A.) Since the price supply equation is linear, it will have the general form

y = ax + b

Let y = the number of bushels and x the price per bushel:

y = a($0.73) + b ⇒ 545 bushels = ($0.73)a + b

y = a($0.49) + b ⇒ 305 bushels = ($0.49)a + b

Subtract the two equations

(545 bushels - 305 bushels) = a($0.73 - $0.49)

240 bushels = a($0.24)

∴ a = (240 bushels)/($.24) = 1000 bushels per $

To find the value of b, plug the value of a into either of the original equations:

y = 545 = (1000)($0.73) + b

b = 545 - 730 = -185

So the price-supply equation may be written as: **y = (1000)x - 185**

B.) For the price-demand equation use the same procedure

y = a($0.73) + b ⇒ 435 bushels = ($0.73)a + b

y = a($0.49) + b ⇒ 515 bushels = ($0.49)a + b

(435 bushels - 515 bushels) = a($0.73 - $0.49)

-80 bushels = ($0.24)a

a = (-80 bushels)/($0.24) = -333.33

435 bushels = ($0.73)(-333.33) + b

b = 435 bushels - ($0.73)(-333.33) = 678.33

The price-demand equation is: **y = -333.33x + 683.33**

C.) The equilibrium price and quantity are at the point where these two lines intersect.

** y = (1000)x - 185**

** y = -333.33x + 683.33**

1000x - 185 = -333.333x + 683.333

x(1000 + 333.333) = 683.333 + 185

1333.333*x = 868.333

x = (683.333)/(1333.333) =** $0.65 (equilibrium)**

y = (1000)($0.65) - 185 = **466.25 bushels (equilibrium)**

** **

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