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 abovenormal 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.

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

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 }+ (8583.33)^{ 2} + (7583.33)^{ 2}
Number of observations – 1
= √ 44.44 + 2.78 + 69. 44
2
= √58.333
Standard deviation = 7.6373

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.

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 crossprice 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.

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 

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 
(XX bar) 
(YYbar) 
(XX bar)^{2} 
(XX bar)* (YYbar) 
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 
1.11E05 
0.001444 
8 
0.65 
15 
9.75 
0.00333 
1.43333 
1.11E05 
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 


Evaluate this model by computing the coefficient of determination and by performing a ttest of the significance of the price variable.
The coefficients of determination are: = 12.597 – 19.105* Price
TTest:

What is the price elasticity of demand at a price of 50 cents?
Price elasticity = percentage change in quantity demanded
Percentage change in price
= ( 2120)
(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 TPold 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 

Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?
Increasing returns – up to 5^{th} worker
Constant returns – at 3 workers where AP = 1
Decreasing returns– starting from the 6^{th} worker
Negative returns – starting at 12^{th} worker

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.

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.

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 shortrun production function (where L = variable input, Q=Output)
Q =10L0.5L^{2.. } 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.

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 

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 

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 rightofways. 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 profitgenerating facilities.