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## Learning Objectives

• Subsidy: Basic Concept
• Analysis of consumer surplus and producer surplus with subsidy
• Elasticity and Subsidy

## Subsidy: Basic Concept

A subsidy is a sum of money granted by the state or a public body to help an industry or business keep the price of a commodity or service low[1]. It is a negative or reverse tax. Instead of collecting money in the form of a tax, the government gives money to consumer or producers. Governments generally provide it to those industries that produce socially desirable goods and/or services.
Subsidized goods and/or services are sold at a lower price in the marketplace, which benefits the buyer, and on the other hand, lower cost of production keeps suppliers in better off position. Hence, it is the difference between the price paid by the buyer and the cost incurred by the supplier.
In the figure, X-axis measures Quantity and Y-axis measures Price. Initially, the firm was at equilibrium at E with Quantity 'Qe' and Price 'Pe', where the Demand curve (D) and Supply curve (S) intersected with each other. When the government provides a subsidy to the firm, the supply curve shifts from 'S' to 'Ss'. The shift in the supply curve will shift the equilibrium position of the firm from 'E' to 'E1'. The quantity a with a subsidy is 'Qs', which is greater than 'Qe'. Similarly, the cost of a subsidy is obtained by multiplying the 'quantity' of goods and/or services produced and the per unit of subsidy. The portion in the 'sky-blue' color is 'the cost of the subsidy'.

A subsidy is the transfer payment by the government to the consumers and producers for the production of socially beneficial goods and/or services. It provides an incentive to the producer to produce more as it reduces the cost of production and it provides an incentive to the buyer as it increases the purchasing power of the consumer. As a result, it increases the volume of production of goods and/or services, which results in wasteful trade. Hence, the excess production that is not desired by society results in a dead-weight loss. The dead-weight loss due to subsidy can be illustrated by the figure.
Figure 2 clearly presents the dead-weight loss resulted due to the subsidy. As the supply curve shifted from S to SS, the production increased from Qe to QS. Due to the impact of subsidy, the price for the buyer has decreased to PB and the price to the supplier has increased to PS. On those additional units, the cost to the suppliers supplying those units exceeds the value to demanders of those units.
In other words, at Qs, the benefit the buyer will derive is less than the price the supplier is willing to accept. Hence, the portion in the red color is the dead-weight loss. We will deal with why the red portion in Figure 2 is dead-weight loss in the next section.

## Analysis of consumer surplus and producer surplus with subsidy

Consumer surplus is the difference between what the producer is willing to charge for a good and the actual payment made by the buyer.
According to Marshall (1890), "Excess of the price that a consumer would be willing to pay rather than go without a thing over that which he actually pays."
Producer surplus is the difference between the price of the product or the buyer's payment for the payment and the marginal cost.  There is a trade-off between consumer surplus and producer surplus, that is, if a producer is able to charge a higher price to the consumer, then producer surplus exceeds consumer surplus, else the consumer surplus exceeds producer surplus.
Figure 3 clearly illustrates the consumer and producer surplus associated with the subsidy. The blue color in the left is the consumer surplus and the area in purple color in the right figure is the producer surplus. So, the subsidy increases both consumer surplus and the producer surplus.

## Elasticity and Subsidy

Elasticity has a negative association with the subsidy. The higher elasticity of supply, the lower benefit of subsidy to the supplier and vice-versa. In tax, elasticity is 'Escape', but it is just reverse in subsidy. The inelastic supply signifies that there are very few suppliers. To understand it, let us move to perfect competition.
We often wonder, why is the demand curve of a firm in perfect competition is horizontal or perfectly elastic? The simple answer is 'the presence of a large number of buyers and sellers'. Likewise, inelastic supply curve implies that there are few sellers in the market. So, the few sellers can enjoy more portion of the subsidy. But in case of a tax, few sellers shall bear a significant amount of tax, mean that the per-head tax for an individual seller is high.
Figure 4(A) and Figure 4(B) depicts why elasticity matters. If the supply curve is elastic keeping the elasticity of demand constant, then the firms derive more benefit from the subsidy, which is apparent through Figure 4(A). Likewise, if the supply curve is inelastic keeping the elasticity of demand constant, then the firms derive less benefit from the subsidy as in Figure 4(B).
Hence, the distribution of benefit from the subsidy among the producer and the consumer depends on the elasticity of demand and supply. 'Inelastic' derives more benefit from the subsidy.

## Our articles related to Economics

Difference between Economic and Econometric Model
Models in Economics: Meaning, Importance, and Limitation
Tax: Concept, Dead-weight loss, and implications

Ahuja. H.L. (1970). Advanced Economic Analysis: Microeconomic Analysis. New Delhi: S. Chand & Company Pvt. Ltd.
Kutosoyiannis, A. (1979). Modern Microeconomics. Houndsmill: Macmillan Press Ltd.
Varian. H.R. (2010). Intermediate Microeconomics - A Modern Approach. W W Norton & Company: New York.