The demand for corn (measured in billions of bushels) is given by rn-5-2Poorn+ A

Question

The demand for corn (measured in billions of bushels) is given by rn-5-2Poorn+ AP potatos-0.25Pbuttor+0.0003 M. The supply of corn is given by a f potatoes cost $3.00 per pound, butter costs 8.00 per pound, diese fue costs $2.50 per gallon, soybeans cost $8.00 per bushel, an per year, what is the equilibrium price of corn as determined by the demand and supply functions? average income . S 2000 Instructions: Round your answer to 1 decimal place. b. How much corn is bought and sold (equilibrium quantity)? Instructions: Round your answer to 1 decimal place. billion bushels. c. If the price of diesel fuel increases to $4.50 per gallon, what is the new equilibrium price? Instructions: Round your answers to 2 decimal places If the price of diesel fuel increases to $4.50 per gallon, what is the new equilibrium quantity? billion bushels.

Explanation / Answer

(a)

Demand for corn is as follows -

Qdcorn = 5 - 2Pcorn + 4Ppotatoes - 0.25Pbutter + 0.0003M

Ppotatoes = $3

Pbutter = $8

M = $42,000

Qdcorn = 5 - 2Pcorn + (4*3) - (0.25*8) + (0.0003 * 42,000)

Qdcorn = 5 - 2Pcorn + 12 - 2 + 12.6

Qdcorn = 27.6 - 2Pcorn

Supply of corn is as follows -

Qscorn = 9 + 5Pcorn - 2Pfuel - 1.25Psoybeans

Pfuel = $2.50

Psoybeans = $8

Qscorn = 9 + 5Pcorn - (2*2.50) - (1.25 * 8)

Qscorn = 9 + 5Pcorn - 5 - 10

Qscorn = 5Pcorn - 6

At equilibrium, demand equals supply

Qdcorn = Qscorn

27.6 - 2Pcorn = 5Pcorn - 6

7Pcorn = 33.6

Pcorn = 33.6/7 = 4.8

Thus,

The equilibrium price of corn is $4.8 per bushel.

(b)

Qdcorn = 27.6 - 2Pcorn

Qdcorn = 27.6 - (2*4.8) = 27.6 - 9.6 = 18

Thus,

The equilibrium quantity of corn is 18 billion bushels.

(c)

Demand for corn is as follows -

Qdcorn = 5 - 2Pcorn + 4Ppotatoes - 0.25Pbutter + 0.0003M

Ppotatoes = $3

Pbutter = $8

M = $42,000

Qdcorn = 5 - 2Pcorn + (4*3) - (0.25*8) + (0.0003 * 42,000)

Qdcorn = 5 - 2Pcorn + 12 - 2 + 12.6

Qdcorn = 27.6 - 2Pcorn

Supply of corn is as follows -

Qscorn = 9 + 5Pcorn - 2Pfuel - 1.25Psoybeans

The price of diesel fuel increases to $4.50 per gallon

Pfuel = $4.50

Psoybeans = $8

Qscorn = 9 + 5Pcorn - (2*4.50) - (1.25 * 8)

Qscorn = 9 + 5Pcorn - 9 - 10

Qscorn = 5Pcorn - 10

At equilibrium, demand equals supply

Qdcorn = Qscorn

27.6 - 2Pcorn = 5Pcorn - 10

7Pcorn = 37.6

Pcorn = 37.6/7 = 5.37

Thus,

The new equilibrium price of corn is $5.37 per bushel.

Qdcorn = 27.6 - 2Pcorn

Qdcorn = 27.6 - (2*5.37) = 27.6 - 10.74 = 16.86

Thus,

The new equilibrium quantity of corn is 16.86 billion bushels.

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