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 & MARKETEQUILIBRIUM

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 4 6 8 10

Qx/DY 500 400 300 200 100

-

8 64

2

10

0100 200 300 400 500

Dx

Dx

Qx

Px

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 Dx

6- CONSUMER EXPECTATIONS(EXP): (P)EXP Dx

+

-

+

-

+

+

CHANGES IN THE DEMAND

Px I, Py, T, #Cs, PExp

A CHANG IN THE ABOVE FACTORONLY WILL CAUSE A MOVEMENT ALONG THE SAME (D) CURVE

A CHANGE IN ONE OR ALL OFTHE ABOVE FACTORS ONLY WILL CAUSE SHIFTS IN THE (D) CURV

Qx

Px

0

D

D

10

6

100 300

A

B

Qx

Px

0

D

D

D1

D1

D2

D2++

-

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 QX(Inverse Demand Function)

- 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 risesb. the price of SONY TVs risesc. personal income fallsd. dramatic price reductions occur for video recorderse. 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 Pxb. 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 2 4 6 8 10

QSx 100 200 300 400 500

2-PRODUCTION COST (PROD.cost):

( PROD.cost ) Sx

3-TECHNOLOGY (TECH):

( BETTER TECH) Sx

+

-

+2

4

6

8

10

0100 200 300 400 500

S

S

Qx

Px

B-SUPPLY CONT’D – FACTORS AFFECTING (Sx)

4-FISCAL POLICY:GOV’T POLICIES REGARDING TAXEX & SPENDING

HIGHER TAXES LESS Sx (VICE VESA) MORE SUBSIDY 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

Px COST, Py, TECH., #Ps, Pexp, FISCAL POLICY

A CHANG IN THE ABOVE FACTORONLY WILL CAUSE A MOVEMENT ALONG THE SAME (S) CURVE

A CHANGE IN ONE OR ALL OFTHE ABOVE FACTORS ONLY WILL CAUSE SHIFTS IN THE (S) CURV

Qx

Px

0S

S

10

6

500300

A

B

Qx

Px

0

S

S

S1

S1

s2

s1+

-

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 Px 2 4 6 8 10

THIS BECAUSE: QDx 500 400 300 200 100

1- Qs = Qd QSx 100 200 300 400 500 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)

2

4

6

8

10

0100 200 300 400 500

S

S

Qx

PxD

D

Pe

Qe

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)

Pe & Qe INCREASE Pe & Qe DECREASE

D

DS

S

6

300O

4

200

Px

QxD1

D1

6

D

D

D2

D2

0 300

Sx

Sx

8

400 Qx

PX

A-CHANGES (+&-) IN (Dx) , NO CHANGE IN (Sx ):

- INCREASE IN (Dx): - DECREASE IN (Dx)

Pe & Qe INCREASE Pe & Qe DECREASE

6

D

D

D2

D2

0 300

Sx

Sx

8

400

PX

B-CHANGES (+&-) IN (Sx) , NO CHANGE IN (Dx):

- INCREASE IN (Sx): - DECREASE IN (Sx )

Pe DECREASE & Qe INCEASE Pe INCREASE & Qe DECREASE

DS1

DS1

S

S S

S

D

S2

D

S2

6

4

0300 400

Qx

PX PX

Qx0200 300

6

8

C- CHANGES (+&-) IN BOTH (Sx) &AND (Dx):

- INCREASE IN BOTH (Sx)& (Dx): - DECREASE IN BOTH (Sx )&(Dx):

Pe INCREASE & Qe INCEASE Pe NO CHANGE & Qe DECREASEB/C + IN Dx > + Sx B/C - IN Dx = - IN Ax

DS1

DS1

S

S S

S

D

S2

D

S2

6

7

0300 500

Qx

PX PX

Qx0200 300

6

D1

D1

D2

D2

4- GOV’T. INTERVENTION IN MARKETS:

A-PRICE CEILING : B- PRICE FLOOR: CAUSE SHORTAGE (AB) CAUSE SURPLUS(CD)

Qx

Px

D

D S

S

e

0

6

300

4

200 400

PcA B

D

D

S

S

6

8

Px

Qx0300200 400

Pfe

C D

Px

6

4Pc

Px

6

4Pc

0

Px

6

4Pc

300200 4000

Px

6

4Pc

6

8

Px

Pf

CASE STUDY DISCUSSION: RENT CONTROL IN EGYPT

Market Pe = 800 Ceiling price (P)= 500 Black market (P) = 1000

SHORTAGE = 100,000 UNITS

Ceiling price 500

200,0000

D

D S

S

Qx

Px

e

100,000 300,000

Black market price 1000

Market price 800

Black market price 1000

Market price 800

Ceiling price 500

0

Black market price 1000

Market price 800

200,000

D

100,000 300,000

Ceiling price 500

0

Black market price 1000

Market price 800

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)

0

D

S

D

1000

400

1200

D1

S1

Ox

Px

0

1000

1200

Px

1000

1200

Px

1000

1200

Px

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

Chapter (4) - ELASTICITIES (Cont’d)

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

PEDx = THE SIGN IS NORMALLY( - ) , IF :

∞ >PED > 1 PED=1 0<PED< 1 ELASTIC UNITE ELASTIC INELASTIC EX :LUXTURIES(TRIPS) NECESSITIES(MEDICIN)

Q x Q x

Px Px

A-DEMAND ELASTICITES:PED (CONT’D)

-ARC ELASTICITY FORMULA:

PED = THE SIGN NORMALLY( - )

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 .

Qx Q1 + Q2 2

Px P1 + P22

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 = THE SIGN COULD BE :

( + ) IF THE GOOD IS NORMAL OR ( - ) IF THE GOOD IS INFERIOR

3- CROSS PRICE ELASTICITY OF DEMAND (CPED):

CPED = THE SIGN COULD BE :

( - ) IF GOOD x COMPLEMENT GOOD y

( + ) IF GOOD x SUBSTITUTE GOOD y

Qx Qx

I I

Qx

Py

Qx

Py

B-THE PRICE ELSTICITY OF SUPPLY(PES)

PES = THE VALUE COULD TAKE 5 CASES:

1-PES = 0 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

Qsx

Px

Qsx

Px

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:a- an inferior goodb- a substitute for good Rc- a normal goodd- a complement for good Re- both c and d

Equations: Demand ,supply & the Market Equilibrium (Cont’d)

2. If M = $15,000 and PR = $20, the demand function isQx = 680 - 9 Px + 0.006 M – 4 PR

a.

b.

c.

d.

e.

690 9 dP Q

690 9dQ P

680 9dQ P

680 9 dP Q

800 19dQ P

3. If M = $15,000 and PR = $20 and the supply function is , equilibrium price and quantity are, respectively,

a. P = $55 and Q = 195.

b. P = $9 and Q = 609.

c. P = $12 and Q = 200.

d. P = $50 and Q = 170.

e. P = $40 and Q = 250.

30 3sQ P

4. If M = $15,000 and PR = $20 and the supply function is , then, when the price of

the good is $12a. there is a shortage of 516 units of the good.B. there is equilibrium in the market.C. there is a surplus of 60 units of the good.D. the quantities demanded and supplied are

indeterminate.

30 3sQ P

5-If M = $15,000 and = $20 and the supply function is , then, when the price of

the good is $60,

a. there is equilibrium in the market.b. there is a shortage of 180 units of the good.c. there is a surplus of 60 units of the good.d. there is a shortage of 80 units of the good.

30 3sQ P

II- Use the following demand and supply functions to answer the next 3 questions: Demand: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

50 4dQ P

20 2sQ P

2.If the price is $10, there is a a. surplus of 30 units.b. shortage of 30 units.c. surplus of 40 units.d. shortage of 10 units.e. none of the above

3. If the price is $2, there is aa. 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 AnalysisElfiky 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 REGRESS : dependent variable (Demand for x 2002 5.05 3.10 computer Using the income per head as 2003 5.25 3.30 independent variable during the period

2004 5.40 3.65 (2000 – 2006) 2005 5.60 3.902006 5.70 4.102007 5.65 4.15

Variable Coefficient Std Err T-stat CONST -5.20679 0.616404 -8.44704

(I) 1.63750 0.114037 14.3594 No. of Observations = 7

R² = .9763 (adj)= .9716Sum of Sq. Resid. = .260089E-01Std. Error of Reg.= .721234E-01

Durbin-Watson = 2.0012F ( 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. $ 4.62 million b. $ 4.95 million c. $ 4.99 million d. $ 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 parentheses1.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 whena. 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 models1- 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 modelEx. 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 (pp.125,126)Problems: 3,6,8,9,12 (pp.126-129)

Chapter (4)Questions: 3,5,11,13,18 (pp.162,163)Problems: 4,7,8,12,13 (pp.164,165)

Chapter (5)Questions: 1,3,5,7,8,9 (pp.238,239)Problems: 2,4,5,7 (pp.239-242)

Chapter (6)Questions: 5,13,15,18 (pp.282,283)Problems: 4,5,7,11, (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) iscombined with a fixed input (capital) at some points the additionaloutput (i.e., MPL)

K L TPL MPL APL

1 0 - - -1 1 2 2 21 2 6 4 31 3 12 6 4

1 4 20 8 51 5 30 10 61 6 36 6 6

1 7 38 2 5.401 8 38 0 4.751 9 36 -2 4

L

TPL

0

L0

MR

AP

MPAP

Stage I Stage II Stage III

8

Derived Demand & The Optimal Level of Labor

K L TPL MPL APL TRP MRP TLC MLC (TRP-TLC) (MRP-LC)

1 0 0 0 - 0 0 0 0

1 1 2 2 2 20 20 20 20 ( 0 ) 0

1 2 6 4 3 60 40 40 20 (20 ) 20

1 3 12 6 4 120 60 60 20 (60 ) 40

1 4 20 8 5 200 80 80 20 (120) 60

1 5 30 10 6 300 100 100 20 (200) 80

1 6 36 6 6 360 60 120 20 (240) 40

1 7 38 2 5.40 380 20 140 20 (240) 0

1 8 38 0 4.75 380 0 160 20 (220) -20

1 9 36 -2 4 360 -20 180 20 (180) -40

PX = LE 10 wL = LE 20 MRP = MPL × PX TLC = L × W MLC=∆TLC /∆L

A profit maximizing firm operating in a perfectly competitive markets willdemand the number of labor at the point where : MRP = MLC (W)

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 TPL Return to scale: if a firm increase its scale1 1 2 by a certain proportion result in an increase

in 2 2 8 output by a greater proportion, the firm 3 3 16 experiences increasing return to scale (IRTS) , 4 4 24 if output increases by the same proportion , the firm 5 5 30 experiences a constant return to scale (CRTS) ,

and if 6 6 36 output increases by less proportion , the firm7 7 40 experiences a decreasing return to scale (DRTS)

8 8 429 9 45

Measuring Return to scale

1- Output Elasticity (EQ) = % ∆ in Output / % ∆ in all inputs

If: (EQ) > 1 increasing return to scale (IRTS),

(EQ) = 1 Constant return to scale (CRTS) ,

(EQ) < 1 Decreasing return to scale (DRTS)

2- hQ = f ( mL , mK)

If: h > m increasing return to scale (IRTS) ,

h = m Constant return to scale (CRTS) ,

h < m decreasing return to scale (DRTS)

Q

L,Ko

o

L,kQ

L,k

o

Q

IRTS

CRTS

DRTS

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 - cL²Q = a L ( power function)log Q = log a + b log L

2- Cobb-Douglas production function.

Q = a L K It assumes CRTS, (b +1-b =1)

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 < 11- MPL = b Q / L 2- MPK = c Q / K , Decreasing Marginal Product.2- The function can be converted to linear function using logarithms.

b 1- b

b c

b

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 curvesmay 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 downwardand 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 – 0.5L³a- 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 40- hour 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 .

1- Q = 75 L K 2- Q = 75 L K C

3- Q = 75 L K 4- Q = 100 + 50 L + 50 K

5- Q = 50 L + 50 K 6- Q = 50 L + 50 K + 50 LK

0.25 0.75 0.15 0.40 0.45

0.70 0.60

2 2

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 = ∆ TC/ ∆Q

0 100 0 100 ∞ - ∞ 01 100 100 200 100 100 200 1002 180 280 50 90 140 80 3 240 340 33.3 80 113..3 604 280 380 25 70 95 405 340 440 20 68 88 60 6 420 520 16.7 70 86.7 807 520 620 14.3 74.3 88.6 1008 640 740 12.5 80 92.5 1209 780 880 11.1 86.7 97.8 14010 940 1040 10 94 1004 160

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 tothe sequence of short-term SATC curves is a long run average total cost curve, LATC. It is

also referredto 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 long-run "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 theLATC curve. Empirical data for a variety of industries suggests that some of the other shapesmay 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 theCompany attempts to build larger-scaleplants. These long-run cost conditions areconducive to the development of a market populated by a rather larger number of smaller firms (or firms with a multiplicityof small-capacity plants).Shape(2) depicts long-run cost conditions characterized by the progressive, though gradual, exploitation ofeconomies of scale which never seem to reach exhaustion. A market characterized by these longRun cost conditions will tend to be populated by a rather smaller number of larger-sized firms, andperhaps ever fewer firms as time passes and competition ensues. Economists classify such amarket 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 minorscale economies as firms grew from very small size at start-up, and could eventually reach a rangeof diseconomies of large scale if existing firms Grow much larger. But the salient characteristic ofLATC curve is that it is flat-bottomed, i.e., there are no significant scale economies to be exploited ordiseconomies 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 CostsWhether 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.

(h) Due to the absence of successful product differentiation, there is little or no point in advertising the firm's product characteristics or its price.

(i) Supernormal and subnormal profits in the competitive market, although they may occur, are fleeting; profits tend toward the economically normal level of opportunity cost (what the firm can realize in the next best alternative application of its resources).

A Firm in a Purely Competitive Industry

The general principle that govern output decision making when the goal isto maximize profit is to: P(MR) =MC

increase Q if MR > MC, but todecrease Q if , MR < MC.MR is easy to identify in thepurely 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 equationsprobably required a costly datacollection and model specificationand estimation process.Incremental cost can be computed more cheaply from data for twodifferent output levels, but it is onlyan approximation to truemarginal cost

The Operate vs. Shut-Down Criterion in the Short Run

It may be rational to shut-down operations in the short-run 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 Q³TC = 100 + 600 Q – 3 Q² TC = 100 + 600 Q1- 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.II-The demand and cost function for a company are estimated to be

as follows: p = 170 – 5QTC = 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 greaterthan AVC by the average fixed cost ateach level of output. Under thecircumstances illustrated by P1 and TR1, firms presently operating in the market can cover all of their variable and fixedcosts 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 ofincreasing 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.