Suppose the demand and supply for milk are described by the following equations: QD = 600 - 100P; QS = -150 + 150P, where P is price in dollars, Q D is quantity demanded in millions of gallons per year, and Q S is quantity supplied in millions of gallons per year

1. Use these equations to determine equilibrium price and quantity

Now suppose the U.S. government imposes a $1 per gallon of milk tax on dairy farmers.

1. Using the demand and supply equations from question 1: What is the new equilibrium price and quantity?
1. How much do dairy farmers receive per gallon of milk after the tax? How much do demanders pay?
2. Now suppose the tax is placed on the buyers of milk. Does it matter who pays the tax?

Now, what is the new equilibrium price and quantity assuming the government pays a subsidy of $1 per gallon (no tax now, just the subsidy)?

1. After the subsidy, how much do dairy farmers receive per gallon of milk after the tax? How much do demanders pay?

1. To determine the equilibrium price and quantity, we need to set the quantity demanded (QD) equal to the quantity supplied (QS).

QD = QS
600 - 100P = -150 + 150P

Adding 150P and 100P to both sides, we get:
600 = 250P - 150

Adding 150 to both sides, we get:
750 = 250P

Dividing both sides by 250, we get:
P = 750/250
P = 3

Now we can substitute the value of P back into either the demand or supply equation to find the equilibrium quantity. Let's use the demand equation:
QD = 600 - 100P
QD = 600 - 100(3)
QD = 600 - 300
QD = 300

Therefore, the equilibrium price is $3 and the equilibrium quantity is 300 million gallons per year.

2. After imposing a $1 per gallon tax on dairy farmers, the new equations for demand and supply become:

QD = 600 - 100(P + 1) (demand)
QS = -150 + 150(P - 1) (supply)

To find the new equilibrium price and quantity, we set QD equal to QS:

600 - 100(P + 1) = -150 + 150(P - 1)

Simplifying, we get:
600 - 100P - 100 = -150 + 150P - 150

Combining like terms, we get:
650 - 100P = -300 + 150P

Bringing all the P terms to one side, we get:
650 + 300 = 150P + 100P
950 = 250P

Dividing both sides by 250, we get:
P = 950/250
P = 3.8

Substituting this value back into either the demand or supply equation, we can find the equilibrium quantity. Using the demand equation:
QD = 600 - 100(P + 1)
QD = 600 - 100(3.8 + 1)
QD = 600 - 100(4.8)
QD = 600 - 480
QD = 120

Therefore, the new equilibrium price is $3.8 and the new equilibrium quantity is 120 million gallons per year.

3. After the tax, dairy farmers receive $2 per gallon of milk. Demanders would pay $3.8 per gallon.

4. If the tax was placed on the buyers of milk instead, it would not matter who pays the tax. The equilibrium price and quantity would remain the same.

5. Now, assuming the government pays a subsidy of $1 per gallon (no tax now, just the subsidy), the new equations for demand and supply become:

QD = 600 - 100(P - 1) (demand)
QS = -150 + 150(P + 1) (supply)

To find the new equilibrium price and quantity, we set QD equal to QS:

600 - 100(P - 1) = -150 + 150(P + 1)

Simplifying, we get:
600 - 100P + 100 = -150 + 150P + 150

Combining like terms, we get:
700 - 100P = 0 + 150P

Bringing all the P terms to one side, we get:
700 = 250P

Dividing both sides by 250, we get:
P = 700/250
P = 2.8

Substituting this value back into either the demand or supply equation, we can find the equilibrium quantity. Using the demand equation:
QD = 600 - 100(P - 1)
QD = 600 - 100(2.8 - 1)
QD = 600 - 100(1.8)
QD = 600 - 180
QD = 420

Therefore, the new equilibrium price is $2.8 and the new equilibrium quantity is 420 million gallons per year.

6. After the subsidy, dairy farmers receive $3.8 per gallon of milk. Demanders would pay $2.8 per gallon.

To determine the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the price. Let's start by setting QD equal to QS:

600 - 100P = -150 + 150P

To solve for P, we can manipulate the equation.

First, let's combine the P terms on one side:

600 = -150 + 250P

Next, let's bring the constants to the other side:

750 = 250P

Now, divide both sides by 250:

P = 3

So the equilibrium price is $3.

To find the equilibrium quantity, we can substitute this price into either the demand or supply equation. Let's use the supply equation (QS):

QS = -150 + 150P

QS = -150 + 150(3)

QS = -150 + 450

QS = 300

Therefore, the equilibrium quantity is 300 million gallons per year.

Now, let's consider the effect of a $1 per gallon tax on dairy farmers. This tax is imposed on producers, so it affects the supply equation. The new supply equation becomes:

QS = -150 + 150(P - 1)

To find the new equilibrium price and quantity, we need to set the new quantity supplied equal to the quantity demanded:

600 - 100P = -150 + 150(P - 1)

Now, we can solve for P:

600 - 100P = -150 + 150P - 150

750 = 250P

P = 3

The new equilibrium price is still $3.

To find the new equilibrium quantity, we can substitute this price into either the demand or supply equation. Since we've already solved for the original equilibrium quantity using the supply equation, let's use the demand equation (QD):

QD = 600 - 100P

QD = 600 - 100(3)

QD = 600 - 300

QD = 300

The new equilibrium quantity is 300 million gallons per year, which remains unchanged.

Now, let's calculate how much dairy farmers receive per gallon of milk after the tax. With the tax of $1 per gallon, the amount received by dairy farmers will be the original price minus the tax, which is $3 - $1 = $2.

On the other hand, demanders will pay the original price plus the tax, which is $3 + $1 = $4.

Next, let's consider the situation where the tax is imposed on the buyers of milk. In this case, the tax affects the demand equation. The new demand equation becomes:

QD = 600 - 100(P + 1)

To find the new equilibrium, we still set the new quantity demanded equal to the quantity supplied:

600 - 100(P + 1) = -150 + 150P

Simplifying the equation:

600 - 100P - 100 = -150 + 150P

500 = 250P

P = 2

So the new equilibrium price is $2.

To find the new equilibrium quantity, we can substitute this price into either the demand or supply equation. Using the supply equation (QS):

QS = -150 + 150P

QS = -150 + 150(2)

QS = -150 + 300

QS = 150

The new equilibrium quantity is 150 million gallons per year.

Now, let's consider the case where the government pays a subsidy of $1 per gallon to the dairy farmers. This means the farmers receive an additional $1 for each gallon of milk they produce, effectively increasing the price received by dairy farmers.

Since there is no tax, the price received by dairy farmers would be the equilibrium price plus the subsidy, which is $3 + $1 = $4 per gallon.

Demanders, however, still pay the equilibrium price, which remains at $3 per gallon.

To summarize:

1. After the tax imposed on dairy farmers, the new equilibrium price is $3, and the new equilibrium quantity is 300 million gallons per year.
2. Dairy farmers receive $2 per gallon of milk after the tax, and demanders who pay the tax pay $4 per gallon.
3. When the tax is placed on the buyers of milk, the equilibrium price decreases to $2, and the equilibrium quantity decreases to 150 million gallons per year.
4. After the $1 subsidy paid by the government, dairy farmers receive $4 per gallon of milk, and demanders still pay $3 per gallon.