If demand is given by qd = 20 – P and supply is given by qs = P, then producer surplus is: a. 50 b. 100 c. 30 d. 20
Question
If demand is given by qd = 20 – P and supply is given by qs = P, then producer surplus is:
a. 50
b. 100
c. 30
d. 20
Solution
First, we need to find the equilibrium price and quantity. This is where quantity demanded (qd) equals quantity supplied (qs).
Setting qd = qs, we get:
20 - P = P
Solving for P, we get:
P = 20/2 = 10
Substituting P = 10 into the supply equation, we get:
qs = 10
Now, we can calculate the producer surplus. Producer surplus is the area above the supply curve and below the price, up to the quantity sold. In this case, it's a triangle with a base of 10 (the quantity) and a height of 10 (the price minus the minimum price, which is 0 in this case).
The area of a triangle is 0.5 * base * height, so the producer surplus is:
0.5 * 10 * 10 = 50
So, the correct answer is:
a. 50
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