Question

This question is about producer surplus and consumer surplus.

(a) Given a linear demand curve, if domestic consumption changes by 10%, does consumer surplus also change by 10%? Why or why not? What is the relationship between change in domestic consumption and consumer surplus? Start with an algebraic form of a demand curve and to answer the question.

(b) Is there a difference between producer surplus and profit? Explain.

Answer 1

(a) Given, the demand curve is linear. Suppose the demand curve is , where the intercept is a. Suppose that the equilibrium quantity is q, and hence the equilibrium price will be or , where p is the equilibrium price. The domestic consumption is q. The consumer surplus will be the area of the triangle between the demand curve, P-axis and equilibrium price line, where the base will be q and the height will be (since a was the intercept of demand curve on P-axis), ie or . Hence, the consumer surplus will be as , ie or . The change in consumption q will change the CS as , ie or . The percentage change can be founded as (and is quite analogous to elasticity measures) or or or . Hence, for a 10% change in q, the change in CS would be double, ie 20%.

(b) The prodfit is the difference between total revenue and total cost, ie . But TC is divided into variable and fixed cost, ie . Hence, the profit will be or . But the area below the supply curve only attributes to the variable cost, and hence the total revenue can be stated as , as area above the supply curve and below the equilibrium price line is the producer surplus. Thus, . Since, , we have . hence, the profit and PS would be only same for no fixed cost. The existence of fixed cost implies that profit is less than the PS by the TFC.