An economist models the market for rice by the following equations. Let p represent the price per bushel (in dollars) and y represent the number of bushels produced and sold (in millions). Find the best approximation for the equilibrium price.
A) The equilibrium price is $1.23 per bushel.
B) The equilibrium price is $5.86 per bushel.
C) The equilibrium price is $3.97 per bushel.
D) The equilibrium price is $154.21 per bushel.
E) The equilibrium price is $2.58 per bushel.

Question

An economist models the market for rice by the following equations.  Let p represent the price per bushel (in dollars) and y represent the number of bushels produced and sold (in millions). Find the best approximation for the equilibrium price.
A) The equilibrium price is $1.23 per bushel. 
B) The equilibrium price is $5.86 per bushel. 
C) The equilibrium price is $3.97 per bushel. 
D) The equilibrium price is $154.21 per bushel. 
E) The equilibrium price is $2.58 per bushel.

Quizplus · Accepted Answer

To find the equilibrium price, we need to find the price level at which the quantity demanded equals the quantity supplied (i.e., where the two equations intersect). This can be achieved by setting the two equations equal to each other and solving for p.

200 - 8p = 2p - 20

10p = 220

p = 22/10 = $2.20

However, this calculation gives us the exact equilibrium price, and none of the answer choices correspond to it. Therefore, we need to round our answer to the nearest cent. Since the third answer choice, $3.97, is closest to $2.20, it is the best approximation for the equilibrium price.

An Economist Models the Market for Rice by the Following