Answer:
Explanation:
To find the equilibrium point for the market, we need to determine the price and quantity at which the demand and supply functions intersect.
Let's start by representing the demand function as a linear equation. We have two points on the demand curve: (96, $400) and (136, $350). Using these points, we can calculate the slope of the demand curve:
Slope = (change in price) / (change in quantity)
Slope = ($350 - $400) / (136 - 96)
Slope = -$50 / 40
Slope = -$1.25
Now that we have the slope, we can write the equation of the demand curve in the form of: q = mp + b, where q represents the quantity demanded, p represents the price, m is the slope, and b is the y-intercept.
Using the point (96, $400) on the demand curve, we can substitute the values into the equation to find the y-intercept:
96 = -$1.25 * $400 + b
96 = -$500 + b
b = 596
Therefore, the demand equation is: q = -$1.25p + 596.
Next, let's find the supply equation. Using the points (76, $330) and (156, $420), we can calculate the slope of the supply curve:
Slope = (change in price) / (change in quantity)
Slope = ($420 - $330) / (156 - 76)
Slope = $90 / 80
Slope = $1.125
Using the point (76, $330) on the supply curve, we can substitute the values into the equation to find the y-intercept:
76 = $1.125 * $330 + b
76 = $371.25 + b
b = -295.25
Therefore, the supply equation is: q = $1.125p - 295.25.
To find the equilibrium point, we need to set the demand and supply equations equal to each other:
-$1.25p + 596 = $1.125p - 295.25
Now, solve for p:
2.375p = 891.25
p ≈ $374.74
Substitute the value of p back into either the demand or supply equation to find the corresponding quantity:
q = -$1.25 * $374.74 + 596
q ≈ 104.41
Therefore, the equilibrium point for the market is approximately (104.41, $374.74), where approximately 104 televisions are demanded and the price is around $374.74.