The quantity of wheat, in billions of bushels, that wheat suppliers are willing

Question

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.)

Explanation / Answer

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.

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