Question

1. Calculate consumer surpluses for the following demand functions and prices:

a. D:Q^D=30-5p^D;P*=2

b. D:Q^D=20-4P^D;P*=3

1b. Calculate producer surpluses for the following supply functions and prices:

a. S:Q^s=-3+P^s;P=6

b. S:Q^s=-12+3P^s;P*=10

Answer 1

Q.1

a) Q = 30 - 5P

Maximum price consumers are willing to pay : Put Q = 0,

0 = 30 - 5P

P = 30/5 = 6

$6 is the price which consumers are willing to pay maximum.

Equilibrium price is $2.

and equilibrium output is : Q = 30 - 5(2) = 30 - 10 = 20

Thus consumer surplus is ;

CS = 1/2 * (maximum price consumers willing to pay - equilibrium price) * equilibrium output.

CS = 1/2 * (6-2) * (20) = 40

b) Q = 20 - 4P

Maximum price consumers are willing to pay : Put Q = 0,

0 = 20 - 4P

P = 20/4 = 5

$5 is the price which consumers are willing to pay maximum.

Equilibrium price is $3.

and equilibrium output is : Q = 20 - 4(3) = 20 - 12 = 8

Thus consumer surplus is ;

CS = 1/2 * (maximum price consumers willing to pay - equilibrium price) * equilibrium output.

CS = 1/2 * (5-3) * (8) = 8

Q.1b

a) Q = -3 + P

Minimum price sellers are willing to accept: Put Q = 0,

0 = -3 + P

P = 3

$3 is the price which sellers are willing to accept at minimum.

Equilibrium price is $6.

and equilibrium output is : Q = -3 + 6 = 3

Thus producer surplus is ;

PS = 1/2 * (minimum price sellers willing to accept - equilibrium price) * equilibrium output.

PS = 1/2 * (6-3) * (3) = 4.5

b)

Q = -12 + 3P

Minimum price sellers are willing to accept: Put Q = 0,

0 = -12 + 3P

P = 4

$4 is the price which sellers are willing to accept at minimum.

Equilibrium price is $10.

and equilibrium output is : Q = -12 + 3(10) = 18

Thus producer surplus is ;

PS = 1/2 * (minimum price sellers willing to accept - equilibrium price) * equilibrium output.

PS = 1/2 * (10-4) * (18) = 54