Consumer And Producer Surplus

Economics 101 Dr. Smith

Consumer and Producer Surplus How can we determine if an economic policy (a tax, promoting free trade, a price floor, etc.) is “good” or “bad”? Specifically, do we have any objective way of evaluating the economic impact of a policy on the market(s) that it affects? The answer, of course, is yes – we do have tools that would aid us in performing this type of analysis. In fact, one of the most useful tools we have is something known as Consumer Surplus. (We will also develop the producer’s analog to consumer surplus – Producer Surplus.) In order to understand consumer surplus, let’s begin by looking at the market for compact discs. The market demand and supply functions are given by the equations below: Qd = 1000 − 50 P Qs = −200 + 50 P Let’s graph these equations, but first let’s turn the demand and supply functions into inverse demand and inverse supply functions. Inverse Demand:

P = 20 − 501 Q

Inverse Supply:

P = 4 + 501 Q

Now, let’s form the graph: P 20 S

12

D 400

1000

Q

You will notice that I have labeled the market equilibrium – the equilibrium price is $12 and the equilibrium quantity is 400. How did I find the equilibrium? Set demand equal to supply! In equilibrium, set Qd = Qs So,

1000 − 50 P = −200 + 50 P

And

1200 = 100 P

P* = 12

Q* = 1000 − 50(12) = 400

Now, let’s turn our attention to the concept of consumer surplus. We will begin with the definition: Consumer Surplus – Consumer surplus is the difference between what a consumer(s) would have been willing to pay for a certain quantity of a good, and what that consumer(s) actually had to pay. To get a firm grasp of what consumer surplus is all about, let’s return to our CD example. If we use our demand function, then we may determine what a consumer would have been willing to pay for the first CD sold in the market - $19.98. Where does this figure come from? P = 20 − 501 Q If Q is equal to one, then: P = 20 − 501 (1) = 20 − 0.02 = 19.98 Therefore, for the first CD a consumer is willing to pay $19.98. What did that consumer actually have to pay? The equilibrium price of $12! Therefore, the consumer who was willing to pay $19.98 is able to enjoy a “surplus” of $7.98 (the difference between what they were willing to pay $19.98, and what they had to pay $12.) The important thing to notice is that there will be surplus of this sort associated with every CD sold except the very last one! (The 400th.) How can we calculate the total consumer surplus that is being enjoyed by consumers in the compact disc market? Well, the easiest way to do this is to return to our graph…

P 20 S

12

D 400

1000

Q

I have colored in two areas on our graph. Let’s think about what these areas represent. First, let’s begin with the red rectangle. The red rectangle has height of 12 (the equilibrium price) and width of 400 (the equilibrium quantity). Therefore, the area of the red rectangle represents the total amount consumers had to spend to buy 400 compact discs. Remember, though, that the consumers would have been willing to pay more than the red rectangle in order to acquire the 400 compact discs. How much would consumers have been willing to pay? The demand curve gives us our answer. At any quantity we choose the demand curve tells us how much consumers would have paid in order to acquire that CD. Therefore, the total willingness to pay for compact discs is given by the area underneath the demand curve. In our example, consumers’ total willingness to pay is represented by the red rectangle added to the blue triangle. So, this brings us back to our key question. How can we calculate the total consumer surplus in this market? We simply need to perform the following calculation: Consumer surplus = (Consumers’ total willingness to pay for Q* units; the blue triangle added to the red rectangle) – (What consumers actually had to pay for Q* units; the red rectangle) CS = (Red Rectangle + Blue Triangle) – Red Rectangle = Blue Triangle Specifically,

CS = 12 ⋅ (400) ⋅ 8 = 1600 Now, let’s look at Producer Surplus. Producer Surplus – Producer surplus is the difference between what a producer(s) received when supplying a certain quantity of a good, and what the producer(s) would have been willing to accept for that quantity of the good. Graphically, P 20 S

12

4

D 400

1000

Q

So, what do our colored areas represent in this instance? The purple trapezoid and the green triangle should be familiar to us, for when we add them together we have a rectangle of height 12 and base 400. In other words, the purple trapezoid and the green triangle represent the total amount the producers received from selling 400 compact discs. However, we will find that they would have been willing to accept less than this in order to provide the 400 discs. How much would they have been willing to accept? For the first compact disc a firm would have been willing to accept $4.02 – let’s check to see where that figure is coming from: P = 4 + 501 Q If Q is equal to one, then: P = 4 + 501 (1) = 4 + 0.02 = 4.02

Therefore, the amount that producers needed in order to be willing to supply 400 discs is given to us by the area under the supply curve! (The purple trapezoid.) To calculate producer surplus: Producer surplus = (What producers received for Q* units; the purple trapezoid added to the green triangle) – (What producers would have been willing to accept for Q* units; the purple trapezoid) PS = (Purple Trapezoid + Green Triangle) – Purple Trapezoid = Green Triangle Specifically, PS = 12 ⋅ (400) ⋅ 8 = 1600 To see how we use these concepts take a look at the problems on Problem Set 2!