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Lecture # 4 – More on Supply and Demand
I. Consumer Surplus
- Consumer surplus is the difference between what consumers are willing to pay for a good and what consumers actually pay when buying it. o Graphically, it is the area under the demand curve and above the market price. o From the experiment last Wednesday, it is the sum of all the net benefits consumers gained in a single round, as shown in the example on the following page. Using the equilibrium quantity of 14 and the average price of $21, we get a total consumer surplus of $77. o It can be calculated by finding the area of the triangle described above.
Consumer Surplus example from experiment
The detailed calculations are as follows. This example reviews how to solve for equilibrium and calculate consumer and producer surplus.
Demand: P = 100 – 2 Q Supply: P = 0.5Q
The equilibrium occurs where supply equals demand. Begin with the graph:
From the demand equation, we know that the y -intercept (on the price axis) for demand is $100. To see this, note that when Q is 0, the price would be $100. Similarly, in this example, the supply curve starts at the origin, as the y -intercept of the supply equation is
- Note that this won’t always be the case, but is here since there is nothing added to 0.5 Q in the supply equation.
To find the equilibrium price and quantity, we set supply and demand equal to each other and solve. Begin by solving for Q :
100 – 2 Q = 0.5 Q 100 = 2.5 Q Q = 100/2. Q = 40 To find the price, we substitute the equilibrium quantity into either the demand or supply equation: Either: P = 100 – 2(40) = $ Or: P = 0.5(40) = $ Making sure you get the same answer using either equation is a good way to check your work.
Q*
D
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P
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P*
Now that we know the equilibrium quantity and price, we have the information we need to calculate consumer and producer surplus.
Consumer surplus is the triangle below the demand curve and above the price (labeled CS below). Producer surplus is the triangle above the supply curve and below the price (labeled PS below).
The area of a triangle is 0.5 x base x height. For consumer surplus, the height of the triangle is 80 (= 100- 20), and the base is 40. Thus, the consumer surplus is 0.5(40)(80) = $.
For producer surplus, the height of the triangle is 20 and the base is 40. Thus, the producer surplus is 0.5(40)(20) = $.
D
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PS
We continue with a numerical example of a price floor.
In our policy example, the price floor is $40. Begin by adding the price floor to our graph:
Since the price floor is above the equilibrium price, there will be an excess supply – more producers will want to sell goods at $40 than consumers will demand. Thus, the new quantity demanded will thus be limited by the demand of consumers at $40 per hour, as shown on the graph above. Thus, to find the quantity, we simply substitute $40 for P in the demand equation, and solve for Q :
40 = 100 – 2Q 2 Q = 60 Q = 60/ Q = 30
D
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QPF
With this information, we can now observe how consumer and producer surplus changes after the price floor. The graph appears below.
Consumer Surplus Before the price floor, consumer surplus was everything above the original $20 price and below the demand curve. This is areas A, B and C above. As calculated before, this equals $.
After the price floor, consumer surplus is everything below demand and above the price of $40. This is area A. This is a triangle with a height of 60 (= 100 - 40) and a base of
- Its area = 0.5(30)(60) = $.
Producer Surplus Before the price floor, producer surplus was everything below the original $20 price and above the supply curve. This is areas D, E and F above. As calculated before, this equals $.
After the price floor, the producer surplus includes the rectangle B and D , as well as the triangle F. To find the area of the rectangle, we need to know the value of the bottom line. This is the price at which suppliers would make 30 units of the good available. Plugging 30 into supply gives us 0.5(30) = 15. Thus, this rectangle has a height of 25 (= 40-15) and a width of 30. Its area = (25)(30) = $750. The triangle F has a height of 15 and a base of 30. Its area = 0.5(30)(15) = $225. The total producer surplus is the sum of these two areas, $750 + $225, which equals $.
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