Question

Suppose the market supply curve in a competitive market is given by is Q = 2p- 10. At a price of $15, producer surplus equals 37.5 O 25. 12.50. 100

Answer 1

The producer surplus is calculated by using the formula for area of a triangle = 1/2 * base * height

In the given question above, note that the supply curve does not start from the origin. This we know because when we put Q = 0 in the given equation Q = 2p - 10 …..(1), the result is as follows:

0 = 2p - 10

2p = 10

p = 10/2 = 5

This means that the supply curve starts at the point where p=5, ie, the producer will not supply anything for a price less than $5 OR that the supply curve has an intercept of 5 units on the y axis.

Now, given that p = $15, we calculate the quantity demanded at this price by substituting p = $15 in (1), then,

Q = 2p - 10

Q = 2*15 -10 = 30 - 10

Q = 20

Now, we know that quantity supplied at p =$15 is 20 and no quantity is supplied (0 quantity) at p<$5

For calculating the producer surplus with the formula 1/2 * price (p) * quantity (q), we have

p1= $15, p2 = $5 and q = 20

p= (p1 - p2) = $(15 - 5) = $ 10

Hence, the required producer surplus is 1/2 * p * q = 1/2 * 10 * 20 = 10 * 10 = 100

Ans- Required producer surplus = $ 100