Supply Function and Law of Supply

Supply Function And Equation:
A supply function is a mathematical expression of the relationship between quantity demanded of a product or service, its price and other associated factors such as input costs, prices of related goods, etc.A supply function has single dependent variable (i.e. the quantity supplied) and many independent variables i.e. market price, price of related goods, input costs, etc. A supply equation can be formulated by studying the relationship between supply (the dependent variable) and the independent variables and determining whether the relationship is positively-related or negatively-related. For example, in general the supply and market price are inversely related. The same is the case with supply and input prices i.e. at higher input prices, supply is lower. On the other hand, supply and technological progress are inversely related, i.e. better technology means more supply, etc.

A supply function can be used to find out the expected quantities of a product which will enter the market if we know the market price, input costs and other variables. If we have a demand function and supply function for a market, we can solve them to find out the equilibrium price (i.e. the market clearing price) and the equilibrium quantity.

It explains the relationship between the supply of a commodity and the factors determining its supply. We can better represent the supply function in the form of the following equation:

Sx = f (Px, PI, T, W, GP)

Where,
Sx = supply of commodity x
Px = Price of commodity x
PI = Price of inputs
T = Technology
W = Weather conditions
GP = Government Policy

Law Of Supply:
Law of supply expresses a relationship between the supply and price of a product. It states a direct relationship between the price of a product and its supply, while other factors are kept constant.
For example, in case the price of a product increases, sellers would prefer to increase the production of the product to earn high profits, which would automatically lead to increase in supply.
Similarly, if the price of the product decreases, the supplier would decrease the supply of the product in market as he/she would wait for rise in the price of the product in future.

The law of supply is a basic micro-economic concept that states that price and quantity supplied are directly related. Thus, when the price of a product increases, the quantity supplied increases. Equally, when the price of a product decreases, the quantity supplied decreases. This is always true as long as its assume that all factors affecting supply remain equal (ceteris paribus).

Assumptions in Law of Supply:
The law of supply expresses the change in supply with relation to change in price. In other words the main assumption of law of supply is that it studies the effect of price on supply of a product, while keeping other determinants of supply at constant.

Apart from this, there are certain assumptions that are necessary for the application of law of supply, which are as follows:

i. Assumes that the price of a product changes, but the change in the cost of production is constant. This is because if the cost of production rises with increase in price, then sellers would not supply more due to the reduction in their profit margin. Therefore, law of supply would be applicable only when the cost of production remains constant.

ii. Assumes that there is no change in the technique of production. This is because the advanced technique would reduce the cost of production and make the seller supply more at a lower price.

iii. Assumes that there is no change in the scale of production. This is because if the scale of production changes with a period of time, then it would affect the supply. In such a case, the law of supply would not be applicable.

iv. Assumes that the policies of the government remain constant. If there is an increase in tax rates, then the supply of product would decrease even at the higher price. Therefore, for the application of law of supply, it is necessary that government policies should remain constant.

v. Assumes that the transportation cost remain the same. In case the transportation cost reduces, then the supply would increase, which is invalid according to the law of supply.

vi. Assumes that there is no speculation about prices in future, which otherwise can affect the supply of a product. If there is no speculation about products, then the economy is assumed to be at balance and people are satisfied with the available products and do not require any change.

Supply Schedule:
Supply schedule represents the relationship between prices and the quantities that the firms are willing to produce and supply. In other words, at what price, how much quantity a firm wants to produce and supply.
Suppose the following is an individual’s supply schedule of bananas:

Price Per Dozen ($)	Quantity Supplied (in dozens)
4	3
6	6
8	9
10	12
12	13

Supply Curve:
Supply curve is the graphic representation of the relationship between product price and quantity of product that a seller is willing and able to supply. Product price is measured on the vertical axis of the graph and quantity of product supplied on the horizontal axis.
The supply curve will move upward from left to right, which expresses the law of supply: As the price of a given commodity increases, the quantity supplied increases (all else being equal).
Note that this formulation implies that price is the independent variable, and quantity the dependent variable. In most disciplines, the independent variable appears on the horizontal or x-axis, but economics is an exception to this rule.