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 − 0.65

.

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

P = 2.55 − 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.)

The quantity of wheat, in billions of bushels, that wheat suppliers are willing to produce in a year and offer for sale, determined by the price P of wheat, is:

P = 2.13*S - 0.65

On the other hand, you know that the amount of wheat, in billions of bushels, that wheat consumers are willing to buy in a year, determined by the price P of wheat, is:

P = 2.55 - 0.55*D

The market equilibrium or point of equilibrium is that point where there is an equilibrium because the demanders are willing to buy the same units that the suppliers want to manufacture, for the same price.

Being at the equilibrium price, the quantity supplied and the quantity demanded must be equal. So, being:

P = 2.13*S - 0.65 → P + 0.65=2.13*S → [tex]\frac{P+0.65}{2.13} =S[/tex]

P = 2.55 - 0.55*D → P+ 2.55= - 0.55*D → [tex]\frac{P+2.55}{-0.55} =D[/tex]

the quantity supplied S must be equal to the quantity demanded D:

S=D

[tex]\frac{P+0.65}{2.13} =\frac{P+2.55}{-0.55}[/tex]

Solving:

[tex](-0.55)*\frac{P+0.65}{2.13} =P+2.55[/tex]

[tex]\frac{-0.55}{2.13} *(P+0.65) =P+2.55[/tex]

[tex]-\frac{55}{213} *(P+0.65) =P+2.55[/tex]

[tex]-\frac{55}{213} *P-0.168 =P+2.55[/tex]

[tex]-\frac{55}{213} *P-P =2.55+0.168[/tex]

[tex]0.742*P =2.718[/tex]

P=2.718÷0.742

P=3.663

The equilibrium price for wheat is 3.663 dollars per bushel