BZ
Benny Zhuang
Answers (8)
BZ
Answered
The supply and demand curves for corn are as follows:
QD = 3,750 - 725P
QS = 920 + 690P,
where Q = millions of bushels and P = price per bushel.
a. Calculate the equilibrium price and quantity that would prevail in the free market.
b. The government has imposed a $2.50 per bushel support price. How much corn will the government be forced to purchase?
c. Calculate the loss in consumer surplus that would occur under the support program.
QD = 3,750 - 725P
QS = 920 + 690P,
where Q = millions of bushels and P = price per bushel.
a. Calculate the equilibrium price and quantity that would prevail in the free market.
b. The government has imposed a $2.50 per bushel support price. How much corn will the government be forced to purchase?
c. Calculate the loss in consumer surplus that would occur under the support program.
On Jul 31, 2024
a.set QD = QS
3,750 - 725P = 920 + 690P
2,830 = 1,415P
P = 2.00
QD = 3,750 - 725(2) = 2,300
b.To solve for government quantity, QG, we realize that:
QG = QS - QD
920 + 690P = 3750 - 725P + QG
QG = 1415P - 2830
Quantity supplied at the support price of $2.50 is:
QS = 920 + 650(2.50)
QS = 2645
Quantity demanded at the support price of $2.50 is:
QD = 3750 - 725(2.50)
QD = 1937.50
Government quantity purchased is then 707.5 bushels.
c.Solve supply and demand for P in terms of Q:
QD = 3750 - 725P
P = 5.17 - 0.0014Q
QS = 920 + 690P
P = -1.33 + 0.00145Q
QD at P = 2.50
QD = 3750 - 725(2.50)
QD = 1937.50
C.S. under free market: = 0.5(5.17 - 2.00) × 2300
C.S. under free market = 3645.5
C.S. under support price: = 0.5(5.17 - 2.50) × 1937.50
C.S. under price support = 2586.56
Price support results in a loss of $1058.94 in consumer surplus.
3,750 - 725P = 920 + 690P
2,830 = 1,415P
P = 2.00
QD = 3,750 - 725(2) = 2,300
b.To solve for government quantity, QG, we realize that:
QG = QS - QD
920 + 690P = 3750 - 725P + QG
QG = 1415P - 2830
Quantity supplied at the support price of $2.50 is:
QS = 920 + 650(2.50)
QS = 2645
Quantity demanded at the support price of $2.50 is:
QD = 3750 - 725(2.50)
QD = 1937.50
Government quantity purchased is then 707.5 bushels.
c.Solve supply and demand for P in terms of Q:
QD = 3750 - 725P
P = 5.17 - 0.0014Q
QS = 920 + 690P
P = -1.33 + 0.00145Q
QD at P = 2.50QD = 3750 - 725(2.50)
QD = 1937.50
C.S. under free market: = 0.5(5.17 - 2.00) × 2300
C.S. under free market = 3645.5
C.S. under support price: = 0.5(5.17 - 2.50) × 1937.50
C.S. under price support = 2586.56
Price support results in a loss of $1058.94 in consumer surplus.
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