ECON 625 Managerial Economics Problem Set 3

1)            Questions 1 through 5 are based on the following scenario (adapted from Chapter 5 demand estimation question number 3, p.163)

The maker of a leading brand of low-calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:

Q = -5,200 – 42P + 20Px + 5.2l + 0.20A + 0.25M

       (2.002)  (17.5)  (6.2)   (2.5)   (0.09)   (0.21)

R2 = 0.55  n = 26   F = 4.88

Assume the following values for the independent variables:

Q = Quantity sold per month

P (in cents) = Price of the product = 500

Px (in cents) = Price of leading competitor’s product = 600

I (in dollars) = Per capita income of the standard metropolitan statistical area (SMSA) in which the supermarket is located = 5,500

A (in dollars) = Monthly advertising expenditure = 10,000

M = Number of microwave ovens sold in the SMSA in which the supermarket is located = 5,000

Calculate the quantity using the given values for the independent variables.

2)            Refer to question 1. Calculate the price elasticity of demand. Hint: Use the point elasticity method described on page 72. A numeric example is demonstrated in the second paragraph on that page.

3)            Based on the price elasticity of demand, do you think that this firm should cut its price to increase its market share?

No, demand is inelastic so cutting price would reduce revenue.

No, demand is elastic so cutting price would reduce revenue.

Yes, demand is inelastic so cutting price would increase revenue.

**Yes, demand is elastic so cutting price would increase revenue.

4)            Using the information in question 1, compute the income elasticity.

5)            Based on the price elasticity of income, do you think that this company would be extremely concerned about the impact of a recession on its sales?

Yes, income elasticity is relatively high, so a recession (with lower income) would likely reduce sales.

Yes, income elasticity is relatively low, so a recession (with lower income) would likely reduce sales.

No, income elasticity is relatively high, so a recession would not have a large impact on sales.

No, income elasticity is relatively low, so a recession would not have a large impact on sales.

6)            What proportion of the variation in sales is explained by the independent variables in question 1?

7)            Office Enterprises (OE) produces a line of metal office file cabinets. The company’s economist, having investigated a large number of past data, has established the following equation of demand for these cabinets:

Q = 10,000 + 60B – 100P + 50Cwhere

            Q = Annual number of cabinets sold

            B = Index of nonresidential construction

            P = Average price per cabinet charged by OE

            C = Average price per cabinet charged by OE’s closest competitor

It is expected that next year’s nonresidential construction index will stand at 160, OE’s average price will be $40, and the competitor’s average price will be $35.

Forecast annual sales. Enter your response as a whole number without the dollar sign.

8)            What will be the new sales forecast if the competitor lowers its price to $32?

9)            What will be the new sales forecast if OE reacts to the decrease mentioned in the previous question by lowering its price to $37? (The competitor’s price will now be $32 and the firm’s own price will be $37.)

10)         If the index forecast was wrong, and it turns out to be only 140 next year, what will be OE’s projected sales assuming the original price information of P = $40 and C = $35? Enter your answer as whole numbers.

11)         The Ocean Pacific fleet has just decided to use a pole-and-line method of fishing instead of gill netting to catch tuna. The latter method involves the use of miles of nets strung out across the ocean and therefore entraps other sea creatures besides tuna (e.g. porpoises, sea turtles). Concern for endangered species was one reason for this decision, but perhaps more important was the fact that the major tuna canneries in the United States will no longer accept tuna caught by gill netting.Ocean Pacific decided to conduct a series of experiments to determine the amount of tuna that could be caught with different crew sizes. The results of these experiments follow.

Number of Fishermen

Daily Tuna Catch (lb)

0

0

1

50

2

110

3

300

4

450

5

590

6

665

7

700

8

725

9

710

At what point (what number of fishermen) does diminishing returns occur?

12)         Refer to the previous question. Indicate the number of fishermen at the points that delineate the three stages of production. Enter your answers as whole numbers.

13)         Refer to question 11. Suppose the market price of tuna is $3.50/pound. How many fishermen should the company use if the daily wage rate is $100?

14)         Refer to question 11. a glut in the market for tuna causes the price to fall to $2.75/pound. At this new price, how many fishermen should the company now use if the daily wage rate remains at $100?

15)         Refer to question 11. Suppose the price of tuna rises to $5.00/pound. At this new price, how many fishermen should the company now use if the daily wage rate remains at $100?

16)         The owner of a small car rental service is trying to decide on the appropriate numbers of vehicles and mechanics to use in the business for the current level of operations. He recognizes that his choice represents a trade-off between the two resources. His past experience indicates that this trade-off is as follows:

Vehicles

Mechanics

100

2.5 (includes part-time)

70

5

50

10

40

15

35

25

32

35

If the annual leasing cost per vehicle is $6000 & the annual salary per mechanic is $25,000. What combination of vehicles & mechanics should he employ?

17)         An American company that sells consumer electronics products has manufacturing facilities in Mexico, Taiwan, and Canada. The average hourly wage, output, and annual overhead cost for each site are as follows:

Mexico

Taiwan

Canada

Hourly Wage Rate

$1.50

$3.00

$6.00

Output per Person

10

18

20

Fixed Overhead Cost

$150,000

$90,000

$110,000

If we use output per person as a proxy for marginal product, what is output/wage rate for each country?

18)         Which location has the highest MP per dollar?

Mexico

Taiwan

Canada

Cannot determine with the information available.