Question

At a price of $1.94 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,300 million bushels. At a price of $1.82 per bushel, the supply is 9,400 million bushels and the demand is 9,500 million bushels.
a) Find a price-supply equation of the form p mx b, where p is the price in dollars and x is the corresponding supply in millions of bushels.
b) Find a price-demand equation of the form p mxb, where p is the price in dollars and x is the corresponding supply in millions of bushels.
c) Using Excel, graph the price-supply and price-demand equations in the same coordinate system and find their point of intersection (equilibrium point)

Answer 1

Answer:

Hi there!

1) Supply ecuation: P = -0.0006 * Q + 7.52

2) Offer ecuation:   P = 0.0003 * Q - 1

3) Equilibrium point : Q = 9,466.67 ; P = 1.84

Explanation:

1) First, we find the slope of the supply ecuation

$m= \frac{P2-P1}{Q2-Q1} = \frac{1.94-1.82}{9500-9300}= \frac{0.12}{200} \\\\m = 0.0006$

Then, we replace with a value for the price and another for the quantity, both that correspond, and we will obtain the supply function

$P = -0.0006 Q + b\\1.82 = -0.0006 * 9500 +b\\1.82 = -5.7 + b\\b = 1.82 + 5.7\\b = 7.52$

2) First, we find the slope of the offer function

$m= \frac{P2-P1}{Q2-Q1} = \frac{1.94-1.82}{9800-9400}= \frac{0.12}{400} \\\\m = 0.0003$

Then, we replace with a value for the price and another for the quantity, both that correspond, and we will obtain the offer function

$P = 0.0003Q +b\\1.82 = 0.0003 * 9400 + b\\1.82 = 2.82 + b\\b = 1.82 - 2.82\\b= -1$

3)To calculate the equilibrium point, we must match the demand and supply function

$-0.0006 * Q + 7.52 = 0.0003 * Q - 1\\-0.0006 * Q - 0.0003 * Q = - 1 - 7.52\\-0.0009 * Q = -8.52\\Q=\frac{-8.52}{-0.0009}\\\\Q= 9,466.67$

We replace the amount of equilibrium in some of the equations and obtain the equilibrium price

$P = 0.0003 * Q - 1\\P = 0.0003 * 9,466.67 - 1\\P = 2.84 - 1\\P = 1.84$