Problema Solution
An economist models the market for corn by the following equations:
Supply: y = 4.18p − 10.5
Demand: y = −2.06p + 19.3
Here, p is the price per bushel (in dollars), and y is the number of bushels produced and sold
(in billions).
Use the model for supply to determine at what point the price is so low that no corn is
produced.
Use the model for demand to determine at what point the price is so high that no corn is
sold.
Find the equilibrium price and the quantities that are produced and sold at equilibrium.
Answer provided by our tutors
If no corn is produced, then y = 0 in the supply equation.
0 = 4.18p − 10.5
p = $2.51
So at the low price of $2.51 per bushel, the production of the corn halts completely.
If no corn is sold, then y = 0 in the demand equation.
0 = −2.06p + 19.3
p = $9.37
So at the high price of $9.37 per bushel, no corn is sold.
To find the equilibrium point, we set the supply and demand equations equal to each other and solve.
4.18p − 10.5 = −2.06p + 19.3
p = $4.78
So the equilibrium price is $4.78.
Evaluating the supply equation for p = 4.78, we get
y = 4.18(4.78) − 10.5
y = 9.48 billions
So for the equilibrium price of $7.45 per bushel, about 9.48 millions bushels of corn are produced and sold.