Question

The market supply curve for paper is currently estimated to be:

Q(S) = 100 + 10P

What is the producer surplus when the market price is equal to $50?

my answer is producer surplus (1/2)*600*40=12000

Answer 1

Producer surplus (PS) is the area of a triangle formed by the three end points – market price, quantity at that price, and the minimum price.

Given,

Q = 100 + 10P

The minimum price would be at a point where (Q = 0)

Therefore, 0 = 100 + 10P

10P = - 100

P = - 100 / 10 = - 10

Now quantity at $50 price,

Q = 100 + 10P

    = 100 + 10 × 50

    = 100 + 500

    = 600

Now, by the PS formula,

PS = 0.5 × (Difference in price) × (quantity at $50 price)

      = 0.5 × {50 – (-10)} × 600

      = 0.5 × (50 + 10) × 600

      = 0.5 × 60 × 600

    = $18,000 (Answer)