This is FOR KIM ONLY

DEMAND ESTIMATION 2

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.

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

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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

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

Option 1:

Each elasticity is the differentiation of the demand function with respect the variables.

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

A) Derivative with respect P= -42

B) Derivative with respect PX= 20

C) Derivative with respect I= 5.2

D) Derivative with respect A= 0.2

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E) Derivative with respect M= 0.25

Using the values for the independent variables, then the function for the demand is:

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

Where

P=500 cents PX= 600 cents I= 5500 A= 10,000 M= 5000

Qd  = - 5200 – 42(500)+ 20(600) + 5.2(5500) + 0.20(10,000) + 0.25(5000)= 17,650

A) Calculate the price elasticity of the demand:

Ed= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

Ed= (-42)*(500/17650)= -1.19

B) Calculate the cross-price elasticity of demand

EPx= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

EPx= (20)*(600)/(17650)= 0.68

C) Calculate the Income Elasticity of demand

EI= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

EI= (5.2)*(5500)/(17650)= 1.62

D) Calculate the demand elasticity for A:

EA= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

EA= (0.2)*10000/(17650)= 0.11

F) Calculate the demand elasticity for M:

EM= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

EM= (0.25)*5000/(17650)= 0.07

DEMAND ESTIMATION 5

Calculations 2:

QD   =    -2,000 - 100P + 15A + 25PX + 10I

F) Derivative with respect P= -100

G) Derivative with respect PX= 25

H) Derivative with respect I= 10

I) Derivative with respect A= 15

Using the values for the independent variables, then the function for the demand is:

QD       =    -2,000 - 100P + 15A + 25PX + 10I

Where:

P=200 PX= 300 I= 5000 A= 640

Qd  = -2000-100(200) +15(640) + 25(300) + 10(5000) = 45100

A) Calculate the price elasticity of the demand:

Ed= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

Ed= (-100)*(200/45100)= -0.44

B) Calculate the cross-price elasticity of demand

EPx= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

EPx= (25)*300/(45100)= 0.17

C) Calculate the Income Elasticity of demand

EI= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

EI= (10)*(5000)/45100= 1.11

D) Calculate the demand elasticity for A:

EA= (rate of change of quantity)/(rate of change of price) *(Price/Quantity)

DEMAND ESTIMATION 6

EA= (15)*640/(45100)= 0.21

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

The supermarket is targeting two options with different prices to see how consumers demand will be affected with the changes of prices and other variables. For the first option the price elasticity is -1.19 while the second option is -0.44. If the price for option 1 increases 1% then the quantity demanded will decrease 1.19%. For the second option is the price increases 1% , then the quantity demanded will decrease 0.44%. Option 2 seems to be less sensitive to the prices than option 1.

The next elasticity computed was the cross price elasticity, this elasticity measures the responsiveness of the quantity demanded for a good to a change in price. Moreover the cross price elasticity indicates if the goods are complements or substitutes depending of the value, the cross price elasticity for option 1 is 0.68 while for option 2 is 0.17, these two elasticities indicate both goods are substitutes, therefore the supermarket needs to be careful with the changes of prices. Both goods show a positive income elasticity, for option 1 is 1.62 and for option 2 is 1.11, this indicates the product is elastic with respect income, if the income of consumers increase 1% , then the quantity demanded will increase 1.62% for option 1 and 1.11% for option 2. The Microwave elasticity and the advertisement elasticity are both inelastic since both options have elasticity less than zero.

DEMAND ESTIMATION 7

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

Since the price elasticity for both options is greater than 1, then the company can cut the price and increase its market share since customers will buy more once the prices are cut. Moreover, the income elasticity shows that higher income will increase revenue for the product; therefore, a cut in the price will motivate buyers to buy more products.

3) 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.

The different prices show the function of demand with a negative slope; this is an indication of the law of demand. The lowest the price, the higher the quantity demanded. If the prices change from 100 to 600 cents, then the consumer will decrease the quantity demanded on the line from around 35,000 to 12,000.

DEMAND ESTIMATION 8

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.

The supply has a positive slope since the higher the price, the higher the quantities supplied. The graph shows how at a price of 600 cents, the quantity demanded and supplied has a big gap since people will demand almost 15,000 units while the supply will generate almost 40,000. The equilibrium or when the demand and supply are the same is shown where they intercept. The graph shows with a price around 380 then the quantities demanded and supplied will be 22,000. The exact figure can be determined by using algebra as the procedure done below.

DEMAND ESTIMATION 9

c. Determine the equilibrium price and quantity.

-7909.89+79.1P= 38650-42P

-7909.89-38650= -42P-79.1P

=-46559.89= -121.1P

P=385

Q= 38650-42(385)= 22480

The equilibrium is when the price is 385 then the quantities are 22480.

(22480, 385)

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

DEMAND ESTIMATION 10

product.

The demand can be shifted to the right or left due to the following factors. The demand can be shifted to the right if consumers believe the low-calorie, frozen microwavable food will help them lose weight. Diets companies can increase their advertising budget especially at the beginning of the year or before the summer to promote their low-calorie products. Moreover, if the company gets negative reviews or claims that the food is not healthy because the use of preservatives, then consumers will decrease the demand shifting it to the left. Another factor that might affect the demand is the increase of income, if the consumers increase their income and can afford buy better quality food in a restaurant or hire a nutritionist instead, then the demand will be reduce shifting to the left.

The shift for the supply is different than the ones for the demand. If the company is able to get a better technology and reduce costs for the production of low-microwavable food then the supply curve will shift to the right increasing the supply. Moreover, if taxes increase the cost of raw material such as the wrapping paper or maybe the ingredients of the food increase, then the supply will decrease shifting to the left. It is important to mention none of the shifts for the demand and supply are affected by the price, as mentioned before if prices changes then the quantities demanded or supply (movements on the line) will change.

4) 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.

DEMAND ESTIMATION 11

If the company increases advertisement and consumers react to it, then the demand will shift to the right. Moreover, if the company hires a celebrity that has lost weight with the low-calorie, frozen microwavable food, then the demand will also shift to the right. If the low calorie frozen microwavable food is a substitute of another food with a higher price, then the demand will increase and shift to the right.

If the company is able to get better prices for the low-calorie ingredients or better technology to increase production at a lower price, then the supply will shift to the right. The supply can also shift to the left if the government imposes a tax on health where the supplier needs to pay it and can not be transferred to the consumer.

DEMAND ESTIMATION 12

References:

Petroff, J. (2013). Demand and Supply.

Stekelenburg, J. V., & Klandermans, B. (2014). Fitting Demand and Supply: How Identification Brings Appeals and Motives Together. Social Movement Studies, 13(2), 179-203.

Lütkepohl, H., & Netšunajev, A. (2014). Disentangling demand and supply shocks in the crude oil market: How to check sign restrictions in structural VARs. Journal of Applied Econometrics, 29(3), 479-496.

Wolf, D. A. (2014). Getting Help From Others: The Effects of Demand and Supply. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, 69(Suppl 1), S59-S64.