Economic

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QUESTION 1

(a) Expected Selling Price
Price (r)| Probability (p)| Expected Selling Price |
| | r= r x p |
10,000| 0.2| 2000|
15,000| 0.3| 4500|
20,000| 0.4| 8000|
25,000| 0.1| 2500|
| | 17000|
| | |
| | |
(b) Standard Deviation
Price (r)| Probability (p)| (r - r )2 p|
 |  |  |
10,000| 0.2| 9,800,000|
15,000| 0.3| 1,200,000|
20,000| 0.4| 3,600,000|
25,000| 0.1| 6,400,000|
 |  | 21,000,000|
| | |
|
σ=(r - r )2 p
σ=21,000,000
σ=4582.5756

(c) Coefficient of variation

v=σr

v=4582.575617,000

v=0.26956

QUESTION 2

(d) Output level of Maximize profits
MR=MC
Q=8

(e) Total Profit at profit maximizing output level
Total Profit = Total Revenue – Total Cost
= 216 – 124
= 92

QUESTION 3

TC = 20 + 5Q + Q2
Q = 25 - P
P = 25 – Q

(a) Total Profit = Total Revenue – Total Cost
= ( P x Q ) – TC
= ( 25 – Q ) (Q) – ( 20 + 5Q + Q2 )
= 25Q – Q2 – 20- 5Q – Q2
= - 2Q2 + 20Q – 20

(b)
TR = 25Q - Q2MR=dTRdQ=25-2Q| TC = 20 + 5Q + Q2MC=dTCdQ=5+2Q|

MR=MC
25-2Q =5+2Q
-2Q-2Q=5-25
-4Q= -20
Q=5

(c)
Total Profit = - 2Q2 + 20Q – 20= - 2(52) + 20(5) – 20 = -50 +100-20 = 30 | Selling Price = 25 – Q = 25 – 5 = 20 | (d)
TP = - 2Q2 + 20Q – 25
dTPdQ=-4Q+20 dTPdQ=0 -4Q+20=0 -4Q= -20 Q=5| Total Profit = - 2Q2 + 20Q – 25= - 2(52) + 20(5) – 25 = -50 +100-25 = 25 | Even fixed cost change, output still 5.

(e)
TR = 25Q - Q2MR=dTRdQ=25-2Q| TC = 20 + 5Q + Q2MC=dTCdQ=5+2Q| QUESTION 4
(a) Ex=Q2-Q1P2-P1 ×P2 + P1Q2 + Q1

-2.2=10,000-8,000P2-2.98 × P2 +2.98110,000 +8,000

-2.2=2,000 (P2 +2.981)18,000 (P2-2.98 )

-2.2=2,000P2 +5,96018,000 P2-53,640 )

QUESTION 5
(a)

(b) Estimated Regression

b=nƩƩxy-ƩƩxƩynƩƩx2-(ƩƩx)2
=7552.34- 50.9(75.6)7374.51- (50.9)2 =3866.33-3848.042621.57-2590.81
=18.3430.76
=0.5962

y=ƩƩyn=75.67=10.8| x=ƩƩxn=50.97=7.2714|

a=y-b x
= 10.8 – 0.5962 (7.2714)
= 10.8 – 4.3352
= 6.4648

Y= 6.4648 + 0.5962X

(c) Hypothesis Testing

H0 : β=0
Ha : β≠0

Se =ƩƩy2-aƩƩy-bƩƩxyn -2
=818.08-6.464875.6- 0.5962(552.34)7 -2
=818.08-488.74- 329.315
=0.08487

Sb =Se2ƩƩx2 –(ƩƩx)2n
=0.084872374.51 –(50.9)27
=0.00720244.3943
=0.04049

t=b- βSb
=0.5962-00.04049
=14.7264

t0.052 , n-2=2.571

From the t-distribution, the value is 2.571. since the calculated t-value (14.7264) is greater than value from the table, we reject null hypothesis that there is no relationship between the variable.

(d) Proportion of total variation

r2=SSRSST= (y - y )2 (y - y )2

= 1.562081.6

=0.9763 @ 97.63%

The regression equation “explains” 97.63% of variation in the company sales.

(e)

F=SSRSST= (y - y )2 (y - y )2 n-2

= 1.562080.037897-2

= 206.1335

The value of (F0.05 , 1,5) from the F-distribution 6.61. Since the calculated F-value (206.1335) is greater than value from the table, we reject null hypothesis that there is no relationship between the no of construction permits issued and sales.

(f) Y= 6.4648 + 0.5962X
Y= 6.4648 + 0.5962(8.00)

Estimated sales for Phoenix Lumber Company in 1998 would be 11.234 million.
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