## Note on Demand Function

• Note
• Things to remember

### Demand

Demand for a commodity is defined as the quantity demanded of that commodity which a consumer is willing and able to purchase at given market price for a specific period of time. The demand for anything at a given price is the amount of it, which will be bought per unit for a time at that price.

Types of demand

• Price demand: It is the various quantities of a commodity that consumer purchases at various prices, other things being constant at a given time. It establishes a negative relationship between price and demand.
• Income demand: It is the various quantities of a commodity that consumer purchases at various level of income, other things being constant at a given time. It establishes a positive relationship between income and demand.
• Cross demand: It is the relationship between the quantity demanded of one good (say ‘X’ good) and price of related goods (say ‘Y’ good), other things being equal. The related goods are of two types: substitutes and complements. There is a direct relationship between the price of wai-wai and the demand of mayos (substitutes).There is a negative relationship between the price of a pen and the demand of ink (complements).

### Demand Function

The mathematical function explaining the quantity demanded in terms of its various determinants, including income and price; thus the algebraic representation of the demand curve is known as Demand function. Mathematically, Qx = f(Px, Y, Pr, A, T, C, W, Sp, Ms, Tr, Ep, etc. … ).
Where, Qx= Demand for X good, f=Function, Px=Price of X good, Y= Income of consumer, Pr=Price of related goods, A=Advertisment Expenditure, T=Taste, preference and fashion of the consumer,C=Customs, W=Weather, Sp= Size of population, Ms= Money supply, Tr= Tax rate, Ep= Expectation about change in price.

#### Types of Demand Function

Basically, Demand function can be classified into two categories:

Single variable demand function

Simply, the mathematical relationship between the quantities demanded of X in terms of its price is known as single variable demand function. Other than price (such as income, taste, a price of other good) remain constants in this relationship. Mathematically, Qx=a-bp OR Qx=a/p^b . Single variable further classified as:

1.Linear Demand function: A simple equation can be used to express the relationship between the price of a good and the demand among that good’s consumers is called Linear Demand function. The slope of demand curve remains constants (i.e. straight line) in Linear Demand function. Mathematically,Qx = a – bp.Where, a= Autonomous Demand, b=Slope of demand curves. Let us compute demand for a commodity X at various prices (Where, Qx=70-4p).

 P (Price per unit) Qx (Quantity demanded) 5 50 10 30 15 10

In the figure, price and quantity demanded are measured on Y-axis and X-axis respectively. DD is the demand curve which establishes the relationship between price and quantity demanded. Here, the consumer is demanding 50kg Mango at the price Rs.5. When the price raised from Rs.5 to Rs.10 then quantity demanded decreases from 50kg to 30 kg. Similarly as price raised from Rs.10 to Rs.15 and quantity demanded decreases from 30Kg to 10Kg. Thus, Demand curve (DD’) is downward sloping due to the inverse relationship between price and quantity demand of a commodity.

2.Non-Linear Demand function: A demand function is said to be non-linear or curvilinear when the slope of demand curve changes along the demand curve. Generally, a non-linear demand function is expressed in power function. Mathematically, Qx=a/P^b . Where, a= Autonomous Demand, b=Slope of demand curves. Let us compute demand for a commodity X at various prices (Where, Qx=300/p^1 ).and X-axis respectively. DD is the demand curve which establishes the relationship between price and quantity demanded. Here, the consumer is demanding 50kg Mango at the price Rs.5. When the price raised from Rs.5 to Rs.10 then quantity demanded decreases from 50kg to 30 kg. Similarly as price raised from Rs.10 to Rs.15 and quantity demanded decreases from 30Kg to 10Kg. Thus, Demand curve (DD’) is downward sloping due to the inverse relationship between price and quantity demand of a commodity.

 P (Price per unit) (Quantity demanded) 5 60 10 30 15 20 20 15

In the figure, price and quantity demanded are measured on Y-axis and X-axis respectively. DD is the demand curve which establishes the relationship between price and quantity demanded. Here, the consumer is demanding 60 kg rice at the price Rs.5. When the price raised from Rs.5 to Rs.10 then quantity demanded decreases from 60kg to 30 kg. Similarly as price raised from Rs.10 to Rs.15 and Rs.15 to Rs.20 quantity demanded decreases from 30Kg to 20Kg and 20kg to 15kg respectively. Thus, Demand curve (DD) is downward sloping due to the inverse relationship between price and quantity demand of a commodity.

Multi-variable Demand function

The mathematical relationship explaining the quantity demanded in terms of its various determinants, including income, the price of same goods and other goods, taste, preference and fashion of the consumer, size of population etc. Multi-variable Demand function.

For example: Qx = a – Px + Pm + Po + T
Where, Qx= Quantity demanded of apple, a= Autonomous Demand, Px = Price of apple, Pm = Price of mango, Po = Price of orange and T = Time dispersion.

Movement along the demand curve

Movement along demand curve itself explains the Law of demand. So, we can define Movement along the demand curve as “The state of increase or decrease in quantity demanded due to fall or rise in price remaining other factors constant or same. It explains how the price-quantity combination moves from one point to another in the same demand curve. In this curve price of any product change the demand of that product which has an inverse relation.

In the above figure, price and quantity demanded are measured in Y-axis and X-axis respectively. As there is a rise in price from P to P1 then the quantity decreases from Q to Q1 that changes the equilibrium point from E to E1 which indicates the contraction in demand. Likewise, there is fall in price from P to P2 then the quantity increases from Q to Q2 that changes the equilibrium point from E to E1 which indicates the expansion in demand. This change in equilibrium point E to E1 and E2 is called movement along the demand curve.

Shift in Demand curve

Shift in demand curve refers to the change in the position of the demand curve. The demand curve will shift either rightward or leftward. Rightward shift indicates more quantity demanded whereas Leftward shift indicates less quantity demanded due to non-price factor such as the size of the population, consumer tastes & preferences, Change in money supply, an income of consumer etc.

In the figure, Price and Quantity demand are shown in Y-axis and X-axis respectively. Here, price P remains constant for all level. Initially, D denotes supply curve which shows Q quantity demanded. An increase in demand shifts the demand curve to the right from D to D2. The rightward shifted demand curve D2 indicates that consumers are ready to purchase large quantities at constant prices due to change in other determinants of demand, say rise in income. A decrease in demand shifts the demand curve to the left from D to D1. The leftward shifted demand curve D1 indicates that consumers are willing to purchase fewer quantities at constant prices due to change in other determinants of demand, say fall in income.

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan

• Demand for a commodity is defined as the quantity demanded of that commodity which a consumer is willing and able to purchase at given market price for a specific period of time.
• A demand function states the relationship between two or more variables, such as price and physical quantities.
• Movement along the demand curve is the state of increase of decrease in quantity demanded due to fall or rise in price remaining other factors constant or same.
• Shift in demand curve refers to the change in the position of demand curve due to change in non-price factor.

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