-1 MP of l =dq/dl

<= q = F(K, L) = A Kα Lβ
• MPK = α A Kα-1 Lβ
MP of k =dq/dk

2nd derivation of above gives negative

value denoting diminishing marginal rate.

β 𝑟𝑟
• MPL / w = MPK / r => L = K
α 𝑤𝑤

alpha/beta>1=>capital intensive
using this q now eevery formula can be calc using basic formula . eg elasticty
 Cobb-Douglas Production Function

β 1
M
K = ( ) ( )
α 𝑤𝑤
β 𝑟𝑟
α+ β 𝑞𝑞
𝐴𝐴
α+ β
q = F(K, L) = A Kα Lβ

and similarly,
MPL / w = MPK / r α 1 L = β 𝑟𝑟 K
L =
α 𝑤𝑤 ( ) ( )
β 𝑟𝑟 α + β 𝑞𝑞
𝐴𝐴
α+ β
α 𝑤𝑤
Cobb-Douglas Production Function

β 1

K = ( ) ( )
α 𝑤𝑤
β 𝑟𝑟
α+ β 𝑞𝑞
𝐴𝐴
α+ β
What do these equations say?

Factor demands, given output!

How do K and L change when:

α 1

( ) ( )
β 𝑟𝑟 α+ β 𝑞𝑞 α+ β w increases?
L = r increases?
α 𝑤𝑤 𝐴𝐴
A increases?
Cobb-Douglas Production Function

β 1

K = ( ) ( )
α 𝑤𝑤
β 𝑟𝑟
α+ β 𝑞𝑞
𝐴𝐴
α+ β
C ( q, w, r) = w L + r K

The cost function.

Can you see that when α + β = 1,

α 1
the firm has has constant returns to scale?

L = ( ) ( )
β 𝑟𝑟
α 𝑤𝑤
α+ β 𝑞𝑞
𝐴𝐴
α+ β
What happens when α + β < 1?
decreasing returns to scale

alpha+ beta>1=> increasing returns to scale