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.
2.
Profit maximization Sales Revenue maximization 3.
4.
5.
Utility maximization Corporate growth maximization 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)
not require a cash outlay e.g. the cost of the owner’s time – do
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
L
(no. of workers)
Q
(bushels of wheat) 0 0 1 2 3 4 5 1000 1800 2400 2800 3000 3,000 2,500 2,000 1,500 1,000 500 0 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 = L 0.5 (iii) Q = L 2 Q = 3L = 3 (mL) = m . 3L = m. Q (Constant) Q = L 0.5 = (mL) 0.5 = m 0.5
L 0.5 = m 0.5
Q (Decreasing) Q = L 2 = (mL) 2 = m 2 L 2 = m 2 Q (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. Marginal product of labor (MPL) =
∆Q ∆L
∆Q = change in output, ∆L = change in labor
EXAMPLE : Marginal Product
L
(no. of workers)
Q
(bushels of wheat) 0 0
∆L
= 1
∆L
= 1
∆L
= 1
∆L
= 1
∆L
= 1 1 2 3 4 5 1000 1800 2400 2800 3000
∆Q
= 1000
∆Q
= 800
∆Q
= 600
∆Q
= 400
∆Q
= 200
MPL
1000 800 600 400 200
Relationship between Production Function and MPL
L
(no. of workers)
Q
(bushels of wheat)
MPL
3,000 2,500 0 0 2,000 1000 1 1000 1,500 800 2 1800 1,000 600 3 2400 500 400 4 2800 0 5 3000 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
Q
FC VC TC
0 1 2 $100 100 100 3 4 5 100 100 100 160 210 280 6 100 380 7 100 520
Example: FC = Cost of land VC = Wages to labor
$0 $100 70 120 170 220 260 310 380 480 620 $800 $700 $600 $500 $400 $300 $200 $100 $0
FC VC TC
0 1 2 3 4
Q
5 6 7
Marginal Cost curve
Q
TC
4 5 6 7 1 2 3 0 $100 170 220 260 310 380 480 620
MC
$70 50 40 50 70 100 140 producing one more unit: $150 $125
MC
= ∆TC
∆Q
$100 Usually,
MC
$75 rises as
Q
rises, due to diminishing marginal product. $50 Sometimes,
MC
$25 falls before rising. (In rare cases,
MC
$0 constant.) 0 1 2 3 may be 4 5 6 7
Q
EXAMPLE : Rising Marginal Cost Curve
Q
(bushels of wheat)
TC MC
0 1000 1800 2400 2800 3000 $1,000 $2.00
$3,000 $2.50
$5,000 $3.33
$7,000 $5.00
$9,000 $10.00
$11,000 $12 $10 $8 $6 $4 $2 $0 0 1,000
Q
2,000 3,000
Average Fixed Cost curve
Q
FC AFC
4 5 6 7 0 $100 1 100 2 3 100 100 n.a.
$100 50 33.33
100 100 100 25 20 100 16.67
14.29
is fixed cost divided by the $175 quantity of output: $150
AFC
$125 =
FC
/
Q
$100 $75 $50 $25 $0 0 1 2 3
Q
4 5 6 7
Average Variable Cost curve
Q
VC AVC
0 1 2 3 4 5 6 7 $0 70 120 160 210 280 380 520 n.a.
$70 60 53.33
52.50
56.00
63.33
74.29
quantity of output: $150 =
VC
/
Q
$100 As
Q
rises,
AVC
may fall initially. In most cases,
AVC
$50 will eventually rise as output rises.
$25 $0 0 1 2 3
Q
4 5 6 7
Average Total Cost curve
Q
TC ATC AFC AVC
6 7 4 5 2 3 0 $100 1 170 220 260 n.a.
$170 110 86.67
n.a.
$100 50 33.33
310 380 480 77.50
76 80 620 88.57
25 20 16.67
14.29
n.a.
$70 60 53.33
52.50
56.00
63.33
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 ATC
6 7 4 5 2 3 0 $100 1 170 220 260 n.a.
$170 110 86.67
310 77.50
380 480 76 80 620 88.57
$200 Usually, the
ATC
curve is U $150 $125 $100 $75 $50 $25 $0 0 1 2 3
Q
4 5 6 7
Why ATC Is Usually U-shaped As
Q
rises: Initially, falling
AFC
pulls
ATC
down.
Eventually, rising
AVC
pulls
ATC
up. $200 $175 $150 $125 $100 $75 $50 $25 $0 0 1 2 3
Q
4 5 6 7
The Various Cost Curves Together
ATC AVC AFC MC
$200 $175 $150 $125 $100 $75 $50 $25 $0 0 1 2 3
Q
4 5 6 7
Important Economic Relation: ATC and MC When
MC
<
ATC
,
ATC
is falling.
When
MC
>
ATC
,
ATC
is rising.
The
MC
curve crosses the
ATC
the curve at
ATC
curve’s minimum. $200 $175 $150 $125 $100 $75 $50 $25 $0
ATC MC
0 1 2 3
Q
4 5 6 7
A C T I V E L E A R N I N G 3 : Costs Fill in the blank spaces of this table. 4 5 6
Q
0 1 2 3
VC
10 30 100 150 210
TC
$50 80 150 260
AFC n.a.
16.67
12.50
8.33
AVC n.a.
$10 20 30 35
ATC n.a.
$60.00
36.67
37.50
43.33
MC
$10 30 60 24
A C T I V E L E A R N I N G 3 : Answers 4 5 6
Q
0 1 2 3
VC
$0 10 30 60 100 150 210
TC
$50 60 80 110 150 200 260
AFC n.a.
$50.00
25.00
16.67
12.50
10.00
8.33
AVC n.a.
$10 15 20 25 30 35
ATC n.a.
$60.00
40.00
36.67
37.50
40.00
43.33
MC
$10 20 30 40 50 60 25
Numerical Problem on Costs
Given the cost function: TC = 1000 + 10Q - 0.9Q
2 + 0.04Q
3 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 - 0.9Q
2 + 0.04Q
3
1) MC = Δ TC / Δ Q = d(TC) / dQ = 10-1.8Q+ 0.12Q
2 2) TVC = TC –TFC = 1000 + 10Q - 0.9Q
2 + 0.04Q
3 – 1000 = 10Q - 0.9Q
2 + 0.04Q
3 3) AVC = TVC / Q =(10Q - 0.9Q
2 + 0.04Q
3 )/Q = 10 - 0.9Q + 0.04Q
2 4) Since AVC function is the ATC function, Q at Minimum AVC when: AVC 10 - 0.9Q + 0.04Q
2 = MC = 10-1.8Q+ 0.12Q
2 Or, - 0.08Q
2 + 0.9Q Or, Q(- 0.08Q+ 0.9) = 0 = 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. Avg Total Cost The firm can change to a different factory size in the long run, but not in the short run.
ATC
S
ATC
M
ATC
L Q
EXAMPLE 3: LRATC with 3 Factory Sizes To produce less than
Q
A , firm will choose size
S
in the long run. To produce between
Q
A and
Q
B , firm will choose size
M
in the long run. To produce more than
Q
B , firm will choose size
L
in the long run.
Avg Total Cost
Q
A
ATC
S
ATC
M
ATC
L Q
B
LRATC
Q
A Typical LRATC Curve In the real world, factories come in many sizes, each with its own
SRATC
curve. So a typical
LRATC
curve looks like this:
ATC LRATC
Q
How ATC Changes as the Scale of Production Changes
Economies of scale
:
ATC
falls as
Q
increases.
ATC
Constant returns to scale
:
ATC
stays the same as
Q
increases.
Diseconomies of scale
:
ATC
rises as
Q
increases.
LRATC
Q
The Revenue of a Competitive Firm
Total revenue (TR)
TR
=
P
x
Q
Average revenue (AR)
AR
=
TR
Q
=
P
Marginal Revenue (MR)
: The change in TR from selling one more unit.
MR
= ∆TR
∆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
3 4 5 0 1 2
P
$10 $10 $10 $10 $10 $10
TR
=
P
x
Q
$0
AR
=
TR
Q
n.a.
MR
= ∆TR
∆Q
$10 $10 $10 Notice that $20 $10
MR
=
P
$30 $10 $10 $10 $10 $40 $10 $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. 4 5 2 3 0 1
Q
TR TC
$0 10 20 30 40 50 $5 9 15 23 33 45 Profit
MR MC
Profit =
MR
–
MC
–$5 $10 $4 $6 1 10 6 4 5 10 8 2 7 7 10 10 10 12 0 –2 5
MC and the Firm’s Supply Decision Rule:
MR
=
MC
at the profit-maximizing
Q
.
At Q
a
, MC < MR.
So, increase Q to raise profit. Costs
MC
At Q
b
, MC > MR.
So, reduce Q to raise profit. At Q
1
, MC = MR.
Changing Q would lower profit.
P
1
Q
a
Q
1
Q
b
MR
Q
MC and the Firm’s Supply Decision If price rises to P
2
, then the profit maximizing quantity rises to Q
2
. The MC curve determines the firm’s Q at any price. Hence, the
MC
curve is the firm’s supply curve.
Costs
P
2
P
1
Q
1
Q
2
MC MR
2
MR
Q
Market Structure Problems
Assume the cost function: TC = 1000 + 2Q + 0.01Q
2 is $10 per unit for a firm in the competitive market.
and Price Calculate the profit maximizing output (Q) and economic profit.
Market Structure Problems
Assume the cost function: TC = 1000 + 2Q + 0.01Q
2 $10 per unit for a firm in the competitive market.
and Price is 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(400 2 )) =$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.
Costs
MC
If
P
>
AVC
, then firm produces
Q
where
P
=
MC
.
ATC AVC
If
P
<
AVC
, then firm shuts down (produces
Q
= 0).
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 P
= $10 $6
MC MR ATC
Q
50 49
Answers Costs,
P
profit per unit =
P
–
ATC
= $10 – 6 = $4
P
= $10 $6 Total profit = (
P
–
ATC
) x
Q
= $4 x 50 = $200 A competitive firm profit
MC MR ATC
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
$5
P
= $3
MC
30
ATC MR
Q
51
Answers Costs,
P
Total loss = (
ATC
–
P
) x
Q
= $2 x 30 = $60 $5
P
= $3 loss A competitive firm
MC ATC
loss per unit = $2
MR
Q
30 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 product is horizontal at the market price. The firm can increase Q without lowering P, so MR = P for the competitive firm.
P
A competitive firm’s demand curve
D
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 – 20Q 2 +Q 3. Below what price should the firm shut down operation?
Market Structure Problems
In the competitive market, the firm shut down only when P 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. 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. P 2 P 1 SR & LR Effects of an Increase in Demand A firm begins in long run eq’m… profits for the firm. shifting S …but then an increase in demand raises run eq’m. P ,… to the right, reducing P … P One firm MC P Market S 1 Profit ATC B S 2 Q (firm) P 2 P 1 A Q 1 Q 2 C Q 3 long-run supply D 2 D 1 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 Q s = 1000 x (one firm’s Q s ) P 3 P P 2 P 1 One firm MC 10 20 30 P 3 P P 2 AVC Q (firm) P 1 10,000 Market S Q (market) 20,000 30,000 The LR Market Supply Curve In the long run, the typical firm earns zero profit. P One firm MC LRATC P = min. ATC Q (firm) P The LR market supply curve is horizontal at P = minimum ATC . Market long-run supply Q (market) 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. Firms behaviour in the Long Run Profit Condition
Firms behaviour in the Long Run Loss Condition
The Zero-Profit Condition
Thank you