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Mathematics & Economics
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Assignment: Demand Estimation

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Assignment 1: Demand Estimation
Due Week 3 and worth 200 points
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(dot)sophia(dot)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 + .20A + .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:
Compute the elasticities for each independent variable. Note: Write down all of your calculations.
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.
Recommend whether you believe that this firm should or should not cut its price to increase its market share. Provide support for your recommendation.
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 dollars.
Plot the demand curve for the firm.
Plot the corresponding supply curve on the same graph using the following MC / supply function Q = -7909.89 + 79.0989P with the same prices.
Determine the equilibrium price and quantity.
Outline the significant factors that could cause changes in supply and demand for the product. 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.
Indicate the crucial factors that could cause rightward shifts and leftward shifts of the demand and supply curves.
Use at least three (3) quality academic resources in this assignment. Note: Wikipedia does not qualify as an academic resource.
Your assignment must follow these formatting requirements:
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.
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.
The specific course learning outcomes associated with this assignment are:
Analyze how production and cost functions in the short run and long run affect the strategy of individual firms.
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.
Use technology and information resources to research issues in managerial economics and globalization.
Write clearly and concisely about managerial economics and globalization using proper writing mechanics.
Please follow the grading rubics that is attached and there are also helpful tips attached.

Essay Sample Content Preview:
Demand Estimation: option 1
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The quantity demanded for the widgets is = -5200-42(500) + 20 (600) + 0.2(5000) = 17650
Price elasticity Price/ Quantity* change in quantity/ change in price= (P/Q)*(dQ/dP)
The change in Quantity/change in Price= -42
The price of a three pack unit is 500 when the price is 17, 650
Price Elasticity (Ep) = -42* (500/ 17650) =1.19
Cross elasticity (Ec)= 20* (600/ 17, 650) = 0.68
Elasticity of advertising: EA= P/Q (0.20) (10000/17650) = 0.11
Elasticity of per capita income (EI)= 5.2*(5500/17650) = 1.62
EM =0.25 (5000/17650) = 0.07
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
Since the price elasticity is -1.19 there is an indirect relationship between the quantity demanded and the price of goods. If the organization increases the price of widgets by 1% there will be a 1.19% decrease in the quantity of widgets demanded. As such incrassating the price of widgets may be counterproductive as consumers would buy less of the product, resulting to a fall in revenue.
The cross price elasticity is related to the responsiveness of quantity demanded price in relation to the competitor’s pricing of products product. If the price of the competitor increases by 1% then the quantity of the product will increase by 0.68%. The widget is fairly price elastic meaning that there is no immediate concern on whether this will have a big impact on sales.
The income elasticity for the product is 1.62 indicating that a 1% increase in income levels in the areas of operation will result to a 1.62% increase in the demand of the product. Since the widget is price elastic it is better for the company to raise the price if the average income levels in the areas rise.
The advertisement elasticity of 0.11 indicates that if advertising increases by 1% then the quantity demanded will increase by 0.11%. Since the demand for the product is price inelastic with regards to advertising, the management ought to be cautions when relying on a rise in advertisement to raise the price of products as this may not cause a decrease in the number of customers who purchase the products.
There is a 0.07 degree of elasticity for the microwave indicating that a 0.07% rise in the quantity of products for a 1% increase in ovens and the product is price inelastic.
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.
High price elasticity indicates that consumers are more sensitive to price changes, and in this case the price elasticity is greater than 1 hence the demand is price elastic (Welch & Welch, 2009). Hence, reducing the price of the product would result to increased demand because the negative price elasticity is more than unity. Ideally, businesses seek to maximize profits at the level where the elasticity is one. At the same time, reducing the price of products is associated with more quantity demanded and higher revenue when the degree of elasticity is closer to unity (Hirschey, 2009). Consequently, price red...
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