Answer:
The answer is below
Explanation:
a) Find the price supply equation. b) Find the price demand equation. c) Find the equilibrium price and quantity.
Solution:
a) A linear equation is in the form y = mx + b, where m is the slope, y is a dependent variable, x is an independent variable, b is value of y at x = 0.
Let p represent the price and q represent the quantity. Hence we have the points (306, 0.31), (546, 0.79)
Using the formula:
[tex]p-p_1=\frac{p_2-p_1}{q_2-q_1}(q-q_1)\\ \\p-0.31=\frac{0.79-0.31}{546-306} (q-306)\\\\p=0.002q-0.302[/tex]
b) Let p represent the price and q represent the demand. Hence we have the points (459, 0.31), (439, 0.79)
Using the formula:
[tex]p-p_1=\frac{p_2-p_1}{q_2-q_1}(q-q_1)\\ \\p-0.31=\frac{0.79-0.31}{439-459} (q-459)\\\\p=-0.024q+11.326[/tex]
c) At equilibrium, price supply equation = price supply equation
0.002q - 0.302 = -0.024q + 11.326
0.002q + 0.024q = 11.326 + 0.302
0.026q = 11.628
q = 447.23 bushels
p = 0.002q - 0.302 = 0.002(447.23) - 0.302
p = $1.2
