Answer to Question #258594 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

Solution:

a.). At equilibrium: Q_D = Q_S

58 – 30.4P = 16 + 3.2P

58 – 16 = 3.2P + 30.4P

42 = 33.6P

P = 1.25

Equilibrium price = 1.25

Substitute in either the demand or supply function to derive the equilibrium quantity:

Q_D = 58 – 30.4P = 58 – 30.4(1.25) = 58 – 38 = 20

Equilibrium quantity = 20

 

b.). Consumer surplus = ½ $\times$ 20 $\times$ (1.91 – 1.25) = ½ $\times$ 13.2 = 6.6

Producer surplus = ½ $\times$ (20 + 16) $\times$ 1.25 = ½ $\times$ 45 = 22.5

 

c.). The graph showing consumer and producer surplus is as below:

 

d.). Consumer surplus = ½ $\times$ 6 $\times$ (1.91 – 1.75) = 0.48

Producer surplus = ½ $\times$ 6 $\times$ 1.75 = 5.25

Surplus units of milk produced = 0.48 + 5.25 = 5.73

 

e.). Government will need to spend = 5. 73 $\times$ 1.25 = 7.1625

 

f.). Change in consumer surplus = 6.6 – 0.48 = 6.12

Change in producer surplus = 22.5 – 5.73 = 16.77

 

g.). Yes, such a minimum price will make producers as a whole worse off.