Assignment 5

Consulting Project – Estimating Industry Demand for Fresh Market Carrots

The consulting projects, assigned in this course, are complex situations relating to economics for decision making and strategic management. The projects expose learners to the formats that they might face in actual work situations. It is a method of applying theory to sound practical real world applications. Each selected consulting opportunity provides a description of a problem situation taken from a specific company. The purpose is to augment the course content with applications that enable the CalSouthern Learner to apply text materials to a problem and solve that application problem using Learner selected methods and procedures.

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There are no exact answers or perfect solutions. Indeed, each recommended solution and justification can and is usually different comparatively amongst a group of respondents. The solution must fit the project and must be vigorously supported. You should give a detailed summary of each of the project scenarios and complete all of the questions.

Complete and submit Consulting Project One. This can be found in the Resources Section of the Syllabi under Additional Resources.

Your responses must be complete, using terminology and concepts presented in the primary textbook as well as supplementary resources. Please double-space, use 12 point font, with one inch margins. Be sure to cite your resources and provide the references using APA format. Remember to reference all work cited or quoted by the text authors. Note: This includes your textbook.

Assignment Outcomes

Analyze and determine the relationship between price elasticity and demand.

CONSULTING PROJECT

Estimation and Analysis of Demand for Fast Food Meals

You work for PriceWatermanCoopers as a market analyst. PWC has been hired by the owner of two

Burger King restaurants located in a suburban Atlanta market area to study the demand for its basic

hamburger meal package–referred to as “Combination 1″ on its menus. The two restaurants face competition

in the Atlanta suburb from five other hamburger restaurants (three MacDonald’s and two Wendy’s

restaurants) and three other restaurants serving “drive-through” fast food (a Taco Bell, a Kentucky Fried

Chicken, and a small family-owned Chinese restaurant).

The owner of the two Burger King restaurants provides PWC with the data shown in Table 1. Q is the

total number of Combination 1 meals sold at both locations during each week in 1998. P is the average price

charged for a Combination 1 meal at the two locations. [Prices are identical at the two Burger King locations.]

Every week the Burger King owner advertises special price offers at its two restaurants exclusively in daily

newspaper advertisements. A is the dollar amount spent on newspaper ads for each week in 1998. The owner

could not provide PWC with data on prices charged by other competing restaurants during 1998. For the oneyear

time period of the study, household income and population in the suburb did not change enough to

warrant inclusion in the demand analysis.

TABLE 1: Weekly Sales Data for Combination 1 Meals (1998)

week Q P A week Q P A

1 51,345 2.78 4,280 27 78,953 2.27 21,225

2 50,337 2.35 3,875 28 52,875 3.78 7,580

3 86,732 3.22 12,360 29 81,263 3.95 4,175

4 118,447 1.85 19,250 30 67,260 3.52 4,365

5 48,024 2.65 6,450 31 83,323 3.54 12,250

6 97,375 2.95 8,750 32 68,322 3.92 11,850

7 75,751 2.86 9,600 33 71,925 4.05 14,360

8 78,797 3.35 9,600 34 29,372 4.01 9,540

9 59,856 3.45 9,600 35 21,710 3.68 7,250

10 23,696 3.25 6,250 36 37,833 3.62 4,280

11 61,385 3.21 4,780 37 41,454 3.57 13,800

12 63,750 3.02 6,770 38 50,925 3.65 15,300

13 60,996 3.16 6,325 39 57,657 3.89 5,250

14 84,276 2.95 9,655 40 52,036 3.86 7,650

15 54,222 2.65 10,450 41 58,677 3.95 6,650

16 58,131 3.24 9,750 42 73,902 3.91 9,850

17 55,398 3.55 11,500 43 55,327 3.88 8,350

18 69,943 3.75 8,975 44 16,262 4.12 10,250

19 79,785 3.85 8,975 45 38,348 3.94 16,450

20 38,892 3.76 6,788 46 29,810 4.15 13,200

21 43,240 3.65 5,500 47 69,613 4.12 14,600

22 52,078 3.58 4,365 48 45,822 4.16 13,250

23 11,321 3.78 9,525 49 43,207 4.00 18,450

24 73,113 3.75 18,600 50 81,998 3.93 16,500

25 79,988 3.22 14,450 51 46,756 3.89 6,500

26 98,311 3.42 15,500 52 34,592 3.83 5,650

a. Using the data in Table 1, specify a linear functional form for the demand for Combination 1 meals,

and run a regression to estimate the demand for Combo 1 meals.

b. Evaluate your regression results by examining signs of parameters, p-values (or t-ratios), and the R2.

c. Discuss how the estimation of demand might be improved.

d. Using your estimated demand equation, calculate an own-price elasticity and an advertising elasticity.

Compute the elasticity values at the sample mean values of the data in Table 1. Discuss, in

quantitative terms, the meaning of each elasticity.

e. If the owner plans to charge a price of $4.15 for a Combination 1 meal and spend $18,000 per week on

advertising, how many Combination 1 meals do you predict will be sold each week?

f. If the owner spends $18,000 per week on advertising, write the equation for the inverse demand

function. Then, calculate the demand price for 50,000 Combination 1 meals.

CONSULTING PROJECT

Production Decisions at Harding Silicon Enterprises, Inc.

Harding Silicon Enterprises, Inc. produces less than 1% of the world’s supply of 32 MB random access

memory (RAM) chips for electronic devices. HSE’s RAM chips perform according to globally accepted

performance standards for this type of silicon chip (i.e., its chips are just like every other producers’

chips). HSE has hired you to do undertake three tasks:

1. Perform a statistical analysis of its short-run production costs to estimate its total variable cost

function, average variable cost function, and marginal cost function. HSE believes its total fixed

costs will be $6,500 per month, so you do not need to estimate TFC.

2. Recommend production levels and forecast profits for two chip price scenarios:

a. The price of 32 MB RAM chips reaches $62 per chip, and

b. The price of 32 MB RAM chips falls to $35 per chip.

3. Determine the price below which HSE should shut down operations in the short run.

HSE provides you with the following cost and output data for the past 19 months. Over this time period,

inflation has been so low that you do not need to adjust the cost data for the effects of inflation (the CPI

rose only 0.4% over the 19 month time period). Monthly output of chips is given in the second column,

which is titled “Monthly production of finished product.” Costs are reported in seven categories (some

are fixed costs and some are variable costs). HINT: Remember, cost items are part of fixed costs if the

costs do not vary with output, even though fixed cost items may vary over time.

Month

Monthly

production of

finished product

Business

licenses

& fees

Insurance

premiums

Building

lease

payment

Materials

expenses Telephone

Energy

expenses

Wage

expense

Nov-98 875 0 0 3570 9690 945 7230 12250

Dec-98 670 0 0 3570 6700 945 5115 8995

Jan-99 1675 6000 2200 3570 16295 945 12884 23106

Feb-99 1155 0 0 3570 11285 945 9240 15225

Mar-99 1845 0 0 3570 16550 945 14220 24530

Apr-99 1650 0 0 3570 16230 945 12700 21600

May-99 1955 0 0 3570 19626 945 15640 27484

Jun-99 2845 0 0 3570 27410 945 22760 39830

Jul-99 2265 0 2200 3570 20526 945 17244 31225

Aug-99 3470 0 0 3570 34176 830 25760 48564

Sep-99 3665 0 0 3570 36726 830 28720 50094

Oct-99 3750 0 0 3570 42576 830 32000 54474

Nov-99 4595 0 0 3570 48226 830 37260 66414

Dec-99 4060 0 0 3570 41095 830 33155 57840

Jan-00 3575 7200 2450 4200 34550 830 27400 50050

Feb-00 4380 0 0 4200 41800 830 34460 61320

Mar-00 5575 0 0 4200 81750 830 54600 82150

Apr-00 7870 0 0 4200 92360 830 102960 130180

May-00 6750 0 0 4200 89576 830 70000 109774

Cost Items for Harding Silicon Enterprises, Inc.

1. a. Compute total variable cost (TVC) by adding the appropriate columns of cost items.

Compute average variable cost (AVC). [Remember that you are given an estimate of

HSE’s future total fixed costs ($6,500 per month).] Print out the 19 months of data on

output (Q) and total variable cost (TVC) and average variable cost (AVC).

b. Plot a scatter diagram of TVC on the vertical axis and Q on the horizontal axis. Does the

scatter diagram suggest a functional form for TVC? Explain briefly.

c. Plot a scatter diagram of AVC on the vertical axis and Q on the horizontal axis. Does the

scatter diagram suggest a functional form for AVC? Explain briefly.

d. Estimate a quadratic AVC function. Present the estimated equation and evaluate the

regression results (i.e., discuss the algebraic signs of the parameter estimates, the

significance levels, and the R2

).

e. Evaluate the results of your regression equation in part a. Specifically discuss algebraic

signs of parameters, statistical significance, and goodness of fit.

2. a. How many chips should be produced (monthly) if world chip prices are $62 per chip?

Forecast the HSE’s profit at this output level.

b. How many chips should be produced (monthly) if world chip prices are $35 per chip?

Forecast the profit at this output level.

3. At what price should Harding shut down and produce no chips in the short run?

CONSULTING PROJECT

Estimating Industry Demand for Fresh Market Carrots

The market for carrots is comprised of two segments: fresh market carrots, which have excellent,

uniform color and a small core, and processing carrots, which are larger than fresh market carrots but still

have good flavor, color, and sweetness. Annual data for the years 1983–2000 in the fresh market segment

of the carrot industry are presented below. Q is total annual fresh market carrot production (measured in

thousands of hundred weight units, which are 100,000 pound units), P is average annual real price per

hundred weight of fresh market carrots (in constant 1991 dollars),1

and W is a weather index based on

temperature and rainfall (W varies directly with conduciveness of weather for growing carrots). To

account for the increasing popularity of carrots during the sample period, the time variable t is added to

the demand equation to reflect growing popularity of carrots. The production data do not account for

imports and exports of carrots. During the period of this sample, however, net exports of carrots (exports

minus imports) were quite small in every year.

t Q P W

1983 7,242 10.03 100.0

1984 8,220 6.62 108.3

1985 8,886 10.47 109.5

1986 9,300 12.59 96.3

1987 9,593 11.54 98.3

1988 10,758 10.56 101.2

1989 10,356 13.88 101.5

1990 11,322 14.01 100.6

1991 11,741 14.71 111.8

1992 12,486 13.15 109.0

1993 13,927 13.16 112.3

1994 15,072 16.14 115.4

1995 14,969 18.06 107.2

1996 14,163 19.45 90.5

1997 15,589 19.65 92.5

1998 16,192 17.29 95.6

1999 15,479 19.22 94.8

2000 17,992 19.24 98.7

Consider the following specification of empirical demand and supply functions in the fresh market

segment of the carrot industry:

2

s

d

Q

Q a bP ct

d eP f W

= + +

= + +

a. Should the ordinary least-squares (OLS) method or the two-stage least-squares method (2SLS)

method be employed to estimate market demand for carrots? Explain briefly.

b. Which variables are endogenous variables in the system? Which variables are exogenous? For

the model specified above, is the demand for fresh market carrots identified? Explain why or

why not?

1

Since carrots are planted and harvested year-round, carrot prices are computed as average prices for each year.

2 Typically farmers make production decisions for the current year using the previous year’s crop prices (or a

weighted-average of several previous years of crop prices). Since carrots are planted year-round, it is not

unreasonable to specify current annual production as a function of current average price of carrots.

c. Using statistical software, estimate the parameters of the empirical demand function specified in

part a. Write the estimated industry demand equation for carrots.

d. Are the estimated slope parameters of demand statistically significant at the 15 percent level of

significance? Are the algebraic signs of the parameter estimates and reasonable? Explain. ˆ

b cˆ

e. Would you expect the demand for carrots to be elastic or inelastic when measured at the average

price over the period of the sample? (Hint: Consider the discussion in Chapter 3 concerning the

factors that influence demand elasticity.)

f. Compute the price elasticity of demand for carrots measured at the sample mean values of price

(P), quantity (Q), and time (t). Is the demand for fresh market carrots elastic, inelastic, or unitary

elastic when measured at the sample mean values of P, Q, and t?

g. By approximately what percentage amount would the price of carrots have to fall in order for

quantity demanded to increase by 10 percent?

h. Explain, in quantitative terms, the meaning of the estimate of the slope parameter on t.