Consumer & Producer Surplus Example

Business Calculus · Axiom Academy

Calculating consumer and producer surplus in real markets Demand: p = 12 - 0.002q (price per pound consumers will pay) Supply: p = 2 + 0.001q (price per pound farmers require) Find consumer surplus, producer surplus, and total surplus. 2 Tech Gadget Market (Nonlinear) Demand: D(q) = 200 - q^2 (price in dollars) Supply: S(q) = 10 + 2q (price in dollars) Calculate surpluses using integration. Using quadratic formula: q* = 10 (taking positive root), p* = 100 The nonlinear demand curve D(q) = 200 - q^2 models diminishing marginal utility - consumers' willingness to pay drops more steeply as quantity increases. This is common for luxury or novelty items. Using the coffee market from Example 1: A price floor of 9/lb is imposed. Calculate the new surpluses. At p = 9, demand is 1500, supply is 7000. Only 1500 units trade. The price floor creates a deadweight loss of 7,250 - value that would have been created by trades that no longer occur. Consumers pay more for less, and some producers who could profitably sell can't find buyers. A market has equilibrium at q* = 50 units, p* = 80. Demand function: D(q) = 130 - q Supply function: S(q) = 30 + q Quick Method (Linear Functions) For linear demand and supply, surpluses form triangles: When both curves are linear, total surplus = ½ × base × height of the triangle formed between the curves. Here: ½ × 50 × (130 - 30) = 2,500. Based on the example above, which approach is correct?

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