Answer: ps = 1012.5
Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5
Step-by-step explanation:
Given that;
p = 120 + q ; p = 165
Now to find the producer's surplus for supply equation p=f(q) at the indicated unit price; we find p
so from p = 120 + q ; p = 165, if we substitute for q
120 + q = 165
q = 165 - 120 = 45
so
ps = ⁴⁵∫₀ ( 165 - (120+q) dq
ps = ⁴⁵∫₀ ( 45 - q) dq
USING THE EXPRESSION [ xⁿdx = xⁿ⁺¹ / n+1]
ps = [45q - q²/2]₀⁴⁵
ps = [45(45) - 45²/2] [45(0) - (0)²/2]
ps = [2025 - 1012.5] - [0]
ps = 1012.5
Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5
