Please help with this math economic problem =(?

Question

suppose demand function for a product is

D(q)= -0.02q+52

find consumer surplus correspond to q = 1400 units

also have a hint that say:do not round the results until end of calculation, at that point round to nearest tenth if necessary. It may help to sketch the demand curve which cross horizontal at q = 2600.

I have been stuck on this for a long time, and not sure what to do thanks!

Answer 1

Consumer surplus is area above price line and below demand line. So you will need to find area of triangle limited by points:

[A] Q=0 ; P=52,

[B] Q=1400 ; P= -0.02*1400 + 52 = 24 , and

[C] Q=0 ; P=24.

Area of triangle will be length of line AC multiplied by length of line BC and divided by 2, thus

AC = 52 - 24 = 28

BC = 1400 - 0 = 1400

AC*BC/2 = 28 * 1400 / 2 = 19'600

So consumer surplus is 19'600.

Answer 2

Ok you have a supply of 1400 units and according to the demand function, the demand for these units is equal to: -.02(1400)+52

which equals -28 + 52 and simplifys to 24.

Well if you have a supply of 1400 and a demand for only 24, is it not clear that you will have a surplus of 1400 -24 which = 1376?

Consider the other point that the graph crosses the x axis when

q = 2600.   "Pluggin in" 2600 for q in the demand function, we obtain

-.02(2600) + 52 = -52 + 52 = 0.  In terms of a graph the demand functons produces the ordered pair (2600,0) whose geometric representation is a point on the x-axis.  Clearly we see that when

q = 2600, D(q) = 0

I hope this helped....not sure it was in time, but I just ran across your problem today.

Good Luck....and remember MATH RULES !!!  sine qua non

that's Latin, check out the translaton