Demand function (QD) = -5200 - 42P + 20PX + 5.2I + 0.2A + 0.25M
Where; P= 500, PX=600, I=$5,500, A=$10,000 and M=5,000
Replace values in the equation;
QD = -5200 - 42(500) + 20(600) + 5.2(5,500) + 0.2(10,000) + 0.25(5,000)
= -5200 – 21,000 + 12,000 + 28,600 + 2,000 + 1,250
= 17,650
Price elasticity of demand = ∂QD∂P×PQD
∂QD = change in quantity demanded, ∂P = change in price; P= price, QD = quantity demanded
∂QD∂P = -42 QD= 17,650 P= 500
Price elasticity of demand = -42 ×50017,650
= -1.1898
The above elasticity indicates that the product’s quantity demanded increases by 1.19% if there is a 1% decline in its price. This shows that the demand for the microwavable food is price elastic. The elasticity is more than one indicating that a change in price causes a more than proportionate variation in the product’s demand (Parkin, 2008). Since the product is price elastic, it suggests that the microwavable food is a luxury.
Demand elasticity for advertising expenditure
= ∂QD∂A×AdvertisingQD
= ∂QD∂A (coefficient of A in the equation) = 0.2
Spending on advertising, A = $10,000
QD = 17,650 units
= 0.2 ×10,00017,650
= 0.1133
The above result shows that if the firm increases its monthly advertising expenditure by one dollar, the demand for the product increases by 0.1133%. The elasticity is less than one implying the demand is inelastic to changes in advertising spending by the firm. An increase in advertising expenditure will increase the food’s demand but not in the same proportion (Parkin, 2008).
Cross price elasticity of demand = ∂QD∂PX×PXQD
∂QD∂PX= 20, PX= 600, QD= 17,650
= 20 ×60017,650
= 0.6799
The elasticity implies that a 1% rise in the price of product X causes a 0.6799% increase in the demand for the microwavable food. The positive sign shows that the microwavable food and Product X are substitutes. If the company producing Product X increases its price, the demand for the microwavable food will increase. The value is less than one indicating the demand for the low-calorie food is inelastic to changes in the price of Product X (Parkin, 2008).
Income elasticity of demand = ∂QD∂I×IQD
∂QD∂I= 5.2, I= $5,500, QD= 17,650 units
= 5.2 ×50017,650
= 0.1473
The income elasticity of demand above implies that a 1% increase in per capita income of the metropolitan area in which the supermarkets are located causes a 0.1473% in demand for the low-calorie food. The elasticity is less than one implying that the product’s demand is inelastic to changes in per capita income. This further shows that the low-calorie food is a necessity.
Elasticity for the number of Microwave oven
QD = 17,650
Coefficient of M in the equation = 0.25
M = 5,000
Elasticity = 0.25 ×5,00017,650
= 0.0708
The elasticity above implies that a 1% rise in the number of the microwave oven in the area that the supermarkets are located causes a 0.0708% increase in the demand for the low-calorie food. This shows that the two goods are related. The presence of microwaves promotes the demand for low-calorie microwavable food (Mankiw, 2014). However, the elasticity is less than one showing that the demand for the low-calorie food is less responsive to changes in the number of microwave oven sold in the area the supermarkets are located.
Recommendation on price cut
The company can alter the price of the low-calorie food to change its demand and market share in the industry. The above analysis shows that the demand for the low-calorie food is price elastic. A cut in its price will lead to a more than a significant increase in the quantity demanded (Mankiw, 2014). This implies that the firm can increase its revenues from the low-calorie food by reducing the product’s price. Thus, the firm should cut the price of the low-calorie food to increase its market share.
Demand and supply curves
Demand curve (QD) = 38,650 – 42P (all other independent variables are held constant except the price, P).
Supply curve (QS) = -7,909.89 + 79.1P
The demand and supply curves above can be used to estimate demand and supply at given price levels.
As shown in the above graph, the equilibrium price for the low-calorie food is 380 cents while the equilibrium quantity is 22,500.
Algebraic determination of equilibrium point
Qd = 38,650 – 42P
Qs = -7,909.89 + 79.1P
-7,909.89 + 79.1P = 38,650 – 42P
79.1P + 42P = 38,650 + 7,909.89
121.1P = 46,559.89
P = 46,559.89 ÷ 121.1
= 384.5 cents
Qd = 38,650 – (42 * 384.5)
= 38,650 – 16,149
= 22,501
Factors that could affect demand and supply of the low-calorie microwavable food
Factors that could cause leftward and rightward shift in demand curves
Changes in per capita income: An increase in the per capita income due to an improvement in the economy leads to a rise in the demand for the low-calorie food. As shown by the above income elasticity of demand, a rise in income results in quantity demanded of the low-calorie food. Consequently, the demand curve will shift outwards/rightwards. A decline in consumers’ income causes a leftward shift in the demand curve.
Prices of related goods: if the price of substitute goods increase, the demand for the low-calorie will increase. Thus, the demand curve will shift rightwards. However, if competitors lower their prices, the demand for the low-calorie food will decline (Mankiw, 2014). The decline in the demand will cause a leftward shift in the demand curve.
Changes in advertising: As shown by its elasticity of demand above, advertising spending by the firm influences the quantity demanded of the low-calorie food. An increase in advertising spending causes an increase in the demand for the low-calorie food. This further causes a rightward shift in the demand curve for the low-calorie food. However, a cut in advertising spending by the firm leads to a fall in the demand for the commodity. This could cause a leftward shift in the demand curve.
Consumers’ tastes and preferences: A favorable change in the tastes and preferences of consumers will lead to an increase in the demand for the low-calorie food. Thus, the demand will shift rightwards (Frank, Bernanke, & Frank, 2007). However, an unfavorable change in consumers’ tastes and preferences will lead to a reduction in the demand for the product thereby causing a leftward shift in the demand curve.
Factors that could cause a leftward and rightward shift in supply curve
Prices of factors of production. An increase in the cost of inputs will cause a reduction in the production level of eth firm thus reducing the quantity of the low-calorie food supplied in the market (Frank, Bernanke, & Frank, 2007). Consequently, there will be a leftward shift in the supply curve. A reduction in the cost of factors of production will result in a rightward shift in the supply curve.
Taxation and subsidies: An increase in government taxation on the low-calorie food or the firm’s incomes will discourage the production of the food. The resulting decline in the quantity supplied will cause a leftward shift in the supply curve. On the other hand, a reduction in taxes leads to a rightward shift in eth supply curve. An increase or an introduction of subsidies will results in an increase in the production of the low-calorie food thus causing a rightward shift in the supply curve. However, a reduction in or removal of subsidies causes a leftward shift in the supply curve.
Technology: an improvement in the technology used in the production of the low-calorie food could lead to an increase in production. Thus, the supply curve shifts rightwards. A deterioration in the production technology could lead to a decline in the quantity supply thereby causing a leftward shift in the supply curve.
References
Frank, R., Bernanke, B., & Frank, R. (2007). Principles of microeconomics (1st ed.). Boston:
McGraw-Hill/Irwin.
Mankiw, N. (2014). Principles of microeconomics (1st ed.). Stamford, CT: Cengage Learning.
Parkin, M. (2008). Microeconomics (1st ed.). Boston, Mass.: Pearson.
