demand function:
p-18=(140-x)/20
Calculate the consumer surplus if the shirts are sold for $16 each.
To calculate the consumer surplus, we need to find the area under the demand curve and above the price line ($16 in this case).
The demand function in this case is given by: p - 18 = (140 - x) / 20
First, we need to determine the quantity demanded when the price is $16. We can substitute p = 16 into the demand function and solve for x:
16 - 18 = (140 - x) / 20
Simplifying:
-2 = (140 - x) / 20
Multiplying both sides by 20:
-40 = 140 - x
Rearranging the equation:
x = 140 + 40
x = 180
Therefore, when the price is $16, the quantity demanded is 180 shirts.
Next, we calculate the consumer surplus by finding the area under the demand curve and above the price of $16. Since the demand curve is linear, the area of the consumer surplus triangle can be calculated using the formula: CS = 0.5 * base * height
The base of the triangle is the quantity demanded (x = 180), and the height is the difference between the price and the minimum possible price (p = 16 and p = 0, respectively). So, the consumer surplus (CS) can be calculated as:
CS = 0.5 * 180 * (16 - 0)
CS = 0.5 * 180 * 16
CS = 0.5 * 2880
CS = 1440
Therefore, the consumer surplus is 1440 when the shirts are sold for $16 each.