ECONOMICS FOR ECONOMIC TUTOR

Week 3 Assignment Study Guide

Q1. Transportation Business

Sample Example: Chapter 5 Question 1

Donald’s Oyster & Pearl Company:

Divers (V)

Oysters (TP)

V

TP

MP = TP/V

AP = TP/V

3

15

5.00

5

32

2

17

8.5

6.40

6

38

1

6

6

6.33

9

56

3

18

6

6.22

12

74

3

18

6

6.17

14

80

2

6

3

5.71

15

78

1

-2

-2

5.20

17

76

2

-2

-1

4.47

a. Increasing returns (rising MP) appear to prevail up to 5 divers; constant returns appear to prevail from 6-12 divers; and diminishing returns prevail after 12 divers, with negative returns after 14 divers. (Note that missing variables such as weather and tides might also influence the productivity of the divers).

b. Output per diver (Average Product) is apparently highest at 5 divers.

c. Assuming a constant yield of pearls per kilogram of oysters, the Marginal Cost of oysters and pearls are each minimized in the range of 6-12 diverse (MC is constant since MP is constant).

Q2. Average Variable Cost, Marginal Cost, Incremental Cost, and Contribution

Sample Example: Chapter 6 Question 2

a. To derive the AVC curve for Rakita Racquets we first array the data in ascending order of output levels and then calculate AVC = TVC/Q at each output level, as shown below.

b. Gradient analysis finds the ΔTVC values for each change in Quantity (∆Q) and the MC estimate at the middle of each Quantity interval is ∆TVC/∆Q. Note that the MC values do not rise smoothly but contain several reversals most likely due to measurement errors. The MC curve is estimated by drawing a smooth line across these data points – it will fall at first and later rise to cross the minimum point of the AVC curve (at about 38,000 units)

TVC

Q

AVC

MC

Mar

19,520

925

21.103

Feb

22,160

1,525

14.531

4.40

Apr

25,960

1,925

13.486

9.50

Jan

27,860

2,450

11.371

3.62

Dec

31,850

2,850

11.175

9.98

May

32,980

3,500

9.423

1.74

Nov

33,510

4,050

8.274

0.96

Jun

35,490

4,500

7.887

4.40

Oct

37,480

5,325

7.038

2.41

July

42,470

5,575

7.618

19.96

Aug

48,980

6,300

7.775

8.98

Sept

52,530

6,525

8.051

15.78

c. Incremental costs will be the change in TVC over the interval of 3,500 to 5,000 units. The sketched line of best fit to the AVC data indicates that AVC is about $9.40 at 3,500 units and about $7.10 at 5,000 units. Thus TVC is estimated to be about $32,900 and $35,500 respectively, and thus the estimated incremental cost is $2,600. (d) Contribution is equal to incremental revenue ($15 x 5,000 = $7,500) minus incremental costs ($2,600) which equals $4,900.

Assignment

Please, complete the following

 

two applied problems in a Word or Excel document. Show all your calculations and explain your results. Submit your assignment in the drop box by using the Assignment Submission button.

1. Jennifer Trucking Company operates a large rig transportation business in Texas that transports locally grown vegetables to San Diego, California. The company owns 5 large rigs and hires local drivers paid fixed salaries monthly, regardless of the number of trips or tons of cargo that each driver transports each month. The below table presents details about the number of drivers and the total cargo transported by the company at different staff levels.

Drivers employed

Total Cargo Transported (tons)

1
2
3
4
5
6
7
8

5
12
21
32
40
46
51
50

 

a.       Which inputs are fixed and which are variable in the production function of Jennifer Trucking Company? Over what ranges do there appear to be increasing, constant and/or diminishing returns to the number of drivers employed?

b.      What number of drivers appears to be most efficient in terms of output per driver?

c.       What number of drivers appears to minimize the marginal cost of transportation assuming that all drivers are paid the same salary?

 

1.    2.   Over the past 12 months the Four Winds Novelty Company firm has recorded its internet sales (equals monthly output levels) and its monthly total variable costs (TVC) for a particular novelty item as shown in the following table. Sales have grown over this period with relatively few shocks due to uncontrollable weather, political and sporting events. This online retailer carries no inventories; when it receives a pre-paid on-line order from a customer, it simply buys the product from a supplier and ships it out to the customer.

Sales = Output

TVC ($)

102,813

176,163

196,121

222,885

226,356

296,416

378,446

450,666

579,696

607,082

624,680

636,133

 

201,953

340,608

377,940

432,863

441,714

629,267

867,596

1,103,807

1,701,125

1,917,861

2,195,352

2,479,195

 

a.       Using regression analysis, find an equation that best fits the data to represent the TVC function.

b.      At what sales/output level will marginal costs (MC) reach a minimum?

c.       Estimate the value of TVC for sales/output level 250,000 units, and calculate the 95% confidence interval for your estimate.