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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?

enter image description here

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  • $\begingroup$ Given the demand and supply schedules, equilibrium in a free market is to exchange 12 units at price 4. If only 6 units are exchanged, then presumably the market is not entirely free, but we are not told what is preventing exchange of 12 units.. Suppose that demand is the sum of the individual demands of several people, and that only 6 units are exchanged because some of those people are not allowed to buy the good. To find the consumer surplus we would need to know the demand schedule for those who are allowed to buy it, and the answer could easily be less than 36. $\endgroup$
    – Adam Bailey
    Mar 25, 2022 at 20:00

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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):

Supply/Demand Graph

Using the formula for the area of a trapezoid, we have:

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

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  • $\begingroup$ 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! $\endgroup$
    – Amaan M
    Dec 11, 2020 at 23:17
  • $\begingroup$ Great, that makes alot of sense now. Thank you so much! $\endgroup$
    – Komi Alasse
    Dec 12, 2020 at 1:11

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