What is Demand and Supply Function?

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.   

Demand

Demand for a good or a commodity means to the amount of the commodity which the consumer is willing to purchase and are able to purchase during a given period of time at the prevailing market price or at the given price.

There are various factors that determine the demand for a commodity:  

• Price of the commodity: One of the most important factors that determine the demand for a commodity is the price of the commodity itself. Usually, there is an inverse relationship between the price of the commodity and its quantity demanded. This implies that lower the price of a commodity, larger will be the quantity demanded of the commodity. Similarly, we can say that higher the price of the commodity, lower will be the quantity demanded.  
• Income of the consumer: This is one of the basic determinants of the demand for a commodity. It states what kind of purchasing power the consumer is having or what income does the consumer earns in order to purchase some particular kind of commodity. The relationship between the income of the consumer and the demand of the commodity varies between different types of goods.
• Taste and preference of the consumer: The demand level of the consumer is influenced by what kind of taste and preference the consumer has in store. It depends mainly on the social customs, habits of the people, fashion and the general lifestyle that the people lead.

What is the Demand Function? 

The function which shows the relationship between the determinants or factors influencing the demand of an economic good is known as the demand function. In case of determining the elasticity of demand or even the equilibrium of the market (or market equilibrium) which involves knowing the equilibrium price of the economic commodity that needs to be bought and sold, the demand function plays a very important role.

Symbolically it can be written as:  

D_x = f (P_x , Y, T, E, H, G......)  

From the above equation it can be said that D_x  is the demand for a particular commodity X, f represents the functional relationship between the demand of the economic commodity X and the determinants which influence the demand for that economic commodity. P_x is the price of the commodity X, Y is the income of the consumer, T is the pay stamp reference, H indicates the science of the population, E stands for the expectation of rise or fall in the prices of the economic good in a particular period of time.

Since it is known that the demand curve of an economic commodity shows the demand function of that particular commodity, it is also important to note that the quantity demanded or the amount of an economic good which is demanded in an economy by the population of the economy in a given period of time largely depends upon the determinants of demand which includes the income of the consumer, the taste and preference of the individual who is actually demanding the economic good, the size of the population as because the market demand and consequently the market equilibrium of the economy will be determined of how many individual is actually purchasing the commodity and many other factors which influence the demand of the economic good. It can also be indicated that the pictorial representation of the demand function is known as the demand curve which is generally negatively sloped showing that for example the price of a commodity and the demand of an economic commodity are negatively related. Similarly, if a demand curve is expected to show the relationship between the income of a consumer and the demand of an economic good which is considered to be a normal good, the demand curve is positively sloped because it is expected that if income of an individual is increased, the demand for goods and services are also supposed to increase if it is a normal good, which means that it is an upward-sloping curve in this case.

Supply

Supply of a commodity means or refers to the quantity of a commodity which suppliers or producers or sellers are willing to produce and offer to sale at a particular price prevailing in the market during a particular period of time.

Following are some of the factors that determine supply of a commodity:

• Price of the commodity: One of the most important factors that determine the supply for a commodity is the price of the commodity itself. All other things containing constant, larger quantity of a commodity will be supplied at a higher price and smaller will be the quantity supplied if the price of the commodity is lower. This is because of the fact that the higher price will lead to higher profit of the supplier and vice versa.
• Prices of raw materials: Another important factor which influences the level of supply of a commodity is the prices of the raw materials that are being used in the production process or the prices of the factors of production. It is very natural that if the producers have to pay higher prices in order to secure the factors of production or the raw materials, the cost of production will be higher and ultimately the price of the commodity on which it will be sold in the market will also be higher because the goal of the supplier or the producer is always to maximise the profit. 
• Techniques of production: The technique of production used in a production process is having an extremely important influence of the supply of the commodity. If the technique used in the production process is improved then it increases the profit margin and lowers the cost of production. 

What is the Supply Function?

Supply function is the functional relationship between the amounts of an economic good supply in a particular period of time with respect to the determinants that influence the supply of the particular economic good. The determinats can be either the price of the commodity or the price of the input or other factors which form an important determinant of supply of an economic commodity. 

Supply curve

S_x = f ( P_x , T, E, N....) 

The above equation represents the supply of a particular economic commodity which is X as the functional relationship between the price of the economic commodity, the technique of production, the expectation of the future prices, the natural factors and many other determinants which influence the supply of a commodity. 

The supply curve also plays an important role because it is the pictorial representation of the supply function. The supply function is generally positively sloped line because more or less the determinant of supply of a commodity and the actual supply in a given period of time of that particular economic commodity are positively related. For example, the technique of production and the supply of the economic commodity are positively related because if the technique of production increases or gets improved from time to time the supply of the commodity or the economic commodity will automatically increase. Hence, this portrays a positive relationship between the actual supply of the commodity and the determinants which influences supply of the commodity. 

Equilibrium

The quantity of a particular commodity demanded or supplied also determines the market equilibrium or the equilibrium of prices and commodity which is actually bought and sold in a market by the buyer and the supplier respectively. Economic models, the equilibrium price and the equilibrium quantity of a particular good is determined by the supply curve and the demand curve. The particular point at which the supply curve intersects the demand curve is known to be the equilibrium. From this point the desired amount of commodity is calculated or evaluated which needs to be sold and also the equilibrium price is determined at which the consumer will complete the action of purchase and sell or it can be said that the economic activity of trade is completed in the market. For evaluating the equilibrium point, the demand function and supply function are extremely important as the slope of the demand curve and the supply curve determines the market equilibrium to some extent. 

Context and Applications:

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for      

• Bachelor of Science in Mathematics
• Master of Science in Mathematics