Managerial Economics: Calculation Example Essay

Managerial Economics: Calculation Example Essay

1. The demand for MICHTEC’s products is related to the state of the economy. If the economy is expanding next year (an above-normal growth in GDP), the company expects sales to be $90 million. If a recession occurs next year (a decline in GDP), sales are expected to be $75 million. If next year is normal (a moderate growth in GDP), sales are expected to be $85 million. MUCHTEC’s economists estimate the chances that the economy will be either expanding, normal, or in a recession next year at 0.2, 0.5, and 0.3, respectively.

  1. Compute expected annual sales.

Expected Annual Sales (in mil $)

Probability of Growth Rate (in %)

Sales (in mil $)

expanding

90

0.20

18

normal

85

0.50

42.5

recession

75

0.30

22.5

TOTAL EXPECTED

83

ANNUAL SALES

  1. Compute the standard deviation of annual sales.

Scenario

Expected Annual Sales (in mil $)

List of deviations

(Mean – Sales)

Squares of deviations

expanding

90

6.666667

44.44444

normal

85

1.666667

2.777778

recession

75

-8.33333

69.44444

Mean

83.33333

58.33333

Standard deviation

7.63763

Formula : square root of (90 – 83.33)2 + (85-83.33) 2 + (75-83.33) 2

Number of observations – 1

= 44.44 + 2.78 + 69. 44

2

= 58.333

Standard deviation = 7.6373

  1. Compute the coefficient of variation of annual sales.

7.6373

83.33

Coefficient of variation =.0916

2. Two goods have a cross price elasticity of +1.2.

  1. Would you describe these goods as substitutes or complements?

These goods are substitutes. An increase in the price of a good, say a hotdog, induces people to buy more of hamburgers, a substitute good instead. Because the price of hotdogs and the quantity of hamburgers demanded move in the same direction, the cross-price elasticity is positive. Conversely, complements are goods that are used together, hence, increase in the price of good A will definitely decrease demand for good B resulting to a negative cross price elasticity.

  1. If the price of one of the goods increases by 5%, what will happen to the demand for the other product, holding constant the effects of all other factors?

If the price of good A increases by 5%, the demand for good A decreases while demand for good B increases assuming that goods A and B are substitutes. The reverse happens with complement goods. If the price of good A increases by 5%, the demand for A decreases and the demand for good B decreases also.

3. The Pilot Pen Company has decided to use 15 test markets to examine the sensitivity of demand for its new product to various prices, as shown in the following table.

Advertising effort was identical in each market. Each market had approximately the same level of business activity and population.

Test Market

Price Charged

Quantity Sold (Thousands of pens) ©

Total Revenue

1

0.5

20

10.00

2

0.5

21

10.50

3

0.55

19

10.45

4

0.55

19.5

10.73

5

0.6

20.5

12.30

6

0.6

19

11.40

7

0.65

16

10.40

8

0.65

15

9.75

9

0.7

14.5

10.15

10

0.7

15.5

10.85

11

0.8

13

10.40

12

0.8

14

11.20

13

0.9

11.5

10.35

14

0.9

11

9.90

15

0.4

17

6.80

  1. Using a linear regression model, estimate the demand function for Pilot’s new pen.

Test Market

Price Charged X

Quantity Sold (Thousands of pens) Y

Total Revenue

(X-X bar)

(Y-Ybar)

(X-X bar)2

(X-X bar)* (Y-Ybar)

1

0.5

20

10.00

-0.15333

3.566667

0.023511

-0.54689

2

0.5

21

10.50

-0.15333

4.566667

0.023511

-0.70022

3

0.55

19

10.45

-0.10333

2.566667

0.010678

-0.26522

4

0.55

19.5

10.73

-0.10333

3.066667

0.010678

-0.31689

5

0.6

20.5

12.30

-0.05333

4.066667

0.002844

-0.21689

6

0.6

19

11.40

-0.05333

2.566667

0.002844

-0.13689

7

0.65

16

10.40

-0.00333

-0.43333

1.11E-05

0.001444

8

0.65

15

9.75

-0.00333

-1.43333

1.11E-05

0.004778

9

0.7

14.5

10.15

0.046667

-1.93333

0.002178

-0.09022

10

0.7

15.5

10.85

0.046667

-0.93333

0.002178

-0.04356

11

0.8

13

10.40

0.146667

-3.43333

0.021511

-0.50356

12

0.8

14

11.20

0.146667

-2.43333

0.021511

-0.35689

13

0.9

11.5

10.35

0.246667

-4.93333

0.060844

-1.21689

14

0.9

11

9.90

0.246667

-5.43333

0.060844

-1.34022

15

0.4

17

6.80

-0.25333

0.566667

0.064178

-0.14356

sum

9.8

246.5

0.307333

-5.87167

average

0.653333

16.433333

b =

-5.8716667

0.3073333

-19.105206

a=

16.433

– (-5.87167*.6533)

16.433

3.836156

12.597178

Sales = 12.597 – 19.105* Price

  1. Evaluate this model by computing the coefficient of determination and by performing a t-test of the significance of the price variable.

The coefficients of determination are: = 12.597 – 19.105* Price

T-Test:

  1. What is the price elasticity of demand at a price of 50 cents?

Price elasticity = percentage change in quantity demanded

Percentage change in price

= ( 21-20)

(21+20)/2

(.5-.5)

(.5+.5)/2

= not possible to calculate since percentage change in price is equivalent to 0

4. The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed:

Crew Size (Number of Workers)

Amount of Fish Caught Per Week (Hundreds of lbs)

Marginal Product where: MP labor = new TP-old TP / new L

Average Product AP labor = TP/L

2

3

3

6

3

1

4

11

5

1.25

5

19

8

1.60

6

24

5

0.83

7

28

4

0.57

8

31

3

0.38

9

33

2

0.22

10

34

1

0.10

11

34

0

0

12

33

-1

-0.083

  1. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?

Increasing returns – up to 5th worker

Constant returns – at 3 workers where AP = 1

Decreasing returns– starting from the 6th worker

Negative returns – starting at 12th worker

  1. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?

Total product (TP) is maximum, at 34 hundreds of pounds of fish with 11 workers and Marginal Product (MP) is zero.

  1. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per person?

At 5 workers, the Average Product (AP) of each worker is at maximum, at 1.60 hundreds of pounds of fish per worker.

  1. Suppose the owner of the trawler can sell all the fish caught for $75 per 100 pounds and can hire as many crew members as desired by paying them $150 per week. Assuming that the owner of the trawler is interested in maximizing profit, determine the optimal crew size.

Crew Size (Number of Workers) Labor (L)

Cost of Labor at $150 per laborer/per week

Amount of Fish Caught Per Week (Hundreds of lbs) Total Product (TP) or Total Revenue

Price of Fish per 100 pounds = $75

Total Profit = Total Revenues – Total Cost

2

300

3

225

-75

3

450

6

450

0

4

600

11

825

225

5

750

19

1425

675

6

900

24

1800

900

7

1050

28

2100

1050

8

1200

31

2325

1125

9

1350

33

2475

1125

10

1500

34

2550

1050

11

1650

34

2550

900

12

1800

33

2475

675

The optimal crew size is 9 where Total Profit is $1125.00

5. Consider the following short-run production function (where L = variable input, Q=Output)

Q =10L-0.5L2.. Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs as $20 per unit.

  1. Determine the marginal revenue production function.

Marginal revenue production function:

Labor

Quantity

Total Revenue (P x Q) Price: $10/unit

Marginal Revenue

1

9.5

95

2

18

180

85

3

25.5

255

75

4

32

320

65

5

37.5

375

55

6

42

420

45

7

45.5

455

35

8

48

480

25

9

49.5

495

15

10

50

500

5

  1. Determine the marginal factor cost function.

Labor

Quantity

Cost of Labor; $20 per unit of labor

Marginal Cost

1

9.5

20

2

18

40

20

3

25.5

60

20

4

40

80

20

5

50

100

20

6

60

120

20

7

70

140

20

8

80

160

20

9

90

180

20

10

100

200

20

  1. Determine the optimal value of L, given that the objective is to maximize profits.

Labor

Quantity

Total Revenue (P x Q) Price: $10/unit

Marginal Revenue

Cost of Labor; $20 per unit of labor

Marginal Cost

Profit

1

9.5

0

0

2

18

95

95

20

20

75

3

25.5

180

85

40

20

140

4

40

255

75

60

20

195

5

50

320

65

80

20

240

6

60

375

55

100

20

275

7

70

420

45

120

20

300

8

80

455

35

140

20

315

9

90

480

25

160

20

320

10

100

495

15

180

20

315

Optimal value of L is at 9 units because adding another worker causes profit to decline.

6. Mary Graham worked as a real estate agent for Piedmont Properties for 15 years. Her annual income is approximately $100,000 per year. Mary is considering establishing her own real estate agency. She expects to generate revenue during the first year of $2 million. Salaries paid to her employees are expected to total $1.5 million. Operating expenses (i.e., rent, supplies, and utility services) are expected to total $250,000. To begin the business, Mary must borrow $500,000 from her bank at an interest rate of 15 percent. Equipment will cost Mary $50,000. At the end of one year, the value of this equipment will be $30,000, even though the depreciation expense for tax purposes is only $5,000 during the first year.

a. Determine the (pretax) accounting profit for this venture.

Accounting profit is the total revenue minus total of all explicit costs

Accounting Profit = revenue – (wages + operating expenses + interest rate + depreciation expense)

Accounting profit = $2,000,000 – ($1,500,000 + $250,000 + $7,500 + $ 5,000)

Accounting profit = $2.000,000 – $ 1,762,500

Accounting profit = $237,500

b. Determine the (pretax) economic profit for this venture.

Economic profit = revenue – (Mary’s wages if she worked + wages she pays+ operating expenses + interest rate + actual depreciation)

Economic profit = $2,000,000 – ($100,000 + $1,500,000 + $250,000 + $7,500 + $20,000)

Economic profit = $2,000,000 – $1,887,500

Economic Profit = $112,500

c. Which of the cost for this firm are explicit and which are implicit?

Explicit costs of Mary’s firm include wages, operating expenses, interest rate and depreciation expense. Implicit costs, meanwhile, are the firms opportunity costs such as Mary’s wages if she opted to work instead of set up her own firm, interest rates on the loan she borrowed if she invested the funds somewhere else and earned her money instead plus the actual depreciation of the equipment she purchased.

7. The ARA Railroad owns a piece of land along one of its right-of-ways. The land originally cost ARA $100,000. ARA is considering building a new maintenance facility on this land. ARA determined that the proposal to build the new facility is acceptable if the original cost of the land is used in the analysis, but the proposal does not meet the railroad’s project acceptance criteria if the land cost is above $500,000. An investor has recently offered ARA $1 million for the land. Should ARA build the maintenance facility at this location?

Book Value : $100,000

Market Value : $1,000,000

Profit = Market Value – Book Value

Profit = $900,000

Therefore: It is much more profitable to sell the land rather than build a maintenance facility and value the land at $500,000. Note that maintenance facilities are not profit-generating facilities.

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