5.1 Copyright © 2014 Pearson Education, Inc. An Economics Applications: Consumer Surplus and Producer Surplus OBJECTIVE Given demand and supply functions, find the consumer surplus and the producer surplus at the equilibrium point.

Slide 5- 2 Copyright © 2014 Pearson Education, Inc. CONSUMER SURPLUS

Slide 5- 3 Copyright © 2014 Pearson Education, Inc. DEFINITION: Suppose that p = D(x) describes the demand function for a commodity. Then, the consumer surplus is defined for the point (Q, P) as 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide 5- 4 Copyright © 2014 Pearson Education, Inc. Example 1: Find the consumer surplus for the demand function given by When x = 3, we have Then, 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide 5- 5 Copyright © 2014 Pearson Education, Inc. Example 1 (concluded): 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide 5- 6 Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 1 Find the consumer surplus for the demand function given by Finding Then, consumer surplus is:

Slide 5- 7 Copyright © 2014 Pearson Education, Inc. PRODUCER SURPLUS

Slide 5- 8 Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 1 Concluded

Slide 5- 9 Copyright © 2014 Pearson Education, Inc. DEFINITION: Suppose that p = S(x) is the supply function for a commodity. Then, the producer surplus is defined for the point (Q, P) as 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. Example 2: Find the producer surplus for When x = 3, Then, 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. Example 2 (continued): 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 2 Find the producer surplus for When Then,

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 2 Concluded

Slide Copyright © 2014 Pearson Education, Inc. DEFINITION: The equilibrium point, (x E, p E ), is the point at which the supply and demand curves intersect. It is that point at which sellers and buyers come together and purchases and sales actually occur. 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. Example 3: Given find each of the following: a) The equilibrium point. b) The consumer surplus at the equilibrium point. c) The producer surplus at the equilibrium point. 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. Example 3 (continued): a) To find the equilibrium point, set D(x) = S(x) and solve. Thus, x E = 2. To find p E, substitute x E into either D(x) or S(x) and solve. 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. Example 3 (continued): If we choose D(x), we have Thus, the equilibrium point is (2, $9). 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. Example 3 (continued): b) The consumer surplus at the equilibrium point is 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. Example 3 (concluded): c) The producer surplus at the equilibrium point is 5.1 An Economics Application: Consumer Surplus and Producer Surplus

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 3 Given find each of the following. Assume a.) The equilibrium point b.) The consumer surplus at the equilibrium point c.) The producer surplus at the equilibrium point

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus a.) To find the equilibrium point, set and solve. Through the quadratic formula, we see that Since we assume that, we know that To find substitute into either or and solve. Quick Check 3 Continued

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 3 Continued If we choose we have So the equilibrium point is

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 3 Continued b.) The consumer surplus at the equilibrium point is

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Quick Check 3 Concluded c.) The producer surplus at the equilibrium point is

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Section Summary A demand curve is the graph of a function which represents the unit price a consumer is willing to pay for items. It is usually a decreasing function. A supply curve is the graph of a function which represents the unit price a producer is willing to accept for items. It is usually an increasing function.

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Section Summary Continued Consumer surplus at point is defined as Producer surplus at point is defined as

Slide Copyright © 2014 Pearson Education, Inc. 5.1 An Economics Application: Consumer Surplus and Producer Surplus Section Summary Concluded The equilibrium point is the point at which the supply and demand curves intersect. The consumer surplus at the equilibrium point is The producer surplus at the equilibrium point is