Determination and interpretation of elasticities
Demand function, QD = -3,500 – 150P + 30A + 75PX + 10 Y
P = 300 cents, A = $750, PX = 200 cents and Y = $10,000
QD = -3,500 – (150 × 300) + (30 × 750) + (75 × 200) + (10 × 10,000)
= -3,500 – 45,000 + 22,500 + 15,000 + 100,000
= 89,000 units
Price elasticity of demand
Price elasticity of demand = ∂QD∂P × PQD
Change in quantity demanded/change in price, ∂QD∂P is the coefficient of price, P in the demand equation.
∂QD∂P = -150
QD = 89,000
P = 300 cents
PED = -150 × 30089,000
= -0.5056
The above price elasticity of demand indicates that the quantity demanded of the low-calorie, microwavable food decreases by 0.5056% for every increase in price by one cent. The elasticity is less than one (in absolute terms) indicating that the demand for the microwavable food is price inelastic (McEachern 91-111). A variation in price causes a less than comparable variation in the quantity demanded. This suggests the food is a necessity. Necessities are price inelastic while the demand for luxuries is price elastic (McEachern 91-111).
Elasticity of Advertising
Demand elasticity for advertising expenditure
= Change in QDChange in A × AdvertisingQD
Change in QD/Change in A (coefficient of A in the equation) = 30
Advertising spending, A = $750
QD = 89,000 units
= 30 × 75089,000
= 0.2528
The advertising elasticity of demand above implies that an increase in advertising spending by one dollar results in an increase in quantity demanded by 0.2528%. The elasticity is less than one showing that the advertising elasticity of demand is inelastic. This implies that an increase in advertising spending causes a less than proportionate rise in the quantity demanded (Arnold 123-137). The inelasticity could be due to the influence non-advertising factors such as the price of the commodity, prices of related commodities, advertising spending of other firms as well as the nature of the market.
Cross-price Elasticity of demand
Cross-price elasticity of demand = Change in QDChnage in PX × PXQD
Coefficient of PX in the equation = 75
PX = 200 cents
QD = 89,000 units
Cross-price elasticity of demand = 75 × 20089,000
= 0.1685
The cross-price elasticity of demand above implies that an increase in the price of commodity X by one dollar causes an increase in the demand for the microwavable food by 0.1685%. This further implies that the demand for the microwavable food is inelastic to changes in the price of commodity X since the elasticity is less than one (Arnold 123-137). The change in the price of commodity X causes a less than proportionate change in the demand for the microwavable food. This indicates that competition in the market is not based on prices but non-price factors.
The positive sign implies that the microwavable food and commodity X are substitutes (Arnold 123-137). If the price of X increases, there will be an increase in the demand for the microwavable food since the microwavable becomes less expensive than commodity X. Consumers, therefore, shift from commodity X to the microwavable food.
Income elasticity of demand
Income elasticity of demand, YED = Change in QDChnage in Y × YQD
Change in QDChnage in Y (The coefficient of Y in the equation) = 10
Current income, Y = $10,000
QD = 89,000 units
YED = 10 × 10,00089,000
= 1.1235
The elasticity implies that an increase in per capita income by one dollar causes an increase in the demand for the microwavable food by 1.1235%. It further implies that the demand for the microwavable food is elastic to changes in per capita income (Tucker. 95-104). This suggests that it is a luxury since an increase in per capita income causes a more than proportionate increase in quantity demand (Tucker. 95-104).
Increasing market share
The firm should not cut its price if it wants to increase its market share. As shown above, the price elasticity of demand is -0.5056 implying that the demand is price inelastic. A price cut will lead to a less than proportionate increase in the demand for the commodity. Although the demand will increase, it is not a sound decision. Since the change in demand will be less than comparable to the change in price, the total revenue for the firm will decrease if the firm cuts its price. A price reduction improves the company’s market share only if the demand for the product is price elastic (Tucker. 95-104). Thus, the firm should employ non-price measures such as quality improvement, among others.
Demand and supply curves
Demand curve (with all other variables constant except price): QD = 134,000 – 150P
Supply curve; QS = -7,909.79 + 79.0989P
Using the above equations, the quantities demanded and supplied are calculated for each of the prices from 100 cents to 800 cents. Below are the quantity demanded and the corresponding quantity supplied at different prices.
As shown above, the equilibrium price is 620 units, and the equilibrium quantity is 41,000 units.
Determining equilibrium price and quantity algebraically
QD = 134,000 – 150P
QS = -7,909.79 + 79.0989P
QD = Qs
134,000 – 150P = -7,909.79 – 79.0989P
-150P - 79.0989P = -7,909.79 – 134,000
-229.0989P = -141,909.79
P = -141,909.79/-229.0989
Equilibrium price = 619.43 cents
QD = 134,000 – (150 × 619.43)
= 134,000 – 92,914.50
= 41,085.5
Equilibrium quantity = 41,086 units
Short-term and long-term changes that could shift the demand and supply curves
Changes that could shift the demand curve
Changes in per capita income: Per capita income is a measure of consumers’ purchasing power. An increase in per capita income could lead to an increase in the quantity demanded of the microwavable food. Consequently, the demand curve for the microwavable food will shift outwards (McEachern 91-111). On the other hand, a decline in per capita income causes a decline in demand thus could cause an inward shift in the demand curve for the microwavable food.
Changes in prices of related commodities: an increase in the price of a substitute commodity such as product X will lead to an increase in the demand for the microwavable food thus the demand shifts outwards (to the right). If the price of Product X declines, the demand for the microwavable food will decrease (McEachern 91-111). Thus, the demand curve will shift inwards (to the left).
Advertising spending: If the company increases its advertising expenditure, the demand for the microwavable food will increase. The demand curve will shift outwards. An increase in competition could trigger the increase in advertising spending.
Changes in consumers’ tastes: If consumers’ tastes and preferences change in favor of the microwavable food, its demand will increase hence the demand curve will shift outwards.
Changes that could shift the supply curve
Changes in costs of production: Reduction in the cost of labor, raw material, among other inputs, will cause an increase in the quantity supplied. Thus, the supply curve will shift outwards (Tucker. 95-104). Besides, an improvement in technology that enhances efficiency in production and reduces production costs causes the supply curve to shift outwards.
Changes in government taxation and subsidies: an increase in taxation or a reduction in subsidies will cause a decline in supply hence the supply curve will shift inwards (Tucker. 95-104). An increase in subsidies or a cut in taxes will lead to an increase in supply thus the supply curve will shift outwards.
Changes in the supply of related commodities: An increase in the supply of a commodity used together with the microwavable food will cause an increase in the demand for the microwavable food hence firms will produce more of the food. This further leads to an outward shift in the supply curve.
Works cited
Arnold, Roger A. Microeconomics. 1st ed. Mason, OH: Thomson/South-Western, 2008.
Print.
McEachern, William A. Economics: A Contemporary Introduction. 1st ed. [Mason, Ohio?]:
South-Western/Cengage Learning, 2013. Print.
Tucker, Irvin. Survey Of Economics. 1st ed. Cengage Learning, 2014. Print.
