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.

Accepted Solution

Answer:a. P=1.5Qsupplied +1.95b. P= -1.5 Qdemanded+7.80c. eq.q=1.95 eq.p=4.87Step-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 suppliedm= $5.10-4.80/2.1-1.9m= 0.3/0.2m=1.5Then 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 - 2.85y= 1.5x -2.85+4.8y= 1.5x +1.95Supply 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-$4.8/1.8-2m= -1.5y-y1=m(x-x1)y-4.80=-1.5(x-2)y-4.80= -1.5x +3y= -1.5x +3+4.80y= -1.5x +7.80Demand 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+7.81.5q+1.5q= 7.8-1.953q= 5.85q=5.85/3q=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)+7.8P= 4.87The eq.price is 4.87