At $4.80 per bushel the annual supply for soybeans in the Midwest is 1.9 billion

Question

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. (Hint: You can review section 2.2 on equations of lines in the textbook). 2. a) Find the supply equation. b) Find the demand equation. c) Find the equilibrium price and quantity.

Explanation / Answer

Soln : We are considering here that supply and demand equation in linear equation with price.

Please refer the table here for supply, liability and Price :

Now, we will consider m be the slope of supply equation, so , we can say m = (p2-p1)/(x2-x1) = (5.1-4.8)/(2.1-1.9) = 0.3/0.2 = 1.5

equation is p = mx+c or we can say that p = 1.5x +c

put values of x1 and p1 in supply equation to get c = 4.8 - 1.5*1.9 = 4.8 = 1.95

So, supply eqn : p = 1.5x +1.95

b) Let the demand equation is p = My + C , here again M = (5.1-4.8)/(1.8-2.0) = -1.5

So , demand equation shuld be p = -1.5y + C, again put the values of p1 & y1 in this eqn to get

C = 4.8 + 1.5*2 = 7.8

Demad eqn : p = -1.5y +7.8

c) To calculate equilibirium price and quantitty need to equal the pricing from bothe supply eqn and demand eqn :

1.5x + 1.95 = -1.5y + 7.8 or we can say that (x+y) = 5.85 and in equilibirium condition the supply and demand should be same i.e. x +y = 5.85 or 2x = 5.85 , x = y = 2.975

p = 1.5*2.975 +1.95 = 6.4125

c) equilibirium price = $6.4125

and quantity = 2.975 billion bushels.

Supply Price Demand x P y 1.9 4.8 2 2.1 5.1 1.8

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.