CHAPTER (3) :BASIC ELEMENTS OF SUPPLY
AND DEMAND
CHAPTER OUTLINE:
1-DEMAND &SUPPLY (D&S) CURVES
•
THE DEMAND CURVE &SHIFTS IN THE (D) CURVE
•
THE SUPPLY CURVE & SHIFTS IN THE (S) CURVE
2-EQUILIBRIUM PRICE (Pe) & QUNTITY (Qe)
3-ADJUSTMENT TO CHANGES IN(D)OR(S),ITS EFFECTS ON (Pe)&(Qe )
4-GOVERNMENT INTERVENTION IN MARKETS: PRICE CONTROL
RENT CONTROL : WHO BENEFITS , WHO LOSES
CHAPTER ( 3 ):DEMAND,SUPPLY & MARKET
EQUILIBRIUM
I -DEMAND: TOTAL (Qs) THAT CONSUMERS ARE WILLING & ABLE TO
BUY AT A CERTAIN (P) AND DURING A PERIOD OF TIME.
A- FACTORS AFFECTING(D) FOR (X) COMMODITY:
1- ( Px )
Q Dx
THE LAW OF(D):THERE IS AN OPPOSITE RELATIONSHIP B/W (Px) AND
(Q Dx) , IF AND ONLY IF WE HOLD OTHER FACTORS CONSTANT.
Px
2
Qx/DY 500
Px
10
Dx
4
400
6
300
8
6
4
2
Dx
Qx
0
100
200
300 400
500
8
200
10
100
A-DEMAND – FACTORS AFFECTING (Dx) CONT,D
2- INCOME (I):
- NORMAL GOODS:
(I)
+
Dx
-
- INFERIOR GOODS:
(I)
Dx
3- PRICE OF OTHER RELATED GOODS ( Py ):
- SUBSTITUTES
( Py )
+
Dx
-
- COMPLEMENTS
( Py )
Dx
4- TASTE : CONSUMER PREFERANCES WOULD BE AFFECTED BY
COMMERCIALS, SEASONALITY, TRADITION ,..etc.
5- NUMBER OF CONSUMERS (# Cs): # Cs
6- CONSUMER EXPECTATIONS(EXP):
(P)EXP
+
Dx
+
Dx
CHANGES IN THE DEMAND
Px
I, Py, T, #Cs, PExp
A CHANG IN THE ABOVE FACTOR
ONLY WILL CAUSE A MOVEMENT
ALONG THE SAME (D) CURVE
Px
A CHANGE IN ONE OR ALL OF
THE ABOVE FACTORS ONLY WILL
CAUSE SHIFTS IN THE (D) CURV
Px
D
D1
D
++
A
D2
10
B
6
D1
-
D
Qx
0
100
300
0
D
D2
Qx
Demand & Algebra
• Demand
- Algebra
a- QX = 500 – 2 PX + 0.5 PY + 1.5 I (Demand Function)
b- PX = 250 + 0.25 PY+ 0.75 I – 0.5 Q (Inverse Demand Function)
X
- Consumer Surplus
• Benefit buyers receive from paying prices less than they’d be
willing to pay.
• Measured as area below Demand but above Price.
Quiz 2 - Demand
__________________________________________________________________________
Name
ID#
__________________________________________________________________________
1.
What happens to the demand for SONY color television sets when each of the
following happens:
a.
the price of Mitsubishi TVs rises
b.
the price of SONY TVs rises
c.
personal income falls
d.
dramatic price reductions occur for video recorders
e.
Government imposes tariffs on Japanese TVs beginning next year
2.
Suppose the demand for a product (X) can be expressed as a function of its
price (Px ), consumer monthly income (I), and the price of a related good Y
(PY )
QX = 180 - 10 (Px) - 0.2 (I) + 10 (PY)
a.
Interpret the slope coefficient on Px
b.
Is good X a normal or inferior good? Explain.
c.
Are goods X and Y substitutes or complements? Explain.
d.
Forgetting income (I) and the price of a related good (Py), how much
consumer surplus exists in this market if the price of X were $10?
DEMAND & SUPPLY CURVES CONT”D
B-SUPPLY: Qs THAT PRODUCERS ARE WILLING
& ABLE TO SELL
AT A CERTAIN( P) AND DURING A PERIOD OF TIME.
a-FACTORS AFFECTING (S) FOR X COMMODITY:
+
1-THE (Px) :
Q Sx
THE LAW OF (S): THERE IS A POSITIVE RELATIONSHIP B/W (Px)AND
THE (Q Sx),IF WE HOLD OTHER FACTORS CONSTANT
Px
Px
2
QSx 100
4
6
200 300
8
400
10
500
S
10
8
6
2-PRODUCTION COST (PROD.cost):
( PROD.cost )
Sx
3-TECHNOLOGY (TECH):
+
( BETTER TECH)
Sx
4
2
S
Qx
0
100
200
300
400
500
B-SUPPLY CONT’D – FACTORS AFFECTING (Sx)
4-FISCAL POLICY:GOV’T POLICIES REGARDING TAXEX &
SPENDING
HIGHER TAXES
MORE SUBSIDY
+
LESS Sx (VICE VESA)
MORE Sx (VICE VERSA
5- NUMBER OF PRODUCERS( # PRODx):
+
(# PRDs)
Sx
6- PRODUCER’S EXPECTATIONS (P prod exp) :
(P prod exp)
-
Sx
CHANGES IN THE SUPPLY
COST, Py, TECH., #Ps, Pexp, FISCAL POLICY
Px
A CHANGE IN ONE OR ALL OF
THE ABOVE FACTORS ONLY WILL
CAUSE SHIFTS IN THE (S) CURV
A CHANG IN THE ABOVE FACTOR
ONLY WILL CAUSE A MOVEMENT
ALONG THE SAME (S) CURVE
Px
Px
s2
S
-
S
S1
A
10
s1
B
6
+
S
0
S1
S
Qx
300
500
0
Qx
Supply & Algebra
• Supply
– Algebra
– QX = 500 + 2PX =
• Positive relationship between QS and Price
– PX = -250 + 0.5QX (Inverse Supply Function)
• This is graphed
– Producer Surplus
• Benefit sellers receive from receiving prices more than they’d
be willing to accept
• Measured as area above Supply but below Price
2-DETERMINATION OF THE EQUILIBRIUM (Pe) AND (Qe)
EX:THE EQILIBRIUM
Pe = 6 AND Qx = 300
THIS BECAUSE:
1- Qs = Qd
Px
2
4
6
8
QDx 500 400 300 200
QSx 100 200 300 400
2- STABLE , B/C ANY ANY
DEVATION FROM THE (Pe)
WILL CREATE AUOTOMATIC
FORCES ( SHORTAGE OR
SURPLUS )THAT WILL BRING
THE PRICE BACK TO THE (Pe)
10
100
500
Px
D
S
10
8
Pe
6
4
2
D
S
Qx
0
100
200
300
Qe
400
500
3-ADJUSTMENT IN Dx & Sx AND ITS IMPACT ON (Px) &(Qx)
A-CHANGES (+&-) IN (Dx) , NO CHANGE IN (Sx ):
- INCREASE IN (Dx):
- DECREASE IN (Dx)
Sx
PX
D
Px
D2
S
D
D1
8
6
6
4
D2
Sx
0
D
300 400
Pe & Qe INCREASE
D
S
Qx
O
D1
200
300
Pe & Qe DECREASE
Qx
B-CHANGES (+&-) IN (Sx) , NO CHANGE IN (Dx):
- INCREASE IN (Sx):
PX
- DECREASE IN (Sx )
S
S1
D
S2
PX
S
D
8
6
6
S2
4
S
D
S1
0
S
Qx
300
D
400
Pe DECREASE & Qe INCEASE
0
Qx
200
300
Pe INCREASE & Qe DECREASE
C- CHANGES (+&-) IN BOTH (Sx) &AND (Dx):
- INCREASE IN BOTH (Sx)& (Dx):
PX
D1
- DECREASE IN BOTH (Sx )&(Dx):
S
S1
D
S2
PX
S
D
D2
7
6
6
D1
S
D
S1
0
Qx
300
500
Pe INCREASE & Qe INCEASE
B/C + IN Dx > + Sx
0
S2
D
S
D2
Qx
200
300
Pe NO CHANGE & Qe DECREASE
B/C - IN Dx = - IN Ax
4- GOV’T. INTERVENTION IN MARKETS:
A-PRICE CEILING :
CAUSE SHORTAGE (AB)
B- PRICE FLOOR:
CAUSE SURPLUS(CD)
Px
Px
D
S
S
D
D
C
Pf 8
e
6
Pc 4
A
0
6
B
S
D
D
S
Qx
200 300 400
e
0
Qx
200 300 400
CASE STUDY DISCUSSION: RENT CONTROL IN
EGYPT
Market Pe = 800
Ceiling price (P)= 500
Black market (P) = 1000
SHORTAGE = 100,000 UNITS
Px
S
D
Black market price 1000
Market price
800
Ceiling price
500
e
D
S
Qx
0
100,000
200,000
300,000
QUIZ (1)
Assume that a Nokia mobile (x) market Pe
=1000 and Qe =400 , show this graphically. what
will happen if a Samsung mobile market prices
increases and the cost of producing the Nokia
mobile increased (Make shift in D =shift in S)
Px
S1
S
1200
1000
D1
D
D
0
Ox
400
Chapter (4)
Elasticity
• Elasticity
– The relative sensitivity of change in one variable (QDx
or QSx ) to change in another variable (Px )
– Magnitude of change in the variables
• Absolute value of Elasticity greater than, less than or equal to
one
- ELASTICITIES (Cont’d)
Chapter (4)
A- DEMAND ELASTICITIES:
• PRICE ELSTICITY OF DEMAND (PED)
1-DEFINITION (PED):THE DEGREE OF RESPONSIVENESS (SESITIVITY)
OF THE Q Dx TO THE CHANGES IN THE Px.
2-MEASURING THE(PED):
-POINT ELASTICITY FORMULA
Qx
PEDx =
Px
Qx
Px
∞ >PED > 1
ELASTIC
EX :LUXTURIES(TRIPS)
THE SIGN IS NORMALLY( - ) , IF :
PED=1
UNITE ELASTIC
0<PED< 1
INELASTIC
NECESSITIES(MEDICIN)
A-DEMAND ELASTICITES:PED
(CONT’D)
-ARC ELASTICITY FORMULA:
PED =
Qx
Q1 + Q2
Px
P1 + P2
2
THE SIGN NORMALLY( - )
2
FACTORS DETERMINING PED:
1-TYPE OF THE COMMODITY: BASIC GOODS (BREAD) ARE LESS ELASTIC,
WHILE LUXURIES (TRIPS) ARE HIGHLY ELASTIC.
2-NUMBER & DEGREE OF SUBSTITUTES: LESS NUMBER OF
SUBSTITUTES(OIL)MEANS LESS PED , WHILE CLOSE SUBSTITUTES (DELL &
HP COMPUTER) MEANS HIGH PED.
3-PERCENTAGE OF INCOME SPENT ON THE COMMODITY: IF THE % IS
VERY LITTLE (SALT) , THE PED WILL BE LITTLE.
4-THE TIME NEEDED TO ADJUST: IF THE TIME AVAILABLE TO THE CONSUMER
IS NOT ENOUGH TO ADJUST TO THE CHANGES IN THE (P) OF A CERTAIN
GOOD,THEN THE PED IS LESS AND VICE VERSA .
A-DEMAND ELASTICITIES:PED
(CONT’D)
-THE RELATIONSHIP B/W THE PED & TOTAL REVENUE (TR):
1-PED > 1 ,THEN, THERE IS A NEGATIVE RELATIONSHIP B/W
(P) AND (TR). THAT IS WHEN THE (P) , THEN (TR) AND VICE
VERSA.
2-PED< 1 , THEN, THERE IS A POSITIVE RELATIONSHIP B/W
(P) AND (TR) . THAT IS , WHEN THE (P) , THEN (TR) AND VICE
VERSA.
3-PED = 1, THEN, THERE NO CHANGE IN THE(TR) WHEN THE (P)
IS CHANGING
A-DEMAND ELASTICITIES: INCOME ELASTICITY OF (D)
2- INCOME ELASTICITY OF DEMAND (IED)
IED =
Qx
Qx
I
I
THE SIGN COULD BE :
( + ) IF THE GOOD IS NORMAL
OR ( - ) IF THE GOOD IS INFERIOR
3- CROSS PRICE ELASTICITY OF DEMAND (CPED):
CPED =
Qx
Qx
Py
Py
THE SIGN COULD BE :
( - ) IF GOOD x COMPLEMENT GOOD y
( + ) IF GOOD x SUBSTITUTE GOOD y
B-THE PRICE ELSTICITY OF SUPPLY(PES)
Qsx
PES =
1-PES = 0
Px
Qsx
Px
THE VALUE COULD TAKE 5 CASES:
COMPLETELY INELASTIC
2-PES = ∞
COMPLETELY ELASTIC
3-PES < 1
INELASTIC
4-PES = 1
UNIT ELASTIC
5-PES > 1
ELASTIC
FACTORS AFFECTING PES
1-FLEXIBILTY IN USING FACTORS OF PRODUCTION
2-TIME NEEDED TO ADJUST PRODUCTION
TRIAL TEST
1-WHEN THE SONY TV PRICE DECREASE
FROM LE 1000 TO LE 800 , CONSUMERS
INCREASED THEIR Q DEMAND FROM 100,000
UNITS/ MONTH TO 120,000 UNITSE /MONTH.
CLCULATE THE PED.ALSO , IF THIS IS
HAPPENING WHILE THE PRICE OF SAMSUNG
TV IS INCRESING FROM LE 500 TO LE
600.THEN CALCULATE THE CROSS-PRICE
ELASTICITY.
Equations: Demand ,supply & the Market
Equilibrium
I-
Use the following generalized linear demand relation to
answer the following questions:
Qx = 680 - 9 Px + 0.006 M – 4 PR
1- where M is income and PR is the price of a related good,
R. From this relation it is apparent that the good is:
aan inferior good
ba substitute for good R
ca normal good
da complement for good R
eboth c and d
Equations: Demand ,supply & the Market
Equilibrium (Cont’d)
2. If M = $15,000 and PR = $20, the
demand function is
Qx = 680 - 9 Px + 0.006 M – 4 PR
a.
P  690  9Qd
b.
Qd  690  9 P
c.
d.
e.
Qd  680  9 P
P  680  9Qd
Qd  800  19 P
3. If M = $15,000 and PR = $20 and the
supply function is Qs  30  3P , equilibrium
price and quantity are, respectively,
a.
b.
c.
d.
e.
P = $55 and Q = 195.
P = $9 and Q = 609.
P = $12 and Q = 200.
P = $50 and Q = 170.
P = $40 and Q = 250.
4. If M = $15,000 and PR = $20 and the supply
function is Qs  30  3P , then, when the price of
the good is $12
a.
there is a shortage of 516 units of the good.
B.
C.
D.
there is equilibrium in the market.
there is a surplus of 60 units of the good.
the quantities demanded and supplied are
indeterminate.
5-If M = $15,000 and = $20 and the supply
function is Qs  30  3P , then, when the price of
the good is $60,
a.
b.
c.
d.
there is equilibrium in the market.
there is a shortage of 180 units of the good.
there is a surplus of 60 units of the good.
there is a shortage of 80 units of the good.
II- Use the following demand and supply functions
to answer the next 3 questions:
Demand: Qd  50  4 P
Qs  20  2 P
Supply:
1.
Equilibrium price and output are
a.
P = $5 and Q = 30.
b.
P = $11 and Q = 3.32.
c.
P = $12 and Q = 44.
d.
P = $15 and Q = 50.
e.
none of the above
2.If the price is $10, there is a
a.
b.
c.
d.
e.
3.
surplus of 30 units.
shortage of 30 units.
surplus of 40 units.
shortage of 10 units.
none of the above
If the price is $2, there is a
a.
surplus of 10 units.
b.
shortage of 10 units.
c.
surplus of 30 units.
d.
shortage of 18 units.
e.
none of the above
Chapter (5) Demand Estimations
1) The Regression Analysis
Elfiky Company uses the per capita income (in thousand LE)
to help forecast its demand for computer (brand x) units in
million LE . The firm collected the data in the following table
(which is presented on annual basis.
Year
I
Dx
2001 5.15 3.25
2002 5.05 3.10
2003 5.25 3.30
2004 5.40 3.65
2005 5.60 3.90
2006 5.70 4.10
2007 5.65
4.15
REGRESS : dependent variable (Demand for x
computer Using the income per head as
independent variable during the period
(2000 – 2006)
Variable
CONST
(I)
Coefficient
Std Err T-stat
-5.20679 0.616404 -8.44704
1.63750
0.114037 14.3594
No. of Observations = 7
R² = .9763 (adj)= .9716
Sum of Sq. Resid. = .260089E-01
Std. Error of Reg.= .721234E-01
Durbin-Watson = 2.0012
F ( 1, 5) = 206.191
Significance = .05
1-What is the equation of the estimated least
squares regression?
- Dx = -5.20679 + 1.63750 (I)
2-Test the hypothesis that there is no
relationship between the dependent and
independent variable (at the 95 percent
confidence level) in El Fiky Company
Regression. Your results indicate that
- you would reject the null hypothesis and
conclude that the two variables are related
3-The coefficient of determination for this El Fiky
Company regression indicates that
- 97.63 percent of the variation in Dx is explained by
variation in (I)
4-Suppose that per capta income 6,300 is expected in
2007. What would be the estimate of El
Fiky Company's demand for its coputer in year 2007 ?
a.
b.
c.
d.
$ 4.62 million
$ 4.95 million
$ 4.99 million
$ 5.11 million
2- An equation is estimated as:
QDx = 400 - 2.0 (Px) + 0.015 (I) - 0.17Py
(250) (1.0)
(0.010)
(0.10)
standard errors are in parentheses
1.The most statistically significant coefficient
a.
is the constant term.
b.
The most significant coefficient is of Px .
c.
The most significant coefficient is of I .
d.
The most significant coefficient is of Py .
2-The statistic used to test whether the
independent variables taken as group
statistically explain variation in the dependent
variable is the
a.
R-squared statistic.
b.
t-statistic.
c.
Durbin-Watson statistic.
d.
F-test statistic.
3- Serial correlation occurs when
a.
independent variables are correlated across
observations.
b.
dependent variables are correlated across
observations.
c.
error terms are correlated across
observations.
d.
R-squared is near one and the t-statistics are
near zero.
4-The statistic that tests an individual coefficient for
statistical significance is the
a.
R-squared statistic.
b.
t-statistic.
c.
Durbin-Watson statistic.
d.
F-test statistic.
5- Multiple regression differs from simple regression in
that
a.
there can be multiple dependent variables.
b.
the time periods over which observations are
taken are multiplied to increase explanatory
power.
c.
a simple regression is done multiple times to
increase explanatory power.
d.
there are multiple independent variables.
Chapter 6:Forecasting
• Forecast helps in two areas:
1- Setting cos. Objectives.
2- Constructing cos. business plans.
• Subjects of Forecast:
1- Macroecon. Level
2- Sector level
3- Industry level
4- Product level
Demand Estimate & Forecasting
• Prerequisite of a good forecast
1- Consistency with other parts of the business.
2- Adequate knowledge of the relevant past.
3- Take into consideration the econ. & political
environment.
4- Conducted in timely fashion
Forecasting Techniques
Classified into:
A- Qualitative Techs: Based on personal judgments
1- Expert Opinion.
2- Opinion Polls & Market research.
3- Surveys of spending plans.
B- Quantitative Techs: Utilize significant amount of
historical data as a basis for prediction.
1- Naïve
2 - Explanatory
4- Econ. Indicators.
5- Projections.
6- Econometric models.
1- Expert Opinion
• Various types of techs: Choosing the most
important.
1- The jury of executive opinion.
2- Soliciting the views of the sales staff in a co. to
forecast sales.
3- Delphi method.
Opinion Polls & Market research.
Dealing with specific products and are often
conducted by individual firms.
A- Opinion Polls.
– Conducted on samples of population.
– Choice of the representative sample is of utmost
importance.
B- Market research. (very close to the opinion
polls)
3- Surveys of spending plans.
• Quite similar to opinion poll & market
research, but it seeks information about
macro-type data relating to the economy.
• it includes:
1- Consumer intentions.
2- Inventories and sales expectations.
3- Capital expenditure surveys.
B-Quantitative Techs.
4- Econ. Indicators.
• Designed to alert business communities to
changes in general econ. Conditions.
• There are 3 major series of indicators:
- Leading, tells us where we are going, where
we are, and where we have been.
- Coincident, identifies peaks and troughs.
- Lagging, confers upturns and downturns in
econ. activities.
5- Projections.
• A quantitative technique ,naïve metod of forecasting.
- past data are projected into the future without taking
into consideration reasons for the change, It is simply
assumed that the past trends will continue in the future.
- Classification:
1- Constant compound growth rate.
2- Visual time series projection.
3- Time series projection using the least squares
method
6- Econometrics models.
• Causal or explanatory models
1- Single equation model
a- Uni-variate : Dx = f(Px) ;
Dx = a + b1 Px
b- multi-variate ;
Dx = a + b1 (Px) + b2 (Py) + b3 (I)
2- multi-equation model.
Dx = a + b Px ------------------------------------ (1)
Sx = c + d Px -------------------------------------- (2)
Dx = Sx
----------------------------------- (3)
Time series regression model
• Single equation-multi-variete model
Ex. Demand for automobile:
∆ R = a0 + a1 ∆Y+ a2 ∆P/M + a3 ∆S + a4 ∆X
Where: R= retail sales, in millions of new cars.
Y= real disposable income.
P= real retail price of new cars.
M= average credit terms (no. of months of the average installment
contract)
S= Existing stock, in millions of cars.
X= Dummy variable.
Demand for computers
Log (yt /yt-1) = a0 + a1 log Pt – a2 log Yt-1
Where Yt = Stock of comps. In yr. t.
Yt-1 = Stock of comps. In yr. t-1.
P = real price of comps.
Managerial Economics: Trial Questions &
Problems
Chapter (3)
Questions: 12,13
Problems: 3,6,8,9,12
(pp.125,126)
(pp.126-129)
Chapter (4)
Questions: 3,5,11,13,18
Problems: 4,7,8,12,13
(pp.162,163)
(pp.164,165)
Chapter (5)
Questions: 1,3,5,7,8,9
Problems: 2,4,5,7
(pp.238,239)
(pp.239-242)
Chapter (6)
Questions: 5,13,15,18
Problems: 4,5,7,11,
(pp.282,283)
(pp.284-287)
Chapter(7): The theory & Estimation of production
I- The Production Function:
Q = f ( X1 ,X 2,X 3,…..X n)
Where Q = Output = Total Product.
xs = Inputs = Factors of production = Econ. resources.
“The max. output that can be produced by a set of
inputs within a given period of time and with a
given level of technology”.
For the purpose of analysis:
Q = f (L , K)
Where :
Q = Output = Total Product
L = Labor input
K = Capital input
1- Short-run production function: the period during which max .output
can be produced by varying certain inputs (variable inputs like labor)
other inputs remain unchanged ( fixed input like capital)
2- Long-run production function: the period during which max .output
can be produced by varying all inputs (all inputs are variable )
1- The Short-run Production Function
The short-run is e period during which max .output can be produced by
varying certain inputs (variable inputs like labor) other inputs remain
unchanged ( fixed input like capital)
QL = f (L , K)
-Total Product (Q) = The total sum of marginal product of
labor (L) or capital (K) .
Total Product (Q) of labor = Σ (MPL)
- Marginal Product (MP) of labor or capital = The change (∆) in TP due
to a change (∆) in the variable input (labor-L or capital-K) by one
unit.
Marginal Product of labor (MPL) of labor = ∆ TPL / ∆ L
- Average Product (MP) of labor or capital = The TP per unit of the
variable input (labor-L or capital-K) (APL) of labor
Average Product (APL) = TPL / L
1- Short-run Production Function (cont’d)
I- The Law of Diminishing Returns:
As additional homogenous units of a variable input (labor) is
combined with a fixed input (capital) at some points the additional
TPL
output (i.e., MPL)
K L
TPL
MPL
APL
1
1
1
1
1
1
1
0
1
2
3
4
5
6
2
6
12
20
30
36
2
4
6
8
10
6
2
3
4
5
6
6
1
1
1
7
8
9
38
38
36
2
0
-2
5.40
4.75
4
Stage I
Stage II
Stage III
0
L
MP
AP
AP
0
MR
8
L
Derived Demand & The Optimal Level of Labor
K
1
1
1
1
1
1
1
1
1
1
L
0
1
2
3
4
5
6
7
8
9
TPL
0
2
6
12
20
30
36
38
38
36
MPL
0
2
4
6
8
10
6
2
0
-2
APL TRP MRP TLC
0
0
2
20
20 20
3
60
40 40
4
120
60 60
5
200
80 80
6
300
100 100
6
360
60 120
5.40 380
20 140
4.75 380
0 160
4
360
-20 180
MLC (TRP-TLC) (MRP-LC)
0
0
20
(0 )
0
20
(20 )
20
20
(60 )
40
20
(120)
60
20
(200)
80
20
(240)
40
20
(240)
0
20
(220)
-20
20
(180)
-40
MRP = MPL × PX TLC = L × W MLC=∆TLC /∆L
A profit maximizing firm operating in a perfectly competitive markets will
demand the number of labor at the point where : MRP = MLC (W)
PX = LE 10
wL = LE 20
2- The Long-run Production Function
(Return to Scale)
The Long-run is the period during which max .output can be produced by
varying all inputs (all inputs are variable)
K
L
1
2
4
5
6
1
2
3
4
5
6
7
8
9
7
8
9
3
TPL Return to scale: if a firm increase its scale
2
by a certain proportion result in an increase in
8
output by a greater proportion, the firm
16
experiences increasing return to scale (IRTS) ,
24
if output increases by the same proportion , the firm
30
36
40
42
45
experiences a constant return to scale (CRTS) , and if
output increases by less proportion , the firm
experiences a decreasing return to scale (DRTS)
Measuring Return to scale
1- Output Elasticity (EQ) = % ∆ in Output / % ∆ in all inputs
Q
If: (EQ) > 1 increasing return to scale (IRTS),
(EQ) = 1 Constant return to scale (CRTS) ,
IRTS
o
(EQ) < 1 Decreasing return to scale (DRTS)Q
2- hQ = f ( mL , mK)
If: h > m increasing return to scale (IRTS) , o
Q
h = m Constant return to scale (CRTS) ,
h < m decreasing return to scale (DRTS)
L,K
CRTS
L,k
DRTS
o
L,k
The Estimation of Production Function
1- The possible shape of production function.
• Q = f (L)k
( Short-run production function)
Q = a + bL + cL² - dL³
& Q = a + bL - cL²
Q=aL b
( power function)
log Q = log a + b log L
2- Cobb-Douglas production function.
b 1- b
Q=aL K
It assumes CRTS, (b +1-b =1)
b
c
However it could be rewritten as: Q = a L K
It assumes:
IRTS , If b + c >1 , CRTS , If b + c = 1 , and DRTS , If b +c < 1
1- MPL = b Q / L
2- MPK = c Q / K , Decreasing Marginal Product.
2- The function can be converted to linear function using logarithms.
We shall examine a generalized
third-order equation of a production
function with a single variable input, L,
assuming all other inputs constant,
Q = + 10L + 1.5L² + -0.05L³ ,
In this representation, the
power 3 in the third term
on the right side of this
function makes it a third-order
equation. The constant in
this equation is missing,
implicitly having a value
of zero, so that the graphic
depiction of the production
function passes through
the origin. The signs on the
coefficients of L2 and L3
indicate that as L increases from the origin, Q at first ncreases at an in creasing
rate,Then eventually increases at a decreasing rate (the range of diminishing
returns) until Q reaches a maximum value, beyond which Q decreases. The
average and marginal functions to the Q function are displayed in the bottom
panel .
The firm's production function curves
may change either because wear or
weathering (i.e., depreciation) results
in capital consumption, or because the
management of the firm implements
changes in the technologies employed
in the firm's production processes.
Capital consumption may be expected
to shift the product curves downward
and to the right. If the technology changes
are output-increasing, they will shift the product curves
upward.
The management of an organization may gather
output data via its production and inventory
accounting systems; its research staff may perform
regression analyses upon the data to estimate the
parameters of its production functions.
Chapter 7 Problems
A firm has the following short-run production
function:
Q = 50 L +6 L² – 0.5L³
a- when does the law of diminishing returns take effect?
b- Calculate the values for labor over which stages I , II , III occur.
c- Assume each worker is paid LE 10 per hour and works a 40hour week, How many workers should the firm hire if the price
of the output is LE 10 per unit ? Suppose the price of the output
falls to LE 7.50. What do you think would be the short run
impact on the firm’s production ? The long run impact?
2- Following are different algebraic expression
of the production function. Decide whether
each has constant, increasing, or decreasing
return to scale .
0.25 0.75
0.15 0.40 0.45
1- Q = 75 L K
2- Q = 75 L K C
0.70 0.60
3- Q = 75 L K
2
5- Q = 50 L + 50 K
4- Q = 100 + 50 L + 50 K
2
6- Q = 50 L + 50 K + 50 LK
3- The owner of a car wash is trying to decide on the number of
people to employ based on the following short production
function:
Q = 6 L – 0.5 L²
Where Q = No. of car washes per hour
L = No. of workers
a- Generate a schedule showing TP,AP,MP.,
then graph it.
b- Suppose the price for a basic car wash (no under coating ,no
wax treatments etc.) in his area of business is LE 5. How
many people should he hireif he pays each worker LE 6 / he.?
c- Suppose he consider hiring students on a part time basis for
LE 4 \ hr. . Do you think he should hire more students at this
lower rate ? Explain.
CHAPTER (8) : The Theory & Estimation of
Cost
Why should firms incur costs? Why do they exist?
The existence of costs of production is attributable directly to the existence of scarcity.
1- Cost Concepts
a- Implicit Costs. We shall refer to nonpecuniary costs as implicit costs
, economists identify it as
opportunity costs.
b- Explicit Costs. is pecuniary, accounting cost by virtue of the fact that such money-denominated costs
are visible, readily monitored, and hence easily included by accountants
Accounting costs: may be subdivided into two categories:
- Disbursement Costs. Disbursement costs are those out of pocket money
payments from the enterprise to parties who provide services or resources to
the enterprise.such as the payroll, payments for energy, the raw materials, etc.
- Non-disbursement cost: depreciation (capital consumption).
is an allowance for the
decline in the value of the capital stock which is attributable to the using-up of part of the
enterprise's capital equipment during the production (the accounting) period. An
allowance for depreciation is not paid out (disbursed) to any party outside the enterprise;
rather it is in a sense paid to the enterprise itself for the use of the capital equipment
owned by the enterprise.
Spill-Over Costs
Spill-Over Costs: A final example of costs which are irrelevant
to current decision making consists of social or spill-over costs. i.e.,
the negative aspects of production which descend upon members of
society other than the production decision maker? For example, air,
water, and noise pollution are the unfortunate by-products of
production processes which affect parties outside the enterprise.
These spill-over costs, however, are irrelevant to the
production decision context unless or until either the production
decision maker experiences a twinge of conscience, or the
authorities require the firm to prevent, clean-up,or compensate those
who have been harmed.We may say,then, that while such spill-over
costs currently are irrelevant to the production decision context, they
always have the potential for becoming relevant costs and
should not be ignored entirely by the production decision maker.
Variable and Fixed Costs
1- Variable costs (VC): are those which vary with the level
of productive output. Variable costs are always relevant
to the rate-of-production decision.
2- Fixed or overhead costs: are associated with the
existence of the manager, the plant, and the equipment.
Such as contractual salaries and insurance premiums.
They continue at the same levels or rates irrespective of
the rate of production, even if it is zero. Once the plant
has been put in place, these fixed or overhead costs are,
"sunk" costs, and sunk costs are not relevant to any
rate-of-production decisions
Accounting profit and economic profit
Accounting profit is the explicit, money-denominated
revenues realized by the enterprise during an accounting period,
less the explicit,money-denominated costs which are incurred in
that same period. Accounting profit does not include any implicit
costs, .the computation of an enterprise's accounting profit may
over- or understate its true (economic) profit and thereby lead to
erroneous decisions.
Economic profit is the result of the economist's effort to
recognize all benefits (implicit as well as money revenues) and costs
(opportunity costs as well as accounting costs) accruing to the
enterprise. Economic costs are all of the costs which are relevant
to decision making, whether or not money disbursements were
made and whether or not they are recognized in formal accounting
A critical distinction between a "good management" and "poor
management" may lie in the ability of the decision maker to
recognize the implicit costs and benefits of managerial decisions.
Cost Table & Curves in the Short-term
VI- COMPLETE THE FOLLOWING TABLE & graph it:
Q
FC
VC
TC
AFC
AVC
ATC
MC
0
1
2
3
4
5
6
7
8
9
10
100
100
0
100
180
240
280
340
420
520
640
780
940
100
200
280
340
380
440
520
620
740
880
1040
∞
100
50
33.3
25
20
16.7
14.3
12.5
11.1
10
100
90
80
70
68
70
74.3
80
86.7
94
∞
200
140
113..3
95
88
86.7
88.6
92.5
97.8
1004
0
100
80
60
40
60
80
100
120
140
160
= ∆ TC/ ∆Q
COSTS IN THE LONG-RUN
In the long run all enterprise's operations can be adjusted, so all costs are
variable .Any long run cost consists of a sequence of short runs. Costs in the
Long Run
The curve in the figure
which is tangent to
the sequence of short-term
SATC curves is a long run
average total cost
curve, LATC. It is
also referred
to as an "envelope"
curve because it
envelopes the
sequence of SATC curves
COSTS IN THE LONG-RUN (Cont’d)
Each of the SATC curves represents the cost conditions
for a plant of particular capacity which the enterprise
may construct. The LATC curve, however, represents no
single such entity, but rather is a sequence of points
each on a different SATC curve. Each of these points
represents the single optimal plant size, rate of
production, and cost level to meet a particular level of
demand.
The LATC curve may therefore be regarded as a longrun "planning horizon" concept which may assist the
production manager in selecting the appropriate plant
size, given the existing or anticipated level of demand for
the product.
COSTS IN THE LONG-RUN (Cont’d)
The following figures represent possible shapes of the
LATC curve.
Empirical data for a variety of industries
suggests that some of the other shapes
may be more common than the theoretical
U-shape. Shape (1) suggests possible early
(small-plant) scale economies, but after a
rather small least-cost plant size has been
reached, diseconomies of scale if the
Company attempts to build larger-scale
plants. These long-run cost conditions are
conducive to the development of a market
populated by a rather larger number of
smaller firms (or firms with a multiplicity
of small-capacity plants).Shape(2) depicts
long-run cost conditions characterized by the progressive, though gradual, exploitation of
economies of scale which never seem to reach exhaustion. A market characterized by these long
Run cost conditions will tend to be populated by a rather smaller number of larger-sized firms, and
perhaps ever fewer firms as time passes and competition ensues. Economists classify such a
market as oligopolistic. The ultimate end of competitive evolution in such a market might be a single,
very large surviving firm, a so-called "natural monopoly." Shape(3) may have involved a few minor
scale economies as firms grew from very small size at start-up, and could eventually reach a range
of diseconomies of large scale if existing firms Grow much larger. But the salient characteristic of
LATC curve is that it is flat-bottomed, i.e., there are no significant scale economies to be exploited or
diseconomies to be suffered over a very wide range of plant sizes. .
Mathematical Specification and Empirical
Estimation of Cost Functions
TC = b0 + b1Q + b2Q2 + b3Q3,
from which may be derived
MC = dTC/dQ = b1 + 2 b2Q + 3 b3Q2
and
ATC = TC/Q = b0/Q + b1 + b2Q + b3Q2.
If b3 turns out not to be statistically significant but both b1 and b2
are significant, the model may be respecified as a quadratic of form
TC = b0 + b1Q + b2Q2,
from which may be derived
MC = dTC/dQ = b1 + 2 b2Q
and
ATC = TC/Q = b0/Q + b1 + b2Q.
if upon regression analysis of the quadratic form the coefficient b2
appears not to be statistically significant, the equation may be
respecified as a linear form,
TC = b0 + b1Q,
from which may be derived
MC = dTC/dQ = b1,
and
ATC = TC/Q = b0/Q + b1.
cost-function simulation model
The Management of Costs
Whether the management of the firm develops cost-function simulation
model or not, the cost related job involves many facets:
(1) in the long run, selecting the most efficient technology for producing the
selected products;
(2) with that technology, selecting the scale of plant with an output range
which is most compatible with current and expected future levels of
demand for the products;
(3) given the right scale of plant, selecting the appropriate output level to
meet the enterprise's goals (profit aximization, cost minimization, etc.);
(4) for the target level of output, selecting the appropriate internal allocation
of the enterprise's resources, i.e., the most efficient combination of
inputs, given the available input prices;
(5) operating efficiently and without waste, i.e., to operate at points on the
enterprise's production function surface (not below it) and on its
respective cost curve (not above it).
Furthermore, economists can argue that if the goal of the enterprise is to
maximize profits, and if it does so operate to maximize profits without
monopolizing its markets or exploiting its resources, it will also meet a
desirable social objective of efficiency in the allocation of resources .
Perfect Competition
The descriptive characteristics:
(1) There is a large number of very small firms which operate within the same
product market.
(2) The single product which they produce and market is essentially homogeneous
across the member firms.
(3) The member firms have virtually identical managerial capacities; they use
essentially the same technologies; no one of them has or can acquire any
special expertise which is not available to all of the others.
(4) All participants in the market have access to the same information about
changing market conditions
Consequences and behavioral patterns for firms in the purely competitive market
:
Perfect Competition (Cont’d)
a) Entry into the market is easy; entry may be accomplished quickly
because of the ready availability of common technology, and with very little
capital investment.
(b) Exit from the market is likewise easy, i.e., the firm can dispose of its
capital assets quickly and with very little loss of value.
(c) Once a decision has been made to enter the competitive market there is
likely be very little incentive or effort to exercise further entrepreneurship,
except the decision to exit the market.
(d) The atomistic size and limited financial resources of the competitive firm
militate against its acquisition of any special managerial or technical
expertise; firms are unable successfully to differentiate their products, and
no firm can attain any position of market dominance.
(e) Because of the common knowledge of changing market conditions, all
participants in the market become aware of such changes simultaneously,
and all adjust at approximately the same rates.
(f) Because of the large number and atomistic size of sellers, competition is
essentially anonymous; no seller is aware of or concerned about the
identities of other sellers.
(g) A common price likely emerges in the market, and no market participant
finds incentive to try to charge any price higher or lower than the market
price.
(
A Firm in a Purely Competitive Industry
The general principle that
govern output decision
making when the goal is
to maximize profit is to:
P(MR) =MC
increase Q if MR > MC, but to
decrease Q if , MR < MC.
MR is easy to identify in the
purely competitive market
because it is equal to price,
and the MR curve is coincident
with the demand curve.
However, MC is not directly
observable. It can be computed
for any output level if the equation
of the TC or MC curve is known,
but knowing either of these equations
probably required a costly data
collection and model specification
and estimation process.
Incremental cost can be computed
more cheaply from data for two
different output levels, but it is only
an approximation to true
marginal cost
The Operate vs. Shut-Down Criterion in
the Short Run
It may be rational to shut-down operations in the shortrun if the revenue generated by selling the output cannot
cover even the operating costs (or variable costs) of
producing the output. Assuming cubic production and
cost functions, the shut-down criterion can be illustrated
in the above figure at any Qt for which
AR (P) < AVC,In these circumstances, the firm should
not operate because the revenue resulting from
operation would not cover all of the operating costs, and
could make no contribution at all to the overhead costs .
In shut-down mode, the firm minimizes its losses by
incurring only the fixed costs. The fixed costs, which
continue in the short run whether the firm operats or not,
can be saved (or avoided) only by exiting the industry..
I-You have given the following cost function:
TC = 100 + 600 Q – 3 Q² + 0.1 Q³
TC = 100 + 600 Q – 3 Q²
TC = 100 + 600 Q
1- compute the AVC,AC,and MC for each function. Plot them in
graph.
2- In each case , indicate the point at which diminishing returns
occur, also indicate the point of max. cost efficiency.
3- For each function, discuss the relationship b/w MC, AVC ,and
b/w MC and AC, and the relationship b/w AVC and AC.
IIThe demand and cost function for a company are estimated to be
as follows: p = 170 – 5Q
TC = 50 + 80Q – 10Q2 + 0.6Q3
• a. What price should the company charge if it wishes to
maximize its profits in the short run.
• b. What price should it charge if it wishes to maximize its
revenue in the short run?
• c. suppose the company lacks confidence in the
accuracy of cost estimates expressed in a cubic
equation and simply wants to use a linear approximation.
Suggest a linear representation of this cubic equation.
What difference would it make on the recommended
profit maximizing and revenue maximizing prices?
Purely Competitive Adjustment in the Long-Run
We may recall that ATC is greater
than AVC by the average fixed cost at
each level of output. Under the
circumstances illustrated by P1 and TR1,
firms presently operating in the marke
t can cover all of their variable and fixed
costs and enjoy a profit at the current
market price. When these profits are
perceived by outsiders, and if these profits
are greater than can be earned in other
markets, the outsiders may exercise
their entrepreneurship to enter the
market and try to share in the
supernormal profits. This entry into
the market will have the effect of
increasing market supply, shifting it to
the right to some position like S2 in panel (a) of the figure . As a result, market price will fall
toward P2, which will become the new locus of the demand and marginal revenue curves
as well. Correspondingly, the TR curve will rotate downward to its new position, TR2. As
consequence, the firm's profit-maximizing output level will change to q7, and the profit
earned by the firm will be smaller.
Purely Competitive Adjustment in the
Long-Run
driven by continuing entry into the market, could
continue until the price falls to P2 and the total revenue
curve rotates to position TR2; here, supernormal profits
are eliminated and the market price just covers the firm's
variable and fixed costs, allowing only a normal return to
the firm's ownership interest. The important point is that
with no effective way for firms to prevent entry into the
market, all super-normal profits will be competed away.
But no firm in the market will be suffering because each
will be paying or earning normal returns for all of the
resources under its employ. Capital and
entrepreneurship, having entered the market, will
continue in their present occupation until the prospect of
supernormal profits appears elsewhere.
Purely Competitive Adjustment in the
Long-Run
Managers who committed to plants like ATCm or ATC1
may find their firms realizing losses relative to firms
whose managers chose to build a least-cost plant. They
are stuck with plants which are too small or too large for
the duration of the lives of the plant and equipment.
Their short-run options are to continue to operate while
suffering losses if Pe happens to exceed their average
variable cost, or to shut-down if Pe is less than their
average variable cost. If price remains as low as Pe, the
firms which are realizing losses have the option of exiting
the market. Exit from the market will likely involve capital
losses if the plant and equipment cannot be
economically converted to other applications, or if they
must be sold at prices below their depreciated book
values.