A supplier of portable hair dryers will make x hundred units of hair dryers available in the market when the unit price is
p = 324 + 4x
dollars. Determine the producers' surplus if the market price is set at $22/unit. (Round your answer to two decimal places.)
To determine the producer's surplus, we need to understand that it represents the difference between the price at which the product is sold and the cost of producing it. In this case, the price at which the product is sold is the market price, and the cost of producing it is given by the unit price equation:
p = 324 + 4x
First, we'll set the market price at $22/unit, which means that p will equal 22:
22 = 324 + 4x
Now, we can solve this equation to find the value of x. Subtracting 324 from both sides, we get:
4x = 22 - 324
4x = -302
x = -302/4
x = -75.5
Since x represents the number of hundred units, we can interpret this as -75.5 hundred units. However, since it's not meaningful to have a negative number of units, we can conclude that the market cannot be supplied in this case.
Therefore, there will be no producer's surplus in this scenario.