The Computation of Elasticity

The computation of elasticity

Change in variables. They are found with the first derivative with respect to the independent variables

yxP (in cents)=QDP= -42

PX(In cents)= QDPX=20

Income($)=QDI=5.2

Advertisement=QDA=0.20

M=QDM=0.25

Price elasticity

Q/P P/Q = -42*(5/26560) = 0.0079

Cross price elasticity of demand

EPX = Q/PX *PX/Q = 20 *(600/17,560) = 0.045

Income elasticity of demand (ied)

EI = Q/I I/Q = 5.2 *(5500/17,560) = 1.0768

The demand elasticity for M

Uj8EM = Q/M M/Q = 0.25 *( 5,000/17,560 )= 0.0451

Demand elasticity for advertisements

EA = Q/A A/Q = 0.20 *(10,000/17,560) = 0.0753

Question 1

Option 2

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

QD = -2,000 100(2) + 15(640) + 25(3) + 10(5000)

QD = -2,000 - 200 + 9600 + 75 + 50000

QD = 57475

The computation of changes in price and quantity demanded

P (in cents) =QDP= -100

PX (In cents) = QDPX=25

Income ($)=QDI=10

Advertisement=QDA=15

Computation of elasticity

Price elasticity of demand (PED)

Ed = Q/P P/Q = (-100) *( 2/57475) = -0.0035

The cross-price elasticity of demand.

EPX = Q/PX PX/Q = 25 *(3/57,475) = 0.0013

The income elasticity of demand.

EI = Q/I I/Q = 10 *(5000/57,475) = 0.8699

The demand elasticity for A.EA = Q/A A/Q = 15 *( 640/57,475) = 0.1670

Question 2

Option 1

Interpretation of the elasticity

Price elasticity of demand

The price elasticity of demand for the widgets is 0.0079 which means that demand of the Widget is indirectly proportional to the price. The higher the price, the higher the quantity demanded and the lower the price, the lower the quantity demanded of Widget good. It is thus said to be experiencing inelastic demand. Since the increase in price leads to an increase in revenue for the firm, the firm should adopt this pricing strategy so as to maximize revenue and hence profit. (Ruhm & National Bureau of Economic Research, 2011, p. 12-14)

Cross price elasticity of demand

Cross price elasticity of demand is mainly used to determine how sensitive the level of demand is due to changes in the price of other goods. The cross price elasticity for Widget is 0.045 which is a value greater than 0.It simply means that these two goods supplied in the market are substitute goods. Therefore, an increase in the prices of Widget will lead to lower demand for Widget and incline in the price and subsequent increase of the request of the related good X in the short run. Therefore, increasing price in the short run is not the best strategy for the firm if at all their aim is to maximize sales.

Income elasticity of demand

Elasticity of demand for income shows the effect of a change in the level income on demand. The income elasticity is 1.0768 which is positive. It thus shows that the good is a normal good, and the demand is directly more than proportional to income. Therefore, if there is an increase in income among the consumers of the good, demand will increase proportionately.

Advertisement elasticity

The elasticity of supply is very crucial since it gives self-assurance to a business unit hence capitalizing on the advertising activities. It normally shows the response of demand due to the promotional activities. It also gives an overall framework to the firm on how much the level of demand changes as a result of the changes in advertisement expenditure. (Ruhm & National Bureau of Economic Research, 2011, p. 25).The coefficient of advertising elasticity is positive hence, the bigger the coefficient, the greater the impact advertisement has on the quantity demanded on the product. If the coefficient is 0.0753, it shows that if the product increases by 1%, the quantity demanded increases by 7.53%. Therefore, it is advisable for the firm to use this promotional strategy both in the short run and in the long run to boost their sales.

Elasticity of M (sales)

The number of microwaves sold in the location where the supermarket is located will also influence the total demand of the companys product. The elasticity of M is 0.0451.it thus means that 1% increase in sales of M products increases the total demand by 0.0451%. Therefore, the strategy is critical both in the long run and short run since the total demand is increased by the adoption of the strategy. The increase in sales of M will increase total demand which eventually increases the total revenue of the firm both in the short run and long run.

Question 2

Option 2

Interpretations

Price elasticity of demand

The price elasticity of demand for the widgets is - 0.0035which means that the demand for the Widget is indirectly proportional to the price. The higher the price, the lower quantity demanded and the lower the price, the higher the quantity demanded of Widget good. It is thus said to be experiencing elastic demand. Since a decline in prices leads to an increase in revenue for the firm, the firm should adopt this pricing strategy in the short run so as to maximize revenue and hence profit.

Cross price elasticity of demand

Cross price elasticity of demand is mainly used to determine how sensitive the level of demand is due to changes in the price of other goods. The cross price elasticity for Widget is 0.0013 which is a value greater than 0.It simply means that these two goods supplied in the market are substitute goods. Therefore, an increase in the prices of Widget will lead to lower demand for Widget and incline in the price and subsequent increase in demand for the related good (X) in the short run. Therefore, increasing price in the short run is not the best strategy for the firm if at all their aim is to maximize sales in the short run. (Ruhm & National Bureau of Economic Research, 2011, p. 23)

Income elasticity of demand

Income elasticity of demand shows the effect of a change in the level income on demand. The income elasticity is 0.1670 which is positive. It thus shows that the good is a normal good, and the demand is directly more than proportional to income. Therefore, if there is an increase in income among the consumers of the good, demand will increase proportionately both in the short run and in the long run.

Question 3

Recommendation

The firm should consider cutting its prices since its price elasticity of demand is negative(less than negative 1).It simply means that an increase in the price levels will lead to a decrease in the quantity demanded hence a decline in the total revenue. The decline in revenue can be proven from the marginal revenue and elasticity equation

TR=TQ

ddydPTR= Q(dPdP) + P(dQdP)(1/Q)( dTRdP) = (dPdP)+ (P/Q)( (dQdP)) = 1 + E

Therefore, it simply means that when the elasticity is then dTRdP >0. It thus means that a decrease in price will result in an increase in revenue and vice versa.

Question 4

Question 4a: Option 1

Prices 100,200,300,400,500,600

QD = 5200 42P + 20PX + 5.2I + 0.20A + 0.25MSubstituting the values in the equation we get the QD of various prices, and then plot the figures to get the demand curve.

Quantity demanded when the price is 100QD= 5200 (42*100) + (20*600) + (5.2*5500) + (0.20*10000) + (0.25*5000) = 34450

Quantity demanded when the price is 200QD= 5200 (42*200) + (20*600) + (5.2*5500) + (0.20*10000) + (0.25*5000) = 30250

Quantity demanded when the price is 300QD= 5200 (42*300) + (20*600) + (5.2*5500) + (0.20*10000) + (0.25*5000) = 26050

Quantity demanded when the price is 400QD= 5200 (42*400) + (20*600) + (0.20*10000) + (5.2*5500) + (0.25*5000) = 21850

Quantity demanded when the price is 500QD= 5200 (42*500) + (5.2*5500) + (20*600) + (0.20*10000) + (0.25*5000) = 17650

Quantity demanded when the price is 600QD= 5200 (42*600) + (20*600) + (0.20*10000) +(5.2*5500) + (0.25*5000) = 13450.

The demand curves for option 1

Price Quantity demanded Supply

100 34450 0.89

200 30250 7910.78

300 26050 15,820.67

400 21850 23730.56

500 17650 31640.45

600 13450. 39550

45720032575500

Question 4a Option 2

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

Prices 100,200,300,400,500,600

Price=200, PX=300,I=5000,A=640

Quantity demanded when the price is 100QD= 2000 100(100) + 15(640) + 25(300) + 10(5000)

QD=-2000-10000+9600+7500+50000=55100

Quantity demanded when the price is 200

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

QD=-2000-20000+9600+7500+50000=45100

Quantity demanded when the price is 300

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

QD=-2000-30000+9600+7500+50000=35100

Quantity demanded when the price is 400QD= 2000 100(300) + 15(640) + 25(300) + 10(5000)

QD=-2000-40000+9600+7500+50000=25100

Quantity demanded when the price is 500QD= 2000 (100*300) + (15*640) + (25*300) + (10*5000)

QD=-2000-50000+9600+7500+50000=15100

Quantity demanded when the price is 600QD= 2000 (100*300) + (15*640) + (25*300) + (10*5000)

QD=-2000-30000+9600+7500+50000=5100

Demand curve for option 2

Price Quantity demanded Supply

100 55100 0.89

200 45100 7910.78

300 35100 15,820.67

400 25100 23730.56

500 15100 31640.45

600 5100 39550

1428759525000

Question 4b

Q = -7909.89 + 79.0989P with the same prices.

PRICES=100, 200, 300, 400, 500 and 600

Q=-7909+79.0989P=-7909+(79.0989*100) =0.89 =-7909+(79.0989*200) =7910.78 =-7909+(79.0989*300) =15,820.67 =-7909+(79.0989*400) =23730.56 =-7909+(79.0989*500) =31640.45 =-7909+(79.0989*600) =39550

Question 4c

Equilibrium price and quantity.

At equilibrium condition, the quantity demanded= quantity supplied

Optimal quantity for option 1= 22500

Optimal price for option 1= 398

Optimal quantity for option 2=24500

Optimal price for option 2= 400

Question 4d

Factors are causing changes in supply and demand for the low-calorie product.

Causes of changes in demand

Price of the product

-2000251181735P2

P1

D

Q2

Q1

Price

Quantity demanded

0

P2

P1

D

Q2

Q1

Price

Quantity demanded

Own price elasticity of demand of a product; an increase in the price of a product causes a decline in demand for that product since very few people will be willing and able to purchase the product. It will thus cause a movement along the demand curve. It can be shown in the diagram below.

Level of consumers income

The level of consumer income greatly affects the demand for a product. A decline in the level of consumer's income may lead to a decline in demand while an increase in the level of consumers income causes an increase in the quantity demanded. (Creative Educational Video, Inc, 2008, p. 22)The relationship is only applicable in the case of a normal good. When the good is an inferior good, then an increase in income leads to a decline in demand

Changes in the price of substitute good

When the price of substitute good increase the quantity demanded of low-calorie product increases and vice versa

Consumers future expectations

If the customers expect that the prices will increase in the long run, they will prefer purchasing more today thus leading to an increase in demand in the short run. In the long run, when the price will be high, the level of demand will go down thus leading to a decline in revenue.

Factors leading to changes in supply

Prices of goods

When the price of a product increases, the sellers will be motivated to produce more products thus maximizing profits in the short run. In the long-run, the entrants will enter the market and provide the substitute for the product thus lowers the level of demand.

Production costs

An improvement in technology and its efficient application help the firm in the reduction of production costs a...