Transcript
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 Mesbahimahdi.mesbahi@gmail.com
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