# Assignment 1: Demand Estimation

Imagine that you work for the maker of a leading brand of low-calorie, frozen microwavable food that estimates the following demand equation for its product using data from 26 supermarkets around the country for the month of April.

For a refresher on independent and dependent variables, please go to Sophia’s Website and review the Independent and Dependent Variables tutorial, located at http://www.sophia.org/tutorials/independent-and-dependent-variables--3.

Option 1
Note: The following is a regression equation. Standard errors are in parentheses for the demand for widgets.
QD       =          - 5200 - 42P + 20PX + 5.2I + 0.20A + 0.25M
(2.002)  (17.5) (6.2)    (2.5)   (0.09)   (0.21)
R2 = 0.55           n = 26               F = 4.88

Your supervisor has asked you to compute the elasticities for each independent variable. Assume the following values for the independent variables:

Q          =          Quantity demanded of 3-pack units
P (in cents)       =          Price of the product = 500 cents per 3-pack unit
PX (in cents)     =          Price of leading competitor’s product = 600 cents per 3-pack unit
I (in dollars)       =          Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = \$5,500
A (in dollars)     =          Monthly advertising expenditures = \$10,000
M                     =          Number of microwave ovens sold in the SMSA in which the
supermarkets are located = 5,000

Option 2
Note: The following is a regression equation. Standard errors are in parentheses for the demand for widgets.

QD       =          -2,000 - 100P + 15A + 25PX + 10I
(5,234)  (2.29)   (525)   (1.75)  (1.5)
R2 = 0.85           n = 120             F = 35.25

Your supervisor has asked you to compute the elasticities for each independent variable. Assume the following values for the independent variables:

Q          =          Quantity demanded of 3-pack units
P (in cents)       =          Price of the product = 200 cents per 3-pack unit
PX (in cents)     =          Price of leading competitor’s product = 300 cents per 3-pack unit
I (in dollars)       =          Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = \$5,000
A (in dollars)     =          Monthly advertising expenditures = \$640

Write a four to six (4-6) page paper in which you:

1.      Compute the elasticities for each independent variable. Note: Write down all of your calculations.

2.      Determine the implications for each of the computed elasticities for the business in terms of short-term and long-term pricing strategies. Provide a rationale in which you cite your results.

3.      Recommend whether you believe that this firm should or should not cut its price to increase its market share. Provide support for your recommendation.

4.      Assume that all the factors affecting demand in this model remain the same, but that the price has changed. Further assume that the price changes are 100, 200, 300, 400, 500, 600 cents.

a.       Plot the demand curve for the firm.

b.      Plot the corresponding supply curve on the same graph using the following MC / supply function Q = -7909.89 + 79.1P with the same prices.

c.       Determine the equilibrium price and quantity.

d.      Outline the significant factors that could cause changes in supply and demand for the low-calorie, frozen microwavable food. Determine the primary manner in which both the short-term and the long-term changes in market conditions could impact the demand for, and the supply, of the product.

5.      Indicate the crucial factors that could cause rightward shifts and leftward shifts of the demand and supply curves for the low-calorie, frozen microwavable food.

1. Use at least three (3) quality academic resources in this assignment. Note: Wikipedia does not qualify as an academic resource.
3. Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. Check with your professor for any additional instructions.
4. Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.
5. The specific course learning outcomes associated with this assignment are:
6. Analyze how production and cost functions in the short run and long run affect the strategy of individual firms.
7. Apply the concepts of supply and demand to determine the impact of changes in market conditions in the short run and long run, and the economic impact on a company’s operations.
8. Use technology and information resources to research issues in managerial economics and globalization.
9. Write clearly and concisely about managerial economics and globalization using proper writing mechanics.

Grading for this assignment will be based on answer quality, logic / organization of the paper, and language and writing skills, using the following rubric.

Instructions for Assignment 1

This assignment will need both real calculations (elasticities, quantities of demand and supply, equilibrium price and quantity, for this particular demand function) and discussions and explanations of your results, theories about elasticity, factors for demand and supply, equilibrium, graphs of demand and supply.

For the elasticities,  please read carefully chapter 4, which explains to your how to use the coeffients in the regression model to calculate the corresponding elasticity.   Page 102 of your textbook has the formulas.

For the price of this product, and price of competitor’s product, please use the number in cents as given, do not change the cents to dollars.

Before you plot the demand curve, you will want to derive the demand function first (the function with only the price of the product P as the independent variable).   You will want to plug in the values of the other variables to get the demand function.

Then for the different price levels, p= 100, 200, …500,  calculate the demand quantities and supply quantities

Please plot both supply and demand curve on the same graph.

Please make sure the Y-axis is the price, the X-axis is quantity.

To solve the equilibrium, you will need to set the demand = supply, then solve the equation.

The demand is the one you derived above

In discussing the shifts of the demand and supply curves, please make sure you are discussing non-price factors.

For the demand curve, you should discuss the factors in the regression model, describing what kind of change of each variable will shift the demand curve to the left (meaning demand will decrease for the same price), or when the demand curve will shift to the right (meaning the demand will increase for the same price)

For the supply curve, you should discuss the factors affecting the production of the goods, such as cost of inputs, taxes, technology, government regulations, etc.   You will want to discuss how these factors will increase the supply of the goods (supply curve shifts to the right), or decrease the supply of the goods (supply curve shits to the left)

#1:

Using the formula and information given, first calculate the Q

Q = -5,200 – 42(500) + 20(600) + 5.2(5,500) + 0.20(10,000) + 0.25(5,000) =

Now we can compute the elasticities for each independent variable:

ED = ∂QD/∂P * P/QD = – 42 * 500/Q (what you calculated above) =

Similarly for other elasticities

#2  You need to answer what the elasticity numbers you calculate in #1 mean.

For example,

Income elasticity is approximately 1.6,  which shows that an increase by 1 % of the average income will raise the product’s quantity demand by 1.6%.   It means that the demand for this product is very sensitive to income.  The company should target its product to high income customers.

#3   You will need to discuss how the revenue will change based on  the price elasticity of demand

If the demand is elastic (price elasticity is less than -1), a 1% decrease in price increases demand more than 1%, so total revenue will increase.   Thus cutting price will increase its market share, but decrease revenue.  Do you want to cut price then?

#4:   First, you need to get the demand function.  To do that, you plug in all the variable values given in the beginning (except the price).

Q = -5200 - 42*P + 20*600 + 5.2*5500 + 0.2*10000 + 0.25*5000

Simplify this function, you got something like Q = constant – 42 P

Then for the different price levels, p= 100, 200, …500,  calculate the demand quantities and supply quantities

Put the numbers into excel to plot the demand and supply curve.

Please refer to the videos I put in the insight area to learn how to do a graph in excel.

#5

In discussing the shifts of the demand and supply curves, please make sure you are discussing non-price factors.

For the demand curve, you should discuss the factors in the regression model, describing what kind of change of each variable will shift the demand curve to the left (meaning demand will decrease for the same price), or when the demand curve will shift to the right (meaning the demand will increase for the same price)

For the supply curve, you should discuss the factors affecting the production of the goods, such as cost of inputs, taxes, technology, government regulations, etc.   You will want to discuss how these factors will increase the supply of the goods (supply curve shifts to the right), or decrease the supply of the goods (supply curve shits to the left)

Field of study:  