Answer to Question #258592 in Microeconomics for Thando

Question

The market demand and supply functions for milk are: QD = 58 - 30.4P and QS = 16 + 3.2P.

Suppose a price floor of R1.75 is implemented.

a) Calculate the equilibrium price and quantity that would prevail without the price

floor.[1]

b) Calculate producer and consumer surplus at this equilibrium. [3]

c) Provide a rough sketch of the information calculated in (a) and (b). [2]

d) If this price floor is implemented, how many surplus units of milk are being

produced? [2]

e) How much would government need to spend to purchase the surplus units? [1]

f) What is the change in consumer and producer surplus due to the price floor?[3]

g) When the government regulates the price of a good to be no lower than some

minimum level. Can such a minimum price make producers as a whole worse off?

Answer 1

Qd=58-30.4P

Qs=16 +3.2P

Price floor =1.75

a)

At equilibrium

Qd=Qs

58 - 30.4P=16 +3.2P

58 - 16 =3.2P+30.4P

42=33.6P

P=42/33.6

P=1.25

At P=1.25

Qeq=16 +3.2 x 1.25

Qeq=16 +4

=20

Therefore equilibrium price =1.25 and equilibrium quantity =20.

b)

Consumer maximum price willingness to pay can be calculated at Qd=0

0=58 - 30.4P

30.4P=58

P=58/30.4

P=1.90

Consumer surplus =1/2(Pmax - Peq) Qeq

=1/2 x (1.90 - 1.25) x 20

=0.65 x 10

=6.5

Consumer surplus =6.5

Producer minimum price willing to sell can be calculated at Qs=0

0=16 +3.2P

-16=3.2P

P=-16/3.2

P=-5

Producer surplus = 1/2 (Peq - Pmin) Qeq

=1/2 x {1.25 - (-5)} x Qeq

=1/2 x (1.25 +5) x 20

=10 x 5.25

=52.5

Producer surplus =52.5

c)

Above is the required figure showing equilibrium price quantity and consume willing to pay and producer willingness to sell.

d) When price floor is 1.75 quantity supplied is calculated using supply curve:

Qs=16 +3.2 x 1.75

Qs=16 +5.6

Qs=21.6

When price floor is 1.75 quantity demanded is calculated using demand curve:

Qd=58 - 30.4 x 1.75

Qd=58 - 53.2

Qd=4.8

Therefore government will purchase all surplus quantity in market that is Qs-Qd

=21.6 - 4.8

=16.8

e) Government will have to spend Quantity purchased multipled by price

That is: Q surplus x Price floor

=16. 8 x 1.75

=29.4

f) Consumer surplus when price floor is 1.75

CS new = 1/2 x (Pmax - Pfloor) x Qd floor

=1/2 x (1.90 - 1.75) x 4.8

=2.4 x 0.15

=0.36

Change in Consumer surplus = CS new - CS

=0.36 - 6.5

=-6.14

Minus shows decrease in Consumer surplus.

Producer surplus when price floor is 1.75

PSnew =1/2 (Pfloor - Pmin) Qs floor

=1/2( 1.75 - (-5)} x 21.6

=10.8 x 5.75

=62.1

Change in producer surplus = PS new - PS

=62.1 - 52.5

=9.6

g) A minimum price floor which aim setting a minimum price that a producer should get which if above equilibrium price is binding in market and aim at increasing the producer surplus and as calculated above producer surplus increases after price floor so can't make producer worse off as a whole.