At a price of ​$2.23 per​ bushel, the supply of a certain grain is 7400 million bushels and the demand is 7700million bushels.

Question

At a price of ​$2.23 per​ bushel, the supply of a certain grain is 7400 million bushels and the demand is 7700million bushels. At a price of ​$2.32 per​ bushel, the supply is 7800 million bushels and the demand is 7600 million bushels. ​(A) Find a​ price-supply equation of the form pmx​b, where p is the price in dollars and x is the supply in millions of bushels. ​(B) Find a​ price-demand equation of the form pmx​b, where p is the price in dollars and x is the demand in millions of bushels. ​(C) Find the equilibrium point. ​(D) Graph the​ price-supply equation,​ price-demand equation, and equilibrium point in the same coordinate system.

Answer 1

2.23 quantity supplied 74 and quantity demanded 77

2.32 quantity supplied 78 and quantify demanded 76

points on the supply curve are (74, 2.23) and (78, 2.32)

points on the demand curve are (77, 2.23) and (76, 2.32)

in units of one thousand for x and dollars for y

the supply curve slope = (2.32-2.23)/(78-74) = .09/4 = 9/400

the demand curve slope = (2.32-2.23)/(76-77) = -.09 = -9/100

supply curve line: y-2.23 = (9/400)(x-74)= 9x/400 -63/400

demand curve line: y-2.23 = (-9/100)(x-77)= -9x/100 +693/100

9x/400 -63/400 = -9x/100 +693/100

multiply by 400

9x -63 = -36x + 4(693)

45x = 4(693)+63

x =(277+63)/45

x= 340/45

x = 68/9

x = 75.55...= about 75,555 1/2

P = y = 9x-63 = 9(68)/9 -63 = 68-63 = $5 = equilibrium price

when 75,555 1/2 are bought and sold with no shortage or surplus