Question

Suppose that the market for wheat in the U.S. is characterized by the following demand and supply functions:

Supply:     Q_S=5+4P

Demand:   Q_D=30-P

where quantity is measured in billions of bushels and price in dollars per bushel.

1. The government introduces a subsidy program where a subsidy of $5 per bushel is granted to wheat producers. What quantity will be traded in the market under this subsidy program?
   1. 29 billion bushels
   2. 28 billion bushels
   3. 27 billion bushels
   4. 26 billion bushels
   5. 25 billion bushels
2. How much deadweight loss will arise as a result of the subsidy program?
   1. $2 billion
   2. $4 billion
   3. $5 billion
   4. $10 billion
   5. $20 billion
3. Now the government revises its agricultural policy and adopts a price support program rather than a subsidy program. The government implements the price support program by using a price floor equal to $7. What is the (direct) cost of the price support program to the government?
   1. $30 billion
   2. $45 billion
   3. $70 billion
   4. $161 billion
   5. $210 billion

Answer 1

Answer :

Supply:     Q_S=5+4P

Demand:   Q_D=30-P

According to market Equilibrium condition :

Quantity demanded = Quantity supplied

5+4P = 30-P

P = 5 (Equilibrium Price in the market)

Q = 5+4*5 = 25

Q = 30 - 5 = 25 (Market equilibrium quantity)

After Subsidy, market equilibrium condition will be :

Supply:     Q_S=5+4P

After subsidy, producers will receive price of the product plus subsidy, hence new equation will be

Where S = Subsidy = $5 per bushel

Qs = 5 + 4(P+S)

Demand:   Q_D=30-P (Demand funtion will be same)

Calculating new equilibrium points :

5 + 4 (P+S) = 30 - P

5 + 4P + 4S = 30 - P

5 + 4P + 4*5 = 30 - P

5P = 30 -20 - 5

P = 1

Q = 30 - 1 = 29

Q= 5 + 4(1+5) = 29 (With subsidy)

Q = 5 + 4*1 = 9 (Without subsidy)

The government introduces a subsidy program where a subsidy of $5 per bushel is granted to wheat producers. What quantity will be traded in the market under this subsidy program?

Answer : a : 29 billion bushels

Deadweight Loss Calculation:

= 1/2 * (5-1) * (29-25) + 1/2*(6-5)*(29-25)

= 8 + 2

=10

How much deadweight loss will arise as a result of the subsidy program

Answer : d : $10 billion

Now the government revises its agricultural policy and adopts a price support program rather than a subsidy program. The government implements the price support program by using a price floor equal to $7. What is the (direct) cost of the price support program to the government?

When P= 7

Supply:     Q_S=5+4P

Demand:   Q_D=30-P

Qd = 30 - 7 = 23

Qs = 5+4*7 = 33

Surplus = 33 - 23 = 10

Cost of the price support program to the government = 10*7 = 70 (Government will purchase surplus to clear the market, hence it will be cost to the government)

Answer : C : $70 billion