Question

a. Draw the graph for the market demand curve for the 3 following demand curves:

Individual 1: q₁=20−P/2

Individual 2: q₂=5−P/2

Individual 3: q₃=5−P

b. Obtain the consumer surplus for individuals 1, 2, and 3 separately using their individual demand curves for P=$4

c. Add the three consumer surpluses. Then confirm that you get the same answer for CS using the market demand curve you have drawn in part a.

d. Repeat the exercise but now for a price of $8. Which of the three individuals stops buying as a result of this price increase?

Answer 1

The market demand curve can be obtained be adding the individual demand curves.

q₁=20-P/2. The demand for individual 1 has been plotted in figure 1 in red color.

q₂=5-P/2. The demand for individual 2 has been plotted in figure 1 in blue color.

q₃=5-P. The demand for individual 3 has been plotted in figure 1 in green color.

When price is greater than 5, individual 3 does not demand anything because the price is too high for him and the market demand equals summation of individual 1 and 2’s demand curve.

When price is more than 10, both individual 1 and 2 will not buy anything and the market demand will be just individual 3’s demand.

The market demand curve is given by:

Market demand curve has been plotted in figure 1 in black highlight.

Figure 1

b) consumer surplus for individual 1= area above the price line and below the demand curve = ½* (40-4) *18 = 324

consumer surplus for individual 2 = area above the price line and below the demand curve = ½ * (10-4) * 3 = 9

consumer surplus for individual 3 =area above the price line and below the demand curve = ½ *(5-4) * 1 = 0.5

c) Total consumer surplus = 324+9+0.5 = 333.5

Consumer surplus under the market demand = ½ * (40-10) * 15 + (10-4)*(15) + ½ *(10-5) * (20-15) + (5-4) (20-15) + ½ *(5-4) (22-20) = 225+90+12.5+5+1=333.5

Therefore, they are equal.

d) When P =$8, the individual 3 does not demand anything.

Consumer surplus of individual 1 = ½ *(40-8) *16 =256

Consumer surplus of individual 2 = ½ *(10-8) *1 = 1

Total consumer surplus = 256+1 = 257

Market consumer surplus == ½ * (40-10) * 15 + (10-8)*15 + ½*(10-8)*(17-15) = 225+30+2=257

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