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

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

**y = -333.33x + 683.33**

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

**y = -333.33x + 683.33**

**$0.65 (equilibrium)**

**466.25 bushels (equilibrium)**

At $0.49 per bushel, the daily supply for wheat is 305 bushels, and the daily demand it 515 bushels. When the price is raised to $0.73 per bushel, the daily supply increases to 545 bushels, and the daily demand decreases to 435 bushels. Assume that the price-supply and price-demand equations are linear.

A.) Find the price-supply equation

B.) Find the price-demand equation

C.) Find the equilibrium price and equilibrium quantity

I'm particularly having trouble with part C. but if you could work this entire problem out for me I would appreciate it!

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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

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.

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)**

A.) Points for price-supply, (p,s): ($0.49/b, 305 b), ($0.73/b, 545 b)

s(p) - 305 = ((545-305)/(0.73-0.49))(p - 0.49)

s(p) - 305 = (240/(0.24))(p - 0.49)

s(p) = 1000(p - 0.49) + 305

s(p) = 1000p - 490 + 305

s(p) = 1000p - 185 b

B.) Points for price-demand, (p,d): ($0.49/b, 515 b), ($0.73/b, 435 b)

d(p) - 515 = ((515-435)/(0.49-0.73))(p - 0.49)

d(p) - 515 = (80/(-0.24))(p - 0.49)

d(p) = -(1000/3)(p - 0.49) + 515

d(p) = -1000p/3 + 490/3 + 1545/3

d(p) = -1000p/3 + 2035/3 b

C.) Use Substitution:

1000p - 185 = -1000p/3 + 2035/3

Multiply by 3:

3000p - 555 = -1000p + 2035

4000p = 555 + 2035 = 2590

p = 259/400 = 2.59/4 = $0.6475/b

s($0.6475/b) = d($0.6475/b) = 1000(0.6475) - 185 = 647.5 -185 = 462.5 b

Note that answers are exact.

Thank you both for your help! I better understand the process but really the only problem is how the answers are input. The correct answers are:

A.) p=0.001q+0.185

B.) p=-0.003q+2.035

C.) Price=$.65

Quantity=463 bushels

But thanks again for your time!

-Courtnee

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