Question

1. Consider a private supply and private demand that are both linear with the table representing some of the values from those graphs. Assume that the good produced in this market causes $6/unit of damage to people in the economy.

Private Demand                                           Private Supply

P         Q         P         Q                                 P         Q                     P         Q

$40     0          $20     10                                $10     0                      $20     10

$36     2          $16     12                                $12     2                      $22     12

$32     4          $12     14                                $14     4                      $24     14

$28     6          $10     16                                $16     6                      $26     16

$24     8          $8       18                                $18     8                      $28     18

a) Draw a picture of the private supply and private demand. At equilibrium calculate the Consumer Surplus, Producer Surplus and total damage done at the equilibrium price and quantity. (2 points)

b) Assume that, instead of the equilibrium, the market is producing a quantity of 8 at a price of $24. Recalculate the Consumer surplus, producer surplus, at total damage at this new price and quantity. Show that Cons. Surplus + Prod. Surplus – Total Damage is bigger at this new P and Q than at equilibrium. (3 points)

c) Calculate a new table for Social Supply and use that to explain why Q = 8 is the efficient quantity for the economy. Draw a new picture with private supply, private demand, and Social supply consistent with this explanation. (2 points)

Answer 1

a. CS= area of slanted shaded area= 1/2*10*20=100

PS= area of vertically shaded area= 1/2*10*10= 50

Damage=$6* equilibrium quantity= 6*10=$60

b. CS= 1/2*8*16=64

PS=1/2*8*(14+8)=88

Total damage= 8*6=48

Consumer surplus+producer surplus-total damage at new price and q is 64+88-48= 104

while Consumer surplus+producer surplus-total damage at equilibrium is 100+50-60= -10

c. Social supply will take into account the damage done into the prices. So social supply will list the same quantities as before in the supply but the price will be old price plus 6.

Social supply

P Q

16 0

18 2

20 4

22 6

24 8

26 10

28 12

30 14

32 16

34 18

Since the producer must take into consideration the damages it does to the society to arrive at the true value else it would be supplying more than what is efficient for the society. So the scale curve will take the damages into the prices for the good. Hence the social supply curve will shift to left as shown in the figure.