Question

1. A subsidy is a benefit given by the government to groups or individuals, usually in the form of cash payment or tax reduction to encourage production. We can think of a subsidy as a “negative” tax. Suppose the government gives producers a specific subsidy of $4 per unit. (35 points)
   1. Using supply and demand curves, draw a diagram that clearly shows what happens when the specific $4 subsidy is implemented.
   2. What price do sellers receive and what do the consumers pay?
   3. On the diagram from part a, label the areas with letters like we have in class. [BE CAREFUL: there are a lot of areas to the label – make sure your drawing is clear] Indicate the change in consumer surplus, producer surplus, government expenditure, and welfare based on these labeled areas; i.e. compare CS, PS, government expenditure, and W before and after the subsidy to find the change. If there is a DWL, label that too.
   4. Now suppose we know the supply and demand functions:

QD=200-10p and QS=10p.

Find how much the equilibrium price and quantity changes after the subsidy. [Hint: Be careful how you incorporate the per-unit subsidy in the function that changes.]

5. Continuing with the above supply and demand functions, find the values for ∆CS, ∆PS, ∆W, the cost of the subsidy to the government, and the DWL.
6. Who gains and who loses from the subsidy? Why is there a deadweight loss?

Answer 1

a.)

A subsudy will cause the supply curve to shift to the right, from OC to ED in the diagram. This is because the cost to the producers reduces when the subsidy is given to the producers. The diagram is as follows -

b.)

The new price is P2 (falls from P1 to P2) and the new quantity is Q2 (rises from Q1 to Q2)

c.)

Change in consumer surplus: P2P1FG (increases)

Change in producer surplus: P4KFP1 (increases)

Government expenditure: P4KGP2 (increases)

Deaweight loss: FKG

d.)

$Q_d=200-10P$

Q 10P

Q PO

200 – 10P = 10P

$200=20P$

$P=200/20=10$

$Q_d=Q_s=100$

Now, after the subsidy, we get the supply curve as -

$Q_s=10(P+4)$

$Q_s=10P+40$

$Q_d=200-10P$

Q PO

$200-10P=10P+40$

$160=20P$

$P=160/20=8$

$Q_d=Q_s=120$

Therefore, price decreases by $2 and quantity increases by 20 units.

Change in consumer surplus: P2P1FG (increases)

Change in producer surplus: P4KFP1 (increases)

Government expenditure: P4KGP2 (increases)

Deaweight loss: FKG

In the above diagram, we get the value of P4 by putting Q=120 in the supply curve before subsidy is added -

Q 10P

$P=120/10=12$

Hence, we get -

Change in consumer surplus: 1/2 x (100+120) x 2 = 220

Change in producer surplus: 1/2 x (100+120) x 2 = 220

Government expenditure: 4 x 120 = 480

Deaweight loss: 480 - (220 + 220) = 40