Question

# The quantity of wheat, in billions of bushels, that wheat suppliers are willing to produce in...

The quantity of wheat, in billions of bushels, that wheat suppliers are willing to produce in a year and offer for sale is called the quantity supplied and is denoted by S. The quantity supplied is determined by the price P of wheat, in dollars per bushel, and the relation is

P = 2.13S ? 0.95.

The quantity of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year is called the quantity demandedand is denoted by D. The quantity demanded is also determined by the price P of wheat, and the relation is

P = 2.45 ? 0.55D.

At the equilibrium price, the quantity supplied and the quantity demanded are the same. Find the equilibrium price for wheat. (Round your answer to two decimal places.)

At the equilibrium price, the quantity supplied and the quantity demanded are the same i.e. S = D.

We have P = 2.13 S ? 0.95 or, 2.13 S = P+0.95 so that S = (P+0.95)/2.13.

Also, P = 2.45 ? 0.55D or, 0.55D = 2.45-P so that D = (2.45-P)/0.55.

Hence, for the equilibrium price, we have (P+0.95)/2.13 = (2.45-P)/0.55. Now, on multiplying both the sides by 2.13* 0.55 = 1.1715, we get 0.55(P+0.95) = 2.13(2.45-P) or, 0.55P + 0.5225 = 5.2185 -2.13 P or, 0.55P +2.13 P =5.2185 + 0.5225 or, 2.68 P = 5.741 so that P = 5.741/2.68 = 2.142164170 = \$2.14( on rounding off to the nearest cent). Thus the equilibrium price of wheat is \$ 2.14 per bushel.