Transcript Document

Economic Analysis
for Business
Session XI: The Costs of Production
Instructor
Sandeep Basnyat
9841892281
[email protected]
Objectives of the firms
Varieties of objectives:
1. Profit maximization
2. Sales Revenue maximization
3. Utility maximization
4. Corporate growth maximization
5. Etc…
Most Important economic
Objective- Profit Maximization
◦ The economic goal of the firm is to maximize
profits.
Profit = Total revenue – Total cost
the amount a
firm receives
from the sale
of its output
the market
value of the
inputs a firm
uses in
production
Sequence of Presentation
Understanding Costs, Production
functions and their relationship
 Derive various cost curves
 A concept of Revenue
 How firms behave if they are in different
market structures?

Costs: Explicit vs. Implicit

Explicit costs – require an outlay of money,
e.g. paying wages to workers
Accounting profit
= total revenue minus total explicit costs
 Implicit costs (Opportunity Costs) – do
not require a cash outlay
e.g. the cost of the owner’s time
Economic profit
= total revenue minus total costs (including
explicit and implicit costs)
The Production Function
A production function shows the
relationship between the quantity of inputs
used to produce a good, and the quantity
of output of that good.
 It can be represented by a table, equation,
or graph.

Simple Example: Production Function
Q
(no. of (bushels
workers) of wheat)
3,000
Quantity of output
L
2,500
0
0
1
1000
2
1800
3
2400
500
4
2800
0
5
3000
2,000
1,500
1,000
0
1
2
3
4
No. of workers
5
Properties of Production Functions:
Returns to Scale
Increasing Returns to Scale
When inputs are increased by m, output increases by more
than m.
Eg: A 10% increase in labour/capital increases the output by
more than 10%
 Constant Returns to Scale
When inputs are increased by m, output increases by
exactly m.
 Decreasing Returns to Scale
When inputs are increased by m, output increases by less
than m.
Note: Assuming that the value of multiplier >1 (positive)

Properties of Production Functions:
Returns to Scale
Find if the followings production functions have increasing,
constant or decreasing returns to scale.
(i) Q = 3L
(ii) Q = L0.5
(iii) Q = L2
Q = 3L = 3 (mL) = m . 3L = m. Q (Constant)
 Q = L0.5 = (mL)0.5 = m0.5L0.5 = m0.5Q (Decreasing)
 Q = L2 = (mL)2 = m2L2 = m2Q (Increasing)

Marginal Product

The marginal product of any input is the increase
in output arising from an additional unit of that input,
holding all other inputs constant.
∆Q
 Marginal product of labor (MPL) =
∆L
∆Q = change in output, ∆L = change in labor
EXAMPLE :Marginal Product
L
Q
(no. of (bushels
workers) of wheat)
∆L = 1
0
1
∆L = 1
∆L = 1
∆L = 1
∆L = 1
2
3
4
5
0
MPL
∆Q = 1000
1000
∆Q = 800
800
∆Q = 600
600
∆Q = 400
400
∆Q = 200
200
1000
1800
2400
2800
3000
Relationship between Production Function and MPL
Q
3,000
(no. of (bushels MPL
workers) of wheat)
0
0
1000
1
1000
800
2
1800
Quantity of output
L
2,500
2,000
1,500
1,000
600
3
4
5
2400
2800
3000
500
400
0
200
0
1
2
3
4
No. of workers
Diminishing MPL: This property explains why Production Function
flatters as output increases.
5
Why MPL Diminishes
Diminishing marginal product:
the marginal product of an input declines as the
quantity of the input increases (other things equal)
E.g.: Output rises by a smaller and smaller amount for
each additional worker. Why?
 If the number of workers increased but not land,
the average worker has less land to work with,
so will be less productive.
 In general, MPL diminishes as L rises
whether the fixed input is land or capital (equipment,
machines, etc.).

Deriving Costs curves
FC
VC
TC
0 $100
$0 $100
1
100
70
170
2
100 120
220
3
100 160
260
4
100 210
310
5
100 280
380
FC
$700
VC
TC
$600
$500
Costs
Q
$800
$400
$300
$200
$100
6
7
100 380
100 520
Example:
FC = Cost of land
VC = Wages to labor
480
620
$0
0
1
2
3
4
Q
5
6
7
Marginal Cost curve
TC
MC
0 $100
1
2
3
4
5
6
7
170
220
260
310
380
480
620
$70
50
40
50
70
100
140
$200
Marginal
Cost (MC)
is $175
the change in total cost from
producing
one more unit:
$150
∆TC
MC =
∆Q
$100
Usually, MC rises as Q rises, due
$75
to diminishing marginal product.
Costs
Q
$125
$50
Sometimes, MC falls before rising.
$25
(In rare cases, MC may be
$0
constant.)
0
1
2
3
4
Q
5
6
7
EXAMPLE : Rising Marginal Cost Curve
0
$12
TC
MC
$1,000
$2.00
1000
$3,000
$2.50
1800
$5,000
$3.33
2400
$7,000
$5.00
2800
$9,000
3000 $11,000
$10.00
$10
Marginal Cost ($)
Q
(bushels
of wheat)
$8
$6
$4
$2
$0
0
1,000
2,000
Q
3,000
Average Fixed Cost curve
FC
0 $100
1
100
AFC
n.a.
$100
2
100
3
100 33.33
4
100
25
5
100
20
6
50
100 16.67
Average
fixed cost (AFC)
$200
is fixed cost divided by the
$175
quantity of output:
$150
AFC = FC/Q
Costs
Q
$125
$100
$75
$50
$25
$0
7
100 14.29
0
1
2
3
4
Q
5
6
7
Average Variable Cost curve
VC
AVC
0
$0
n.a.
1
70
$70
2
120
60
3
160
53.33
4
210
52.50
5
280
56.00
6
380
63.33
7
520
74.29
$200
Average
variable cost (AVC)
is$175
variable cost divided by the
quantity of output:
$150
Costs
Q
AVC
$125
= VC/Q
$100
As$75
Q rises, AVC may fall initially.
In most cases, AVC will
$50
eventually rise as output rises.
$25
$0
0
1
2
3
4
Q
5
6
7
Average Total Cost curve
Q
TC
0 $100
ATC
AFC
AVC
n.a.
n.a.
n.a.
1
170
$170
$100
$70
2
220
110
50
60
3
260 86.67 33.33
53.33
4
310 77.50
25
52.50
5
380
76
20
56.00
6
480
80 16.67
63.33
7
620 88.57 14.29
74.29
Average total cost
(ATC) equals total
cost divided by the
quantity of output:
ATC = TC/Q
Also,
ATC = AFC + AVC
Average Total Cost Curves
Q
TC
0 $100
ATC
$200
Usually, the ATC curve is U$175
shaped.
n.a.
170
$170
$150
2
220
110
$125
3
260 86.67
4
310 77.50
5
380
76
Costs
1
$100
$75
$50
$25
6
480
80
7
620 88.57
$0
0
1
2
3
4
Q
5
6
7
Why ATC Is Usually U-shaped
As Q rises:
$200
Initially,
falling AFC
pulls ATC
down.
$175
Costs
Eventually,
rising AVC
pulls ATC up.
$150
$125
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
The Various Cost Curves Together
$200
$175
ATC
AVC
AFC
MC
Costs
$150
$125
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
Important Economic Relation: ATC and MC
When MC < ATC,
ATC is falling.
$175
$150
ATC is rising.
$125
Costs
When MC > ATC,
The MC curve
crosses the
ATC curve at
the ATC curve’s
minimum.
ATC
MC
$200
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
ACTIVE LEARNING
3:
Costs
Fill in the blank spaces of this table.
Q
VC
0
1
10
2
30
TC
AFC
AVC
ATC
$50
n.a.
n.a.
n.a.
$10
$60.00
80
3
16.67
4
100
5
150
6
210
150
20
12.50
36.67
8.33
$10
30
37.50
30
260
MC
35
43.33
60
24
ACTIVE LEARNING
3:
Answers
Q
VC
TC
AFC
AVC
ATC
0
$0
$50
n.a.
n.a.
n.a.
1
10
60
$50.00
$10
$60.00
2
30
80
25.00
15
40.00
3
60
110
16.67
20
36.67
4
100
150
12.50
25
37.50
5
150
200
10.00
30
40.00
6
210
260
8.33
35
43.33
MC
$10
20
30
40
50
60
25
Numerical Problem on Costs
Given the cost function:
TC = 1000 + 10Q - 0.9Q2 + 0.04Q3
Find:
1) MC, TVC, AVC functions
2) Discarding the previous TC function, consider
that the existing AVC function became the ATC
function for the firm. Find Q when AVC is
minimum.
Worked out Problem
TC = 1000 + 10Q - 0.9Q2 + 0.04Q3
1) MC = ΔTC / ΔQ = d(TC) / dQ
= 10-1.8Q+ 0.12Q2
2) TVC = TC –TFC
= 1000 + 10Q - 0.9Q2 + 0.04Q3 – 1000
= 10Q - 0.9Q2 + 0.04Q3
3) AVC = TVC / Q =(10Q - 0.9Q2 + 0.04Q3 )/Q
= 10 - 0.9Q + 0.04Q2
4) Since AVC function is the ATC function, Q at Minimum AVC when:
AVC
= MC
10 - 0.9Q + 0.04Q2
= 10-1.8Q+ 0.12Q2
Or, - 0.08Q2 + 0.9Q
=0
Or, Q(- 0.08Q+ 0.9)
=0
Or, Q =0 and - 0.08Q+ 0.9 = 0 i.e, Q = 11.25 (Minimum AVC)
Costs in the Short Run & Long Run
Short run:
Some inputs are fixed (e.g., factories, land).
The costs of these inputs are FC.
 Long run:
All inputs are variable
(e.g., firms can build more factories,
or sell existing ones)

LRATC with 3 Factory Sizes
Firm can choose
from 3 factory
sizes: S, M, L.
Each size has its
own SRATC curve.
The firm can
change to a
different factory
size in the long run,
but not in the short
run.
Avg
Total
Cost
ATCS
ATCM
ATCL
Q
EXAMPLE 3: LRATC with 3 Factory Sizes
To produce less
than QA, firm will
choose size S
in the long run.
To produce
between QA
and QB, firm will
choose size M
in the long run.
To produce more
than QB, firm will
choose size L
in the long run.
Avg
Total
Cost
ATCS
ATCM
ATCL
LRATC
QA
QB
Q
A Typical LRATC Curve
In the real world,
factories come in
many sizes,
each with its own
SRATC curve.
ATC
LRATC
So a typical
LRATC curve
looks like this:
Q
How ATC Changes as the Scale of Production Changes
Economies of
scale: ATC falls
as Q increases.
ATC
LRATC
Constant returns
to scale: ATC
stays the same
as Q increases.
Diseconomies of
scale: ATC rises
as Q increases.
Q
The Revenue of a Competitive Firm
Total revenue (TR)
TR = P x Q

Average revenue (AR)
TR
=P
AR =
Q

Marginal Revenue
(MR):
The change in TR from
selling one more unit.

∆TR
MR =
∆Q
How do firms behave in different
market structures?
1. Perfectly Competitive Market
2. Monopoly Market
3. Oligopoly Market
4. Monopolistically Competitive
Market
Perfectly Competitive Market
1.
Many buyers and many sellers
2.
The goods offered for sale are largely the
same.
3.
Firms can freely enter or exit the market.
 Because of 1 & 2, each buyer and seller is
a “price taker” – takes the price as given.
Sample Data
Q
P
TR = P x Q
0
$10
$0
AR =
TR
Q
MR =
∆TR
∆Q
n.a.
$10
1
2
3
$10
$10
$10
Notice that
$20
$10
MR = P
$10
$30
$10
$10
$10
$10
$10
4
$10
$40
$10
$10
5
$10
$50
$10
36
MR = P for a Competitive Firm
A competitive firm can keep increasing its
output without affecting the market price.
 So, each one-unit increase in Q causes
revenue to rise by P, i.e., MR = P.

MR = P is only true for
firms in competitive
markets.
Profit Maximization
What Q maximizes the firm’s profit?
 If increase Q by one unit,
revenue rises by MR,
cost rises by MC.
 If MR > MC, then increase Q to raise
profit.
 If MR < MC, then reduce Q to raise profit.

Profit
Maximization
(continued from earlier exercise)
At any Q with
MR > MC,
increasing Q
raises profit.
At any Q with
MR < MC,
reducing Q
raises profit.
Q
TR
TC
0
$0
$5
–$5
1
10
9
1
2
20
15
5
3
30
23
7
4
40
33
7
5
50
45
Profit MR MC
5
Profit =
MR – MC
$10 $4
$6
10
6
4
10
8
2
10
10
0
10
12
–2
MC and the Firm’s Supply Decision
Rule: MR = MC at the profit-maximizing Q.
At Qa, MC < MR.
So, increase Q
to raise profit.
At Qb, MC > MR.
So, reduce Q
to raise profit.
Costs
MC
MR
P1
At Q1, MC = MR.
Changing Q
would lower profit.
Q a Q1 Q b
Q
MC and the Firm’s Supply Decision
If price rises to P2,
then the profitmaximizing quantity
rises to Q2.
The MC curve
determines the
firm’s Q at any price.
Hence,
Costs
MC
P2
MR2
P1
MR
the MC curve is the
firm’s supply curve.
Q1
Q2
Q
Market Structure Problems
Assume the cost function: TC = 1000 + 2Q + 0.01Q2 and Price
is $10 per unit for a firm in the competitive market.
Calculate the profit maximizing output (Q) and economic profit.
Market Structure Problems
Assume the cost function: TC = 1000 + 2Q + 0.01Q2 and Price is
$10 per unit for a firm in the competitive market.
Calculate the profit maximizing output (Q) and economic profit.
Solution:
MC = dTC /dQ = 2+0.02Q
In a perfectly competitive market, profit maximizing output is at
where MR = P = MC
10 = 2+0.02Q
Therefore, Q = 400
Economic Profit = TR –TC = 10(400) – (1000 + 2(400) + 0.01(4002))
=$600
When would the firms Shutdown, Exit or Enter?
Shutdown:
A short-run decision not to produce
anything because of market conditions.
 Exit:
A long-run decision to leave the market.
 A firm that shuts down temporarily must
still pay its fixed costs. A firm that exits
the market does not have to pay any
costs at all, fixed or variable.

A Firm’s Short-Run Decision to Shut Down

If firm shuts down temporarily,
◦ revenue falls by TR
◦ costs fall by VC
So, the firm should shut down if TR < VC.
 Divide both sides by Q:
TR/Q < VC/Q
 So we can write the firm’s decision as:

Shut down if P < AVC
A Competitive Firm’s SR Supply Curve
The firm’s SR supply
curve is the portion of
its MC curve above
AVC.
If P > AVC, then
firm produces Q
where P = MC.
If P < AVC, then
firm shuts down
(produces Q = 0).
Costs
MC
ATC
AVC
Q
A Firm’s Long-Run Decision to Exit

If firm exits the market,
◦ revenue falls by TR
◦ costs fall by TC
So, the firm should exit if TR < TC.
 Divide both sides by Q to rewrite the firm’s
decision as:

Exit if P < ATC
A New Firm’s Decision to Enter the Market

In the long run, a new firm will enter the
market if it is profitable to do so: if TR > TC.

Divide both sides by Q to express the
firm’s entry decision as:
Enter if P > ATC
Identifying a firm’s profit or Loss
A competitive firm
Determine
if this firm’s
total has
profit/Loss?
Identify the
area on the
graph that
represents
the firm’s
profit or Loss.
Costs, P
MC
MR
ATC
P = $10
$6
50
Q
49
Answers
A competitive firm
Costs, P
profit per unit
= P – ATC
= $10 – 6
= $4
MC
MR
ATC
P = $10
profit
$6
Total profit
= (P – ATC) x Q
= $4 x 50
= $200
50
Q
50
Identifying a firm’s profit or loss.
A competitive firm
Determine
if this firm has
total profit or
loss.
Identify the
area on the
graph that
represents
the firm’s
profit or loss.
Costs, P
MC
ATC
$5
MR
P = $3
30
Q
51
Answers
A competitive firm
Costs, P
MC
Total loss
= (ATC – P) x Q
= $2 x 30
= $60
ATC
$5
P = $3
loss
loss per unit = $2
MR
30
Q
52
Demand Curve for Individual firm’s product
In a competitive market, the
market demand curve slopes
downward.
but the demand curve
for any individual firm’s
P
product is horizontal
at the market price.
The firm can increase Q
without lowering P,
A competitive firm’s
demand curve
D
so MR = P for the
competitive firm.
Price line represents the level of
demand for the firm’s product
Q
Market Structure Problems
Consider a firm which has a horizontal demand curve for its
products. The firms Total Cost is given by the function:
TVC = 150Q – 20Q2 +Q3.
Below what price should the firm shut down operation?
Market Structure Problems
In the competitive market, the firm shut down only when P<AVC.
The firm continue to operate until:
P = AVC
In competitive market, P =MC
MC =dTVC / dQ = 150 -40Q +3Q2
AVC = TVC /Q = (150Q – 20Q2 +Q3) / Q = 150 -20Q +Q2
Equating, both equations:
MC = AVC or 150 -40Q +3Q2 = 150 -20Q +Q2
Or, 2Q2 – 20Q = 0 or 2Q (Q – 10) = 0
Or, Q = 0 and Q = 10
Substituting Q = 10 into marginal cost, P = MC = 150 – 40(10) + 3 (100) =
$50
Similarly, substituting Q = 0 in the marginal cost, P = $150
Therefore, if the price falls below $50, the firm shuts down.
Firms behaviour in the Long RunProfit Condition
In the LR, the number of firms can change
due to entry & exit.
 If existing firms earn positive economic
profit,

◦
◦
◦
◦
New firms enter.
SR market supply curve shifts right.
P falls, reducing firms’ profits.
Entry stops when firms’ economic profits
have been driven to zero.
Firms behaviour in the Long RunLoss Condition

In the LR, the number of firms can change due
to entry & exit.
 If existing firms incur losses,
• Some will exit the market.
• SR market supply curve shifts left.
• P rises, reducing remaining firms’ losses.
• Exit stops when firms’ economic losses have
been driven to zero.
SR & LR Effects of an Increase in Demand
…but then an increase
A firm begins in
profits
to zero
…leadingeq’m…
to…driving
SR
Over time,
profits
induce
entry,
in
demand
raises
P,…
long-run
andfirm.
restoring
long-run
eq’m.
profits for the
shifting
S to the
right, reducing P…
P
One firm
Market
P
S1
MC
Profit
S2
ATC
P2
P2
P1
P1
Q
(firm)
B
A
C
long-run
supply
D1
Q1 Q2
Q3
D2
Q
(market)
Why Do Firms Stay in Business if Profit = 0?
Recall, economic profit is revenue minus
all costs – including implicit costs, like the
opportunity cost of the owner’s time and
money.
 In the zero-profit equilibrium, firms earn
enough revenue to cover these costs.

Distinction between The SR and LR Market Supply
Curves
Example: 1000 identical firms.
At each P, market Qs = 1000 x (one firm’s Qs)
P
One firm
MC
P
P3
P3
P2
P2
AVC
P1
Market
S
P1
10 20 30
Q
(firm)
Q
(market)
10,000
20,000 30,000
The LR Market Supply Curve
The LR market supply
curve is horizontal at
P = minimum ATC.
In the long run,
the typical firm
earns zero profit.
P
One firm
MC
P
Market
LRATC
P=
min.
ATC
long-run
supply
Q
(firm)
Q
(market)
The Zero-Profit Condition

Long-run equilibrium:
The process of entry or exit is complete –
remaining firms earn zero economic profit.

Zero economic profit occurs when P = ATC.

Since firms produce where P = MR = MC,
the zero-profit condition is P = MC = ATC.

Recall that MC intersects ATC at minimum ATC.

Hence, in the long run, P = minimum ATC.
The Irrelevance of Sunk Costs
Sunk cost: a cost that has already been
committed and cannot be recovered
 Sunk costs should be irrelevant to decisions;
you must pay them regardless of your choice.
 FC is a sunk cost: The firm must pay its fixed
costs whether it produces or shuts down.
 So, FC should not matter in the decision to shut
down.

Thank you