Question

1. In the market for pencils, demand is given by P = 16 – 2Q, and quantity supplied is given by P = 4 + Q.

If the government provides a $3-per-unit subsidy to pencil producers, the cost of the subsidy to the government will be

a. 12

b. 15

c. 6

d.3

e. None of these

2. In the market for pencils, demand is given by P = 16 – 2Q, and quantity supplied is given by P = 4 + Q.

If the government provides a $3-per-unit subsidy to pencil producers, this will result in

a. a deadweight loss of $3

b. a deadweight loss of $1.5

c. an increase in total surplus of $13.5

d. an increase in total surplus of $37.5

e. None of these

Answer 1

1) The given inverse demand function is

P = 16 - 2Q

The given supply function is

P = 4 + Q

Initial market equilibrium at Qd = Qs

16 - 2Q = 4 + Q

16 - 4 = Q + 2Q

12 = 3Q

Q = 12/3 = 4

Substitute Q=4 in either demand or supply function

P = 4 +4 = 8

Initial equilibrium price = 8

Initial equilibrium quantity = 4

When the government provide a $3 subsidy to pencil producers, the new supply function can be written as follows

( P = 4 + Q is the inverse demand function. It can be also written as Q = P - 4)

Q = P - 4

With $3 subsidy it become

Q = (P+3) - 4

Q = P - 1

The new equilibrium quantity with $3 subsidy is

QD = QS

P - 1 = (16 -P)/2 ( the inverse demand function can be also written as (16-P)/2 )

(P -1)2 = 16-P

2P - 2 = 16 -P

2P + P = 16 +2

3p = 18

P = 18/3 = 6

Substitute P = 6 in either function

Q = P-1

Q = 6-1 = 5

Equilibrium price with subsidy = 6

Equilibrium quantity with subsidy = 5

The cost of subsidy to the government = subsidy * quantity

= 3 * 5 = 15

The cost of subsidy to the government = 15

2) Consumer surplus is difference between maximum willingness to pay minus actual price paid by the consumers(area below the demand curve)

Maximum willingness to pay (quantity demand when price is 0) = 16

After subsidy, price paid by the consumers = 6

Consumer surplus = (1/2) * 10 *5 = 25

Producer surplus is the difference between the actual price they receive and minimum price willing to accept.( it is the area above the supply curve)

After subsidy, the minimum price received by the producers = 1 ( based on the supply function with subsidy)

With subsidy, price received by the producers = 6

Producer surplus = (1/2) * 5 * 5 = 12.5

Total surplus = consumer surplus + producer surplus

= 25 + 12.5 = 37.5

Total surplus = 37.5

An increase in the total surplus of $37.5