# Calculating Consumer Surplus Given Table

Can someone help me? The answer is supposed to be 36 but I have no idea how they got that answer. Can someone explain why consumer surplus is 36 in this instance? Thanks!

Refer to Table below. If the price is four dollars but only six units are exchanged in the market, consumer surplus will be? [Hint: Both the supply curve and the demand curve are linear]

Edit: Shouldn't the equation be (1/2)* 8 * 6 = \$24? The key to this is in the hint. It lets you know supply and demand are both linear, so you need to figure out what the functions of those two curves are. In this case, you have

$$Q_D = 18 - 1.5P$$ $$Q_S = 3P$$

Plot these on a supply/demand graph (P on the vertical axis, Q on the horizontal), and the consumer surplus is the shaded area (note, it stops at Q=6 because only 6 units were traded in the question): Using the formula for the area of a trapezoid, we have:

$$CS = \frac{1}{2} [(12-4)+(8-4)]*6 = 36$$

• The supply curve in the image is a little off! it should start at the origin as it does, but then cross demand at (Q = 12, P = 4), sorry about that! Dec 11 '20 at 23:17
• Great, that makes alot of sense now. Thank you so much! Dec 12 '20 at 1:11