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Economic

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.

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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| | | | | ?=(r – r )2 p ?=21,000,000 ?=4582. 5756 (c) Coefficient of variation v=? r v=4582. 75617,000 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=n?? xy-?? x? yn?? x2-(?? x)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=?? yn=75.

67=10. 8| x=?? xn=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 : ? =0Ha : ?? 0 Se =?? y2-a?? y-b?? xyn -2 =818. 08-6. 464875.

6- 0. 5962(552. 34)7 -2 =818. 08-488. 74- 329. 315 =0. 08487 Sb =Se2?? x2 –(?? x)2n =0.

084872374. 51 –(50. 9)27 =0. 00720244. 3943 =0. 04049 t=b- ? Sb =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. 763 @ 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.