Production function economic

ManagerialEconomics

Term ProjectDec. 2011

Managerial Economics (GSM5000)

GROUP MEMBERS:

M. Mahdi Mesbahi (GM04701)

Majid Asadi (GM04711)

Questions

Observations:

Q(kg) Total Cost

Labor per

team

Fruit bunch

Instru-ment

89 sampleDivision 1

Division 2Production Function

Cost Function

Questions

1. Estimate the following production functions:

• Linear function

• Double log (Cobb-Douglas function)?2. Estimate the following total cost functions:

• Quadratic Function

• Cubic Function ?

Questions

3. Under a competitive market, the price is

RM 100/kg, determine the functions and plot:

• Revenue function

• Cost function

• Profit function

Questions

4. At what quantity production is profit

maximized and what is the maximum profit

(Competitive and Monopoly Markets)

Production Function

Production Function

Capital&

Labor

Production

Capital&

Labor

input output

Y X

Production Function

Q(kg) D.V.(areas)

Labor per

team

Fruit bunch

Instru-ment

Production Function

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

1600

Total Cost

Total Cost

Q=2000L=9F.B=8I=7TC=27

AverageQ=252L=84F.B=77I=5TC=537

Production Function

Q=-59.808+0.627L+1.61FB+17.282I+42.017DV

SUMMARY OUTPUT LINEAR

Regression Statistics R Square 0.527 F 23.085

Coefficients t StatIntercept -59.808 -1.557Labor per team 0.627 2.120Fruit bunch 1.610 6.087Instrument 17.282 2.440DV 42.017 1.534

Ln(Q)=-0.59+0.55Ln(L)+0.68Ln(FB)+0.28Ln(I)+0.22DV

SUMMARY OUTPUT LOG

Regression Statistics R Square 0.692 F 46.542

Coefficients t StatIntercept -0.590 -1.176Ln(L) 0.547 4.400Ln(FB) 0.677 7.113Ln(I) 0.283 1.763DV 0.215 1.708

Area 1: DV=1

Q= 0.69L0.55FB 0.68 I0.28

Area 2: DV=0

Q= 0.55L0.55FB 0.68 I0.28

Cost Function

Cost

Production

Cost Function

inputoutput

Y X

Cost Function

TC D.V.(areas)

Q

Cost Function

TC=211.571+2.285Q-0.003Q2+38.709DV

TC=158.186+3.174Q-0.006Q2+0.000003Q3+38.709DV

SUMMARY OUTPUT QUADRATIC

Regression Statistics R Square 0.169 F 5.687

Coefficients t StatIntercept 211.571 2.307Q 2.285 3.843Q2 -0.003 -3.257DV 38.709 0.526

SUMMARY OUTPUT CUBIC

Regression Statistics R Square 0.175 F 4.398

Coefficients t StatIntercept 158.186 1.380Q 3.174 2.467Q2 -0.006 -1.476Q3 0.000003 0.780DV 36.298 0.492

Area 1: DV=1

TC=250.28+2.28Q-0.003Q2

Area 2: DV=0

TC=211.57+2.28Q-0.003Q2

Profit Function

Profit Function

TR=P.Q

Area 1:

TC=250.28+2.28Q-0.003Q2

Area 2:

TC=211.57+2.28Q-0.003Q2

P=0.003Q2+97.72Q-250.28

P=TR-TC

P=0.003Q2+97.72Q-211.57

TR=100Q

Profit Function

0 100 200 300 400 500 600 700 800 9000

10000

20000

30000

40000

50000

60000

70000

80000

90000

TR TC Profit

Suggestion

Cost Function

0 100 200 300 400 500 600 700 800 9000

200

400

600

800

1000

1200

1400

1600

1800

Total Cost Polynomial (Total Cost) Proposed TC Quad

(400,1600)

(300,900)

(200,370)

(0,12)

TC=0.0109Q2-0.39Q+12

Cost Function

0 100 200 300 400 500 600 700 800 9000

200400600800

10001200140016001800

Total CostProposed TC CubicPolynomial (Proposed TC Cubic)

(400,1600)

(300,900)

(200,500)

(0,12)

TC= 0.0000245Q3-0.00705Q2+2.87Q+12

Cost Function

TC=0.0109Q2-0.39Q+12RMSE=1695

TC= 0.0000245Q3-0.00705Q2+2.87Q+12RMSE=3182

New Assumption

Price of the production under the competitive

market is: RM 10/kg

Functions Graph

0 200 400 600 800 1000 1200

-4000

-2000

0

2000

4000

6000

8000

10000

12000

14000

TR Proposed TC Qaud Profit

Q (Kg)

TR, T

C, P

(RM

)

477

Under competitive market

Under competitive market

0 300 600 9000

2

4

6

8

10

12

14

16

18

MR Competition MC

Profit is maximum when

MC=MR=P

Profit is maximum at Q=477 kg

P=Q.P-TC

=(477*10)-2305

=4770-2305=2465

477

Another Assumption

Demand function under the monopoly market is:

P=30-0.05Q

Under monopoly market

Profit is maximum when

MC=MR

Profit is maximum at Q=250 kg

P=Q.P-TC

=(250*17.5)-596

=4770-596=3779

3779 > 2465

0 500 1000 15000

5

10

15

20

25

30

35

Demand MR MonopolyMC

250

17.5

Thank You

Power Point Created by:

Mahdi [email protected]

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