Consumer Surplus formula

Consumer surplus for a commodity is the difference of the maximum price a customer can pay and the
actual price they eventually pay. Mathematically it can be expressed as:

Consumer Surplus = Maximum Price Willing - Actual Price Paid

Measuring consumer surplus

Consumer surplus can be measured using a demand curve which is a graphical representation of the
price of a product and its relationship with quantity of the product wanted at that price. Here price is
plotted on the Y axis and quantity on X axis.

Consider an example where for a particular product the marked price is $ 18. The demand
corresponding to this price is 20 units. However, because of its utility, customers are ready to pay as
high as $ 30 for this commodity.

Graphically this can be represented as:

Demand curve

The highlighted area in the graph signifies Consumer Surplus.

Consumer surplus = (1/2) * base * height

= (1/2) * 20 * (30-18) = $ 120

Applications

Consumer surplus formula is very helpful in evaluating the important economic decisions and their
impact on the pricing pattern of the people and economy as a whole. Following are its some important
applications:

Water Diamond complex

One of the great mysteries and the puzzle for economic experts has been why diamonds though not a
necessity but only a luxury is more expensive than water which by far is the most useful commodity
known to human life. Such was the complexity and confusion that economists started suggesting that
the market system that determines the prices of these contrasting commodities is inefficient and needs
adjustment. This scenario is known as Water- Diamond complex in economic papers.

Looking from the angle of consumer-surplus, this paradox can be solved. Since the actual supply of
water is huge, incremental benefit or in economic terms - marginal utility per unit of water for a
consumer is very low. However, for diamonds it’s all together a different case. The supply is restricted as
the actual amounts of diamond across the globe are limited and hence the marginal utility of diamond is
very high. The scenario can be generalized that when the actual quantity of a commodity is limited then
the marginal utility will be high even though its total utility might not be that great. Market price of a
commodity is determined not by its total use but by the marginal utility to its consumer. Here, the total
utility derived from water is much greater than that provided by diamonds, but its marginal utility is very
low. Hence the consumer surplus is large for water but very less for diamonds and this is why one is
cheaper and other ultra-expensive.

Determine gains or losses from indirect Taxes

Economists apply the concept of consumer-surplus to assess benefits and loss before implementing any
economic policies. The losses and advances from taxes as well as subsidies to a particular section of
society and its effect on the economy as a whole can be analyzed using notion of the demand curve and
consumer’s surplus derived from it.

Let’s consider a hypothetical example where a developing economy decides to impose an additional tax
of $ 5000 per car sold. This additional tax will result in the increased market price of cars for the
consumers. Now conforming to the fundamental law of demand and supply, the increased price will
lead to a fall in the unit of cars sold.

Because of the increase in cost and decrease in the number of cars sold, consumer surplus is reduced.
Mathematically it can be derived that this loss is greater than the increased revenue collected by the
authorities. This net loss in welfare or consumer surplus because of an increased tax collection received
by the Government is called as “dead weight loss” by the economists. This is the prime reason
economists round the globe consider indirect taxes like these as economically inefficient.

Estimating benefits and losses from subsidies

The concept of consumer surplus can be used to evaluate the net social benefit or gain from the
subsidies. Governments these days, provide subsidies on many commodities such as food-grains, farm
machinery, fertilizers, power etc. Let’s say the government decides to provide a subsidy on production
of food-grains and fertilizers which results in decrease in the production cost. This decrease in costs
results in fall in prices of food-grains for the end consumer. Conforming to the fundamental law of
demand and supply, this leads to an increase in the demand of food-grains and eventually results in a
gain in consumer surplus. This gain can be divided into 2 parts:

1 part – Increase in consumer surplus to those consumers who were already buying food-grains before
the subsidy was provided. Now these consumers would be able to buy the same quantity at a much
lower price. 

2 part - Increase in consumer surplus due to the increase in the demand of food grains as the consumers
which were initially not able to afford the food grains would also participate and buy them. This is
because of the lower price made possible by providing subsidies.

There is no free lunch and similarly there is a cost of every subsidy. To provide any subsidy, the
government must take a hit on the revenues. It has been calculated (through demand curve
calculations) that this cost of subsidy is much greater than the gain in consumer surplus. This should be a
lesson for governments who turn towards these short-term measures and impact the economy in the
long run.

Conclusion:

Consumer surplus formula find great application in the field of welfare economics. It can be used in
evaluating the impact of any government expenditure like national highways, flyovers or for any cost
benefit analysis for any project. Additionally, as we see earlier it can be used to formulate economic
policies like taxes and subsidies.