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Name: 1. At $4.80 per bushel, the annual supply for soybeans in the Midwest is 1.9 billion bushels and the annual demand is 2.0 billion bushels. When the price increases to $5.10 per bushel, the annual supply increases to 2.1 billion bushels and the annual demand decreases to 1.8 billion bushels. Assume that the supply and demand equations are linear where q is the number of bushels (in Billions) and p is the price in dollars per bushel. a) Find the supply equation. b) Find the demand equation. c) Find the equilibrium price and quantity.

Respuesta :

Answer:

a. P=1.5Qsupplied +1.95

b. P= -1.5 Qdemanded+7.80

c. eq.q=1.95 eq.p=4.87

Step-by-step explanation:

a. To find supply equation first, you must find the slope with this formula:

m= y2-y1/x2-x1

In this case Y is the price and X is the quantity supplied

m= $5.10-4.80/2.1-1.9

m= 0.3/0.2

m=1.5

Then you use this formula:

y-y1=m(x-x1)

y1 and x1 could be y2 and x2, the answer must be equal.

y-4.80=1.5(x-1.9)

y-4.8= 1.5x - 2.85

y= 1.5x -2.85+4.8

y= 1.5x +1.95

Supply equation: P=1.5Q supplied+1.95 You should notice that the slope is positive.

b. To find demand equation first, you do the same procedure but now x is the quantity demanded:

m= y2-y1/x2-x1

m= $5.10-$4.8/1.8-2

m= -1.5

y-y1=m(x-x1)

y-4.80=-1.5(x-2)

y-4.80= -1.5x +3

y= -1.5x +3+4.80

y= -1.5x +7.80

Demand equation: P=-1.5Qdemanded+7.8 Notice that the slope is negative.

c. To find the eq. price and quantity we must find the intersection point between both equations. Because P and Q should be equal for both equations, we equal them.

1.5q+1.95=-1.5q+7.8

1.5q+1.5q= 7.8-1.95

3q= 5.85

q=5.85/3

q=1.95

The eq.quantity is 1.95. Then you can replace this quantity in the equation you choose, the answer should not change if you choose the other equation.

P=-1.5(1.95)+7.8

P= 4.87

The eq.price is 4.87

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