Operations Decision

Demand Estimation

ECO 550

Walaa Yousif

Mohammad Sumadi

24 January 2015

alculating elasticity for each independent variable

We are given

Demand curve: QD = -2,000 - 100P + 15A + 25PX + 10I …………… (1)

Price of the product (P) = 200

Price of leading competitor’s product (Px) = 300

Per capita income of the standard metropolitan statistical area (I) = $5000

Monthly advertisement expenditure (A) = $640

Given these values, level of demand (Qd) = -2000-100*200+15*640+25*300+10*5000 =$45100

Price elasticity of demand :

Price elasticity of demand = -(dQ/dP)*(P/Q)

Using demand equation (1), we get (dQ/dP) = -100

So, price elasticity of demand = -(-100)*(200/45100) = 0.44346

Advertisement elasticity of demand:

Advertisement elasticity of demand = (dQ/dA)*(A/Q)

Using demand equation (1), dQ/dA = 15

So, advertisement elasticity of demand = 15*(640/45100) = 0.21286

Cross elasticity of demand :

Cross price elasticity of demand = (dQ/dPx)*(Px/Q)

Using demand equation (1), dQ/dPx = 25

So, cross price elasticity of demand = 25*(300/45100) = 0.1663

Income elasticity of demand :

Income elasticity of demand = (dQ/dI)*(I/Q)

Using demand equation (1), dQ/dI = 10

So, income elasticity of demand = 10*(5000/45100) = 1.10865

Implication of computed elasticity for the business

Since price elasticity of demand (in absolute term) is less than one, the demand is price inelastic i.e. change in the price of product would not cause much change in the quantity demanded of the product. In this case, the manufacturer will have more pricing power i.e. the manufacturer will be able to charge higher prices.

Since advertisement elasticity of demand is less than one, the demand is inelastic with respect to advertisement i.e. change in advertisement expenditure would not cause much change in the demand for the product. So in this case, the firm should not follow aggressive marketing strategies i.e. there should be less expenditure on advertisement.

Since cross price elasticity of demand is less than one, the demand of this product is inelastic with respect to price of its competitor product i.e. change in the price of competitors product would not cause much change in the quantity demanded of this product. Hence, this firm can charge higher price of its product without much concern about price charged by its competitor.

Since income elasticity of demand is greater than one, the demand is elastic with respect to income i.e. change in the income level would cause more than proportionate change in the quantity demanded. The implication of this result is that firm should sell the product in higher income areas as higher is the income, higher will be quantity demanded of the product. So, firm should target consumers with higher income in order to generate more profits.

Decision of whether firm should cut or increase the price to increase its market share

When demand is elastic, firm must decrease the price in order to increase the market share because in such a case, a small reduction in price would result in large increase in quantity demanded, causing total revenue/market share to increase. However, when demand is inelastic, firm must increase the price to increase the market share because in such a case, an increase in price would cause very small fall in quantity demanded and therefore there would be increase in total revenue/market share. This can be proved mathematically;

We know total revenue is obtained by multiplying price with quantity sold i.e.

TR = P*Q

Differentiating this with respect to price, we get as

= Q + P* = Q + P*

Putting e =(-) , where e denote absolute value of price elasticity

Simplifying, we get as

= Q(1-e)

This shows that if the absolute value of price elasticity is greater than one i.e. if demand is elastic, then a decline in price would lead to increase in total revenue. However, if absolute value of price elasticity is less than one i.e. if demand is inelastic, then an increase in price would lead to increase in total revenue/market share.

In our case, absolute value of price elasticity is less than one, so firm must increase the price to increase its market share.

Derivation of demand equation and demand curve

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

Given, Px = 300, I = 5000 and A = 640

Demand equation (explaining the relationship between price and quantity demanded of the good) is given as:

Qd = -2,000 - 100P + 15*640 + 25*300 + 10*5000or

Qd = 65100 – 100P ………………….. demand curve ………….. (1)

Supply equation and Supply curve

Supply equation: Qs = -7909.89 + 79.0989P…………….(2)

Demand and supply table:

Price	Qd	Qs
100	55100	0
200	45100	7909.89
300	35100	15819.8
400	25100	23729.7
500	15100	31639.6
600	5100	39549.5

Equilibrium-equality of demand and supply

Equilibrium would occur at point where market demand equals market supply. Graphically, it is the situation where market demand curve intersects market supply curve. [Refer figure1]

At equilibrium; Qs = Qd i.e.

65100 – 100P = -7909.89 + 79.0989P or

73009.9 = 179.0989P, implies equilibrium price (P*) = $408 approx.

And equilibrium quantity (Q*) = 24335 approx.

Figure1:

Factors causing change in demand and supply for the product

There are many factors that cause change in demand and supply of the product;

Factors causing change in demand ; a) Change in income of household, b) Change in price of substitute, c) Change in price of complementary goods, d) Change in taste and preferences, e) Change in expectation about price of product.

Factors causing change in supply ; a) Change in price of related goods, b) Change in input prices, c) Goal of the firm, d) Expectation of change in price in near future and e) Number of sellers

Crucial factors causing leftward and rightward shift of demand and supply curves

Factors causing rightward shift in demand curve : a) Increase in consumer’s income, b) Increase in the price of substitute good, c) Price is expected to increase in the future, d) Increase in advertisement expenditure

Factors causing leftward shift in demand curve : a) Fall in consumer’s income, b) Fall in the price of substitute good, c) Price is expected to decrease in the future

Factors causing rightward shift in supply curve : a) Decrease in input prices, b) Price is expected to decrease in future, c) Increase in number of sellers

Factors causing leftward shift in supply curve : a) Increase in input prices, b) Price is expected to increase in future, c) Decline in number of sellers.

References:

Snyder, C and Nicholson W (2008), Microeconomic Theory: Basic Principles and extensions, 10th edition, Cengage Learning.

Mankiw, G N (2006) , Principles of Microeconomics, 4th edition, Cengage Learning.

Stiglitiz and Walsh, Economics, W.W. Norton and Company, Inc, New York, International Student Edition, 4th edition 2007.