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In a free market, consumer surplus is the difference between the maximum price a consumer is willing to pay for a good or service and the actual price they pay. Producer surplus is the difference between the minimum price a producer is willing to accept for a good or service and the actual price they receive.

Deadweight loss occurs when there is a distortion or inefficiency in the market, resulting in a smaller combined total of consumer and producer surplus. This typically happens when market forces do not reach equilibrium due to factors such as taxes, subsidies, or price floors/ceilings.

To understand deadweight loss, we first need to consider a demand curve (D) and a supply curve (S) in a graph, where the X-axis represents the quantity of goods and the Y-axis represents the price. In a free market, the demand and supply curves intersect at a point known as the equilibrium point (E), where the market price (P) and the quantity of goods exchanged (Q) are determined.

Let's now introduce a tax imposed on the good. When a tax is added, the supply curve shifts upward by the amount of the tax. This is because producers now require a higher price to cover the cost of the tax. The new supply curve (S') intersects the demand curve at a new point (E'), resulting in a higher price paid by consumers (Pc) and a lower quantity exchanged (Q').

Due to the tax, both consumer and producer surplus have decreased. The deadweight loss is the decrease in total surplus as a result of market distortion. To calculate the deadweight loss, we can find the area of the triangle formed by the original supply curve (S), the new supply curve (S'), and the demand curve (D) between the original and new quantity exchanged (Q and Q'). The area of this triangle represents the loss in surplus that is not recovered by the tax revenue. In summary, deadweight loss is the reduction in total consumer and producer surplus due to market inefficiencies or distortions such as taxes or subsidies. It is graphically represented as the area of the triangle formed by the intersection of supply and demand curves and their shifts, reflecting the loss of surplus not recovered by the market distortion.