## Demand Estimation – With Sample Answer

## Assignment Instructions

Imagine that you work for the maker of a leading brand of low-calorie 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.

**Note:** Your professor will provide you with the equation and data necessary for you to complete this assignment. You will find this information attached to Assignment 1 within the course shell.

#### 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 supply function Q = 5200 + 45P 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.

#### 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.

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

Q = Quantity demanded

P (in cents) = Price of the product = 8,000

PX (in cents) = Price of leading competitor’s product = 9,000

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 = 64

## Sample Answer – Demand Estimation

### Variable Elasticity

Elasticity = change in quantity / change in price. To calculate the elasticity for every variable, change in variable quantity divided by change of variable. This results to variable coefficients (Viton, 2012).

QD = -5200 -42P + 20PX + 5.2I + 0.20A + 0.25M

= -5200 – 42 * 500 + 20 * 600 + 5.2 * 5500 + 0.2 * 10000 + 0.25 * 5000

= -5200 – 21000 + 12000 + 28600 + 2000 + 1250

=17650

PED = variable initial value x variable coefficient

PED_{P} = -42 * 500/ 17650 = -21000/17650 = -1.19

PED_{PX }= 20 * 600/17650 = 12000/17650 = 0.68

PED_{I }= 5.2 * 5500/17650 = 28600/17650 = 1.62

PED_{A }= 0.2 * 10000/17650 = 2000/17650 = 0.11

PED_{M} = 0.25 * 5000/17650 = 1250/17650 = 0.07

### Implication of the of Computed Elasticity

PED_{P} = -42 * 500/ 17650 = -21000/17650 = -1.19

The demand elasticity of price demonstrate a negative value of -1.19. This value is close to the unity elasticity which demonstrate equal change of demand to the change of prices. This means that change in the product prices for a certain percentage, influences the change of demand for almost similar percentage. This demonstrates that in the short-run, increase in the prices of frozen, product with low calorie will reduce the demand with a similar magnitude and similarly, decrease of their prices for a certain will increase their demand for a similar magnitude. However, the situation may change in the future as more people are giving extra importance to healthy feeding. This implies that increase in knowledge regarding healthy feeding may increase the products demand due to their important feature of low calorie. This may change the situation such that change in price will not receive similar magnitude in demand change. The demand may change slightly with change of prices or may not be affected at all in the future (Nitisha, 2015).

PED_{PX }= 20 * 600/17650 = 12000/17650 = 0.68

The value in this case is less than one which can be interpreted as relatively inelastic. This implies that change in the price of the competitor for a certain percentage result to change of the company’s product demand decrease but in a less magnitude. This implies that, competitor prices can influence the company’s product demand in the short-run. This may continue to happen in the long-run, unless the company employ measures to ensure that their products are highly competitive, particularly in health related matters to reduce the impact created by the cost of substitutable goods in the market.

PED_{I }= 5.2 * 5500/17650 = 28600/17650 = 1.62

The per capita income elasticity provide a value greater than one. This can be interpreted as relative elastic demand. This implies that a small change in prices create a huge change in the amount demand. Thus, change in the per capita income has a very great influence in the amount demanded. In the short-run, increase in the per capita income of individuals in the region will result to a huge increase in the amount demanded, while a decrease in per-capita will results to a huge decline in the amount demanded. The situation may remain constant in the future. Change of individual per capita may have the same influence in the demand even in the future, since people’s spending is always determined by their earnings (Nitisha, 2015).

PED_{A }= 0.2 * 10000/17650 = 2000/17650 = 0.11

Advertisement expenditure provides elastic value of less than one. This regarded as relatively inelastic demand, where by the level of demand created by advertisement is less than the amount invested in the same. This implies that, advertisement will not make great change to the company’s demand in the short-run and thus, the company will incur losses from advertisement investment. This will change in the future as more and more customers are aware of the company’s product and their health benefits. Thus, advertisement is anticipated to increase the level of products demand in the long-run, since less will be invested in advertisement as people become aware of the product.

PED_{M} = 0.25 * 5000/17650 = 1250/17650 = 0.07

Number of microwave sold affect the level of demand very slightly. The elasticity value tends to zero. This demonstrate inelastic situation where the level of oven sold hardly impact the demand of the company’s product. The situation is tending to almost inelastic s. In this regard, oven purchased may not impact the level of demand even in the future and hence, its significance to the company’s business in almost negligible (Nitisha, 2015).

### Recommendation on Firm Prices

The analysis demonstrates an almost unitary elastic demand situation, where change of price causes an equal change on demand. This implies that decrease in the product prices by 10% will cause a demand increase by only 10%. This may not be very profitable to the company since the demand increase will only be enough to cover the losses incurred as a result of price decrease. Thus, the situation may remain the same forever. In this regard, the company should not consider reducing its prices to enhance the level of demand. This should only happen in the future, in case the analysis will demonstrate that a small change in prices will attract high increase in demand (Hofstrand, 2007).

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