Question
Find the producers’ surplus at a price level of
for the price-supply equation below.
The producers’ surplus is
.
(Round to the nearest integer as needed.)
(Round to the nearest integer as needed.)
Ask by Davey Delgado. in the United States
Nov 17,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The producers’ surplus at a price level of
is approximately
.
Solution

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To find the producers’ surplus at the price level of
, we first need to find the quantity
where the price supply equation equals 62.
Starting from the price-supply equation:
Rearranging gives:
To solve this quadratic equation, we’ll use the quadratic formula:
where
,
, and
.
Calculating the discriminant:
Now substituting back into the formula:
This gives two solutions, but we only consider the positive:
Now rounding
down to 266 for practical purposes.
Next, compute the area under the supply curve (from
to
), which is represented by the integral:
Calculating the integral step-by-step:
Now evaluate this from 0 to 266:
Calculating each term:
Summing those terms:
Now, the total revenue at this quantity level:
Producers’ surplus (P.S.) is calculated as:
Rounding to the nearest integer, the producers’ surplus is approximately: