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Economic Analysis Economic Analysis for Businessfor Business
Session XI: The Costs of Session XI: The Costs of ProductionProductionInstructorInstructorSandeep BasnyatSandeep [email protected][email protected]
Objectives of the firmsObjectives of the firms
Varieties of objectives:1.Profit maximization2.Sales Revenue maximization3.Utility maximization4.Corporate growth maximization5.Etc…
Most Important economic Most Important economic Objective- Profit Objective- Profit MaximizationMaximization◦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 PresentationSequence of PresentationUnderstanding Costs, Production
functions and their relationshipDerive various cost curvesA concept of RevenueHow firms behave if they are in
different market structures?
Costs: Explicit vs. ImplicitCosts: Explicit vs. ImplicitExplicit costs – require an outlay of
money,e.g. paying wages to workers
Accounting profit =total revenue minus total explicit
costsImplicit costs (Opportunity Costs)
– do not require a cash outlaye.g. the cost of the owner’s time
Economic profit=total revenue minus total costs
(including explicit and implicit costs)
The Production FunctionThe Production FunctionA 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.
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Qu
anti
ty o
f o
utp
ut
Simple Example:Simple Example: Production Function Production Function
30005
28004
24003
18002
10001
00
Q (bushels of wheat)
L(no. of
workers)
Properties of Production Properties of Production Functions: Returns to ScaleFunctions: 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 ScaleWhen inputs are increased by m, output increases by exactly m.
Decreasing Returns to ScaleWhen inputs are increased by m, output increases by less than m.
Note: Assuming that the value of multiplier >1 (positive)
Properties of Production Properties of Production Functions: Returns to ScaleFunctions: Returns to ScaleFind 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 ProductMarginal ProductThe 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 = change in output, ∆L = change in labor
∆Q∆L
30005
28004
24003
18002
10001
00
Q (bushels of wheat)
L(no. of
workers)
EXAMPLE :EXAMPLE :Marginal ProductMarginal Product
200
400
600
800
1000
MPL
∆Q = 1000∆L = 1
∆Q = 800∆L = 1
∆Q = 600∆L = 1
∆Q = 400∆L = 1
∆Q = 200∆L = 1
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5No. of workers
Qu
anti
ty o
f o
utp
ut
Relationship between Production Function Relationship between Production Function and MPLand MPL
30005200
28004400
24003600
18002800
100011000
00
MPLQ
(bushels of wheat)
L(no. of
workers)
Diminishing MPL: This property explains why Production Function flatters as output increases.
Why MPL DiminishesWhy MPL DiminishesDiminishing 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 Deriving Costs curvesCosts curves
7
6
5
4
3
2
1
620
480
380
310
260
220
170
$100
520
380
280
210
160
120
70
$0
100
100
100
100
100
100
100
$1000
TCVCFCQ
$0
$100
$200
$300
$400
$500
$600
$700
$800
0 1 2 3 4 5 6 7
Q
Co
sts
FC
VC
TC
Example:FC = Cost of landVC = Wages to labor
Marginal Cost (MC) is the change in total cost from producing one more unit:
Usually, MC rises as Q rises, due to diminishing marginal product.
Sometimes, MC falls before rising.
(In rare cases, MC may be constant.)
Marginal Cost curveMarginal Cost curve
6207
4806
3805
3104
2603
2202
1701
$1000
MCTCQ
140
100
70
50
40
50
$70
∆TC∆Q
MC =
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
EXAMPLE : Rising EXAMPLE : Rising Marginal Cost CurveMarginal Cost Curve
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
TC
$10.00
$5.00
$3.33
$2.50
$2.00
3000
2800
2400
1800
1000
0
Q(bushels of wheat)
$0
$2
$4
$6
$8
$10
$12
0 1,000 2,000 3,000Q
Mar
gin
al C
ost
($)
MC
Average Fixed Cost curveAverage Fixed Cost curve
1007
1006
1005
1004
1003
1002
1001
14.29
16.67
20
25
33.33
50
$100
n.a.$1000
AFCFCQ Average fixed cost (AFC) is fixed cost divided by the quantity of output:
AFC = FC/Q
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
Average Variable Cost curveAverage Variable Cost curve
5207
3806
2805
2104
1603
1202
701
74.29
63.33
56.00
52.50
53.33
60
$70
n.a.$00
AVCVCQ Average variable cost (AVC) is variable cost divided by the quantity of output:
AVC = VC/Q
As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7Q
Co
sts
Average Total Cost curveAverage Total Cost curve
88.57
80
76
77.50
86.67
110
$170
n.a.
ATC
6207
4806
3805
3104
2603
2202
1701
$1000
74.2914.29
63.3316.67
56.0020
52.5025
53.3333.33
6050
$70$100
n.a.n.a.
AVCAFCTCQ Average total cost (ATC) equals total cost divided by the quantity of output:
ATC = TC/Q
Also,
ATC = AFC + AVC
Usually, the ATC curve is U-shaped.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
Average Total Cost CurvesAverage Total Cost Curves
88.57
80
76
77.50
86.67
110
$170
n.a.
ATC
6207
4806
3805
3104
2603
2202
1701
$1000
TCQ
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
Why ATC Is Usually U-shapedWhy ATC Is Usually U-shaped
As Q rises:
Initially, falling AFC pulls ATC down.
Eventually, rising AVC pulls ATC up.
The Various Cost Curves TogetherThe Various Cost Curves Together
AFCAVCATC
MC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
Important Economic Relation: ATC Important Economic Relation: ATC and MCand MC
ATCMC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
When MC < ATC,
ATC is falling.
When MC > ATC,
ATC is rising.
The MC curve crosses the ATC curve at the ATC curve’s minimum.
AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : CostsCosts
Fill in the blank spaces of this table.
24
210
150
100
30
10
VC
43.33358.332606
305
37.5012.501504
36.672016.673
802
$60.00$101
n.a.n.a.n.a.$500
MCATCAVCAFCTCQ
60
30
$10
AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : AnswersAnswers
25
210
150
100
60
30
10
$0
VC
43.33358.332606
40.003010.002005
37.502512.501504
36.672016.671103
40.001525.00802
$60.00$10$50.00601
n.a.n.a.n.a.$500
MCATCAVCAFCTCQ
60
50
40
30
20
$10
Numerical Problem on Numerical Problem on CostsCostsGiven the cost function:
TC = 1000 + 10Q - 0.9Q2 + 0.04Q3
Find: 1) MC, TVC, AVC functions2) 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 ProblemWorked out ProblemTC = 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 & Costs in the Short Run & Long RunLong RunShort 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 SizesLRATC with 3 Factory Sizes
ATCSATCM ATCL
Q
AvgTotalCost
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.
EXAMPLE 3:EXAMPLE 3: LRATC with 3 Factory Sizes LRATC with 3 Factory Sizes
ATCSATCM ATCL
Q
AvgTotalCost
QA QB
LRATC
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.
A Typical LRATC CurveA Typical LRATC Curve
Q
ATCIn the real world, factories come in many sizes, each with its own SRATC curve.
So a typical LRATC curve looks like this:
LRATC
How ATC Changes as the Scale of Production How ATC Changes as the Scale of Production ChangesChanges
Economies of scale: ATC falls as Q increases.
Constant returns to scale: ATC stays the same as Q increases.
Diseconomies of scale: ATC rises as Q increases.
LRATC
Q
ATC
The Revenue of a Competitive The Revenue of a Competitive FirmFirm
Total revenue (TR)
Average revenue (AR)
Marginal Revenue (MR):The change in TR from selling one more unit.
∆TR∆Q
MR =
TR = P x Q
TRQ
AR = = P
How do firms behave in How do firms behave in different market structures?different market structures?
1.Perfectly Competitive Market2.Monopoly Market3.Oligopoly Market4.Monopolistically Competitive
Market
Perfectly Competitive MarketPerfectly 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.
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 DataSample Data
36
$50$105
$40$104
$103
$10
$10
$10
$10$102
$10$101
n.a.
$30
$20
$10
$0$100
TR = P x QPQ∆TR
∆QMR =
TR
QAR =
$10
$10
$10
$10
$10
Notice that MR = P
Notice that MR = P
MRMR = = PP for a Competitive for a Competitive FirmFirm
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.
MR = P is only true for firms in competitive
markets.
Profit MaximizationProfit MaximizationWhat 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 MaximizationProfit Maximization
505
404
303
202
101
45
33
23
15
9
$5$00
Profit = MR – MC
MCMRProfitTCTRQAt any Q with MR > MC,
increasing Q raises profit.
5
7
7
5
1
–$5
10
10
10
10
–2
0
2
4
$6
12
10
8
6
$4$10
(continued from earlier exercise)
At any Q with MR < MC,reducing Q
raises profit.
P1 MR
MC and the Firm’s Supply DecisionMC and the Firm’s Supply Decision
At Qa, MC < MR.
So, increase Q to raise profit.
At Qb, MC > MR.
So, reduce Q to raise profit.
At Q1, MC = MR.
Changing Q would lower profit.
Q
Costs
MC
Q1Qa Qb
Rule: MR = MC at the profit-maximizing Q.
P1 MR
P2 MR2
MC and the Firm’s Supply DecisionMC and the Firm’s Supply Decision
If price rises to P2,
then the profit-maximizing quantity rises to Q2.
The MC curve determines the firm’s Q at any price.
Hence,
Q
Costs
MC
Q1 Q2
the MC curve is the firm’s supply curve.
Market Structure ProblemsMarket 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 ProblemsMarket 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 When would the firms Shutdown, Exit or Enter?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 A Firm’s Short-Run Decision to Shut DownDown
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/QSo we can write the firm’s decision as:
Shut down if P < AVC
The firm’s SR supply curve is the portion of
its MC curve above AVC.
Q
Costs
A Competitive Firm’s SR Supply CurveA Competitive Firm’s SR Supply Curve
MC
ATC
AVC
If P > AVC, then firm produces Q where P = MC.
If P < AVC, then firm shuts down (produces Q = 0).
A Firm’s Long-Run Decision to ExitA 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 A New Firm’s Decision to Enter the MarketMarket
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 LossIdentifying a firm’s profit or Loss
Determine if this firm’s
total has profit/Loss?
Identify the area on the graph that represents the firm’s profit or Loss.
49
Q
Costs, P
MC
ATCP = $10 MR
50
$6
A competitive firm
profit
AnswersAnswers
50
Q
Costs, P
MC
ATCP = $10 MR
50
$6
A competitive firm
profit per unit
= P – ATC= $10 – 6 = $4
Total profit = (P – ATC) x Q = $4 x 50= $200
Identifying a firm’s profit or loss.Identifying a firm’s profit or loss.
Determine if this firm has total profit or loss.
Identify the area on the graph that represents the firm’s profit or loss.
51
Q
Costs, P
MC
ATC
A competitive firm
$5
P = $3 MR
30
lossMRP = $3
AnswersAnswers
52
Q
Costs, P
MC
ATC
A competitive firm
loss per unit = $2
Total loss = (ATC – P) x Q = $2 x 30= $60
$5
30
Demand Curve for Individual firm’s Demand Curve for Individual firm’s productproductIn 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.
D
P
Q
A competitive firm’s demand curve
Price line represents the level of demand for the firm’s product
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 ProblemsMarket 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.
Market Structure ProblemsMarket Structure Problems
Firms behaviour in the Long Firms behaviour in the Long Run-Profit ConditionRun-Profit ConditionIn 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 Firms behaviour in the Long Run-Loss ConditionRun-Loss 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.
S1
Profit
D1
P1
long-runsupply
D2
SR & LR Effects of an Increase in DemandSR & LR Effects of an Increase in Demand
MC
ATC
P1
Market
Q
P
(market)
One firm
Q
P
(firm)
P2P2
Q1 Q2
S2
Q3
A firm begins in long-run eq’m…
…but then an increase in demand raises P,……leading to SR
profits for the firm.Over time, profits induce entry, shifting S to the right, reducing P…
…driving profits to zero and restoring long-run eq’m.
A
B
C
Why Do Firms Stay in Business if Profit = Why Do Firms Stay in Business if Profit = 0?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 Distinction between The SR and LR Market Supply CurvesSupply Curves
MC
P2
Market
Q
P
(market)
One firm
Q
P
(firm)
SP3
Example: 1000 identical firms.
At each P, market Qs = 1000 x (one firm’s Qs)
AVCP2
P3
30
P1
2010
P1
30,00010,000 20,000
The LR Market Supply CurveThe LR Market Supply Curve
MCMarket
Q
P
(market)
One firm
Q
P
(firm)
In the long run, the typical firm earns zero profit.
LRATC
long-runsupply
P = min. ATC
The LR market supply curve is horizontal at P = minimum ATC.
The Zero-Profit ConditionThe Zero-Profit ConditionLong-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 CostsThe 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 youThank you
