Answer :
The equilibrium price is $4.45 per pound.
To find the equilibrium price, we need to determine the point at which the quantity supplied and the quantity demanded are equal.
First, let's find the slope of the supply curve using the two given supply points: (16,235 pounds, $4.98 per pound) and (10,671 pounds, $4.35 per pound).
Slope of the supply curve = (change in supply) / (change in price)
= (10,671 - 16,235) / ($4.35 - $4.98)
= -5564 / -0.63
= 8834.92 pounds per dollar
Next, let's find the slope of the demand curve using the two given demand points: (10,305 pounds, $4.98 per pound) and (12,832 pounds, $4.35 per pound).
Slope of the demand curve = (change in demand) / (change in price)
= (12,832 - 10,305) / ($4.35 - $4.98)
= 2527 / -0.63
= -4012.7 pounds per dollar
Now, we can set the supply and demand equations equal to each other to find the equilibrium price:
Supply equation: quantity supplied = slope of supply * price + y-intercept
Demand equation: quantity demanded = slope of demand * price + y-intercept
Since we only have two points for each curve, we'll use the point-slope form of the equation: y - y1 = m(x - x1)
For the supply equation, using the point (10,671 pounds, $4.35 per pound):
quantity supplied - 10,671 = 8834.92 * (price - $4.35)
For the demand equation, using the point (12,832 pounds, $4.35 per pound):
quantity demanded - 12,832 = -4012.7 * (price - $4.35)
Now, we can set the two equations equal to each other and solve for the equilibrium price:
quantity supplied - 10,671 = quantity demanded - 12,832
8834.92 * (price - $4.35) = -4012.7 * (price - $4.35)
Simplifying the equations, we get:
8834.92 * price - 38485.22 = -4012.7 * price + 17472.96
Combine like terms:
8834.92 * price + 4012.7 * price = 38485.22 + 17472.96
12847.62 * price = 55958.18
Divide both sides by 12847.62:
price = 55958.18 / 12847.62
price ≈ $4.355
Rounding to the nearest cent, the equilibrium price is $4.45 per pound.
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