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# A regression equation

Considering the regression equation below;

R2=0.55 n=26 F=4.88 Solutions QD=-5200-42P+20PX+5.2I+0.20A+0.25M (2.002)(17.5)(6.2)(2.5)(0.09)(0.21)

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

Moreover, Q=3, P=500cts, PX=600cts, I=\$5500, A=\$10000, M=5000.

QD = -5200-42 (500cts) +20 (600cts) +5.2 (\$5500) +0.20 (\$10000) =17650

Each independent variable's elasticity is computed as follows:

Elasticity = (change in quantity per unit change in independent variable price) (price/quantity)

As a result, the elasticity for each independent variable is computed as follows.

Price elasticity of commodities=p/q*P/Q Differentiation from the regression equation yields -42, implying that

P=-42*500/17650=-1.19 Elasticity

Price elasticity of linked products, PX=px/q*P/Q

PX= 20*600/17650=0.67

Per capita income elasticity, I=I/q*P/Q I=5.2*5500/17650=1.62

A=0.2*10000/17650=0.11

Elasticity of each independent variable is calculated as follows;

Elasticity = (change in quantity/unit change in price of independent variable) × (price/quantity)

Therefore elasticity for each independent variable is calculated as follows

Price elasticity of the commodities=Ďp/ďq*P/Q

Differentiation from the regression equation gives, -42 thus,

Elasticity P=-42*500/17650=-1.19

Elasticity of related product prices, PX=ďpx/ďq*P/Q

PX= 20*600/17650=0.67

Elasticity of per capita income, I=ďI/ďq*P/Q

I=5.2*5500/17650=1.62

A=0.2*10000/17650=0.11

Elasticity of sales, M=ďM/ďq*P/Q

M=0.25*5000/17650=0.07

Where P is price and Q is quantity

Implications for each of the above elasticity coefficients

Price elasticity is computed as -1.19 shows that elasticity is elastic this means that one unit change in price will decrease the demand of microwaves ovens by amount equivalent to 1.19%. Therefore in short-run the demand of microwaves will go down by 1.19 percent. In the long-run price changes will have a further decrease demand.

Elasticity of the price of related commodity computed as 0.67 this shows a positive elasticity. This implies that one unit change in prices of related commodities leads to 0.67 percent increase in the demand for microwaves ovens. In the short-run the demand for the microwave may or may not change much but in the long-run the demand for microwaves will go up.

Elasticity of per capita income is 1.62. In this case a one percent increase in the consumers’ income will lead to increase in the quantity demanded. A 1.62 percent increase in demand can be projected from the increase in disposable income of the customers.

Elasticity of monthly advertisement of the commodities is 0.11. This implies that one percent change in advertisements expenditure will lead to a 0.11% increase in the demand of the microwaves in the short-run. In the long-run the sales can increase by a large margin due to continued awareness.

Elasticity of number of microwaves sold in a given area is 0.07. This is a positive inelasticity which implies that one percent change in sales increase the demand for ovens by 0.07% in the short-run. This impact is very small and therefore cannot be put in much consideration when looking at factors the influence quantity demanded.

Option 2

Given QD= -2000-100P+15A+25PX+10I

(5234)(2.295)(25)(1.76)(1.5)

R2=0.85 n=120 F=35.25

Solutions

Elasticity of each independent variable is calculated as follows;

Elasticity =change in quantity /unit change in independent variable ×unit price/unit quantity

And, P=200, PX=300, I=\$5000, A=\$640

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

Elasticity for each independent variable

Elasticity of price= Ďp/dq*P/Q

-100*200/45100=-0.44

Elasticity for price of competitors product (PX) =Ďpx/ďq*P/Q

=25*300/45100=0.0066

Elasticity for I= Ďi/ďq*P/Q

= 10*5000/45100=2.22

Elasticity for monthly adverts, A= Ďa/ďq*P/Q

=15*640/45100=0.21

Implications of elasticity coefficients for the business

Price elasticity is -0.44. This shows that one unit change in the price of the microwave decreases the quantity demanded both in the short-run and in the long-run. This shows that the product has a small degree of elasticity

Cross-price elasticity of related products is 0.0066. This implies that one percent changes in prices of other related commodities have increases the demand for microwaves by 0.066%. This a very small impact on the quantity demanded. In both short-run and long-run the business will continue to sell regardless of the prices of the other products in the market.

Elasticity of per capita income is 2.22. In this case one percent increase in consumers income increases the quantity demanded by 2.22%. This shows how great the impact of consumer income on the demand of this commodity is.

Elasticity of monthly advertisement is 0.21 which is positive. This implies that business advertisements have a positive impact on the demand of the microwaves ovens in the long-run. In the short-run the impact may be small due to lack of awareness. However, advertisement does not usually have a direct impact on the prices of the commodities.

The rationale of the results

The reasoning behind the results is based on the magnitude and the direction of the changes in the independent variables. Expected signs show the direction and the effect on the dependent variable. With regard to magnitude we can see the impact on the depend variable based on the coefficient of the elasticities.

Recommendations

I believe that this firm should cut its prices because any change in price does leads to a great impact on the demand of the microwaves. And also a change in price of related products brings a large impact on the demand of the ovens.

Holding all other factors constant except the price we can get the following data to come up with demand curve of the microwaves ovens.

Holding other factors constant and given prices as 100, 200, 300, 400, 500, 600.

We can say that since

QD=-5200-42p+20px+5.2I+0.20A+0.25M

Therefore QD=-5200-42P+20(600)+5.2(5500)+0.20(10000)

We get QD = 38,650 – 42P

From the equation above we can get the values for quantities at different prices to fill the table below

price

100

200

300

400

500

600

Quantity(QD)

34450

30200

26050

21850

17650

13450

Given a corresponding supply curve function we can come up with the quantities supplied on the same market. Also we have prices stated as 100, 200, 300, 400, 500, 600 and the equation given as MC/Q= -7909.89+79.1P

Q=7909.89+79.1P substituting values of P gives,

Q=-7909.89 + 79.1 (100) = 0.11

Q= -7909.89 + 79.1 (200) = 7910.11

Q=-7909.89 + 79.1 (300) = 15820.11

Q=-7909.89 + 79.1 (400) = 23730.11

Q=-7909.89 + 79.1 (500) = 31640.45

Q=-7909.89 + 79.1 (600) = 39550.11

Price

100

200

300

400

500

600

Quantity QS

0.11

7910.11

15820.11

23730.11

31640.45

39550.11

Graph showing demand and supply of microwave ovens

Equilibrium price and quantity is computed as follows,

QD=38650-42P and QS=-7909.89+79.1P

At equilibrium quantity demanded is equal to quantity supplied

Therefore, 38650-42P=-7909.89+79.1P

This gives, 121.1P=46559.89

Equilibrium price, P=46559.89/121.1= 384.48

Equilibrium quantity on the other hand is given by substituting price=384.84 in any equation, that is

Q=38650-42(384.48)=22501.6

Equilibrium quantity= 22501.6

Significant factors that could cause change in this supply and demand

Income of the consumers in the area can influence the demand for the frozen microwavable food (Marquez, 2013). Also the price of the food could lead to either increase or decrease in demand. Changes are tastes and preferences of the consumers can also affect the demand for this food (Mark, 2012).

In both short-term and long-run the demand of this food will increase given that the price elasticity is elastic so demand will keep on changing with the price.

Some of the crucial factors that can lead to either left or right shifts in the demand and supply curves includes;

Increase in corporate taxes for the company which may increase cost of production hence shifting supply curve to the right.

A change in technology is also another factor that causes a shift in supply curve. Use of technology in production reduces the cost of production hence the company will produce more at low cost. The supply curve thus shifts to the left.

Availability of close substitutes for the microwavable foods may lead to shift in the demand curve. Close substitutes makes the demand curve shift to the left because of decrease in demand (Dick A, 2012)

References

References Dick, A. A. (2012). Demand estimation and consumer welfare in the banking industry. Divisions of Research & Statistics and Monetary Affairs, Federal Reserve Board.

Mark A. Bradley, (2012). Improving ADA Paratransit Demand Estimation: Regional Modeling. Transportation Research Board.

Marquez, J. (2013). Estimating Trade Elasticities. Jaime Marquez.