Question

1. The firm has the following cost function:

C(y)=3y^2+3/4y

What is the firm's producer surplus at y=25? Round answers to 4 decimal places

Answer 1

Marginal cost (MC) is the supply function of a firm.

Given,

C = 3y^2 + 3/4y

   = 3y^2 + 0.75y

Therefore, MC is the derivative of C.

MC = (d/dy) [3y^2 + 0.75y]

       = (3 × 2)y + 0.75

       = 6y + 0.75

Now, at (y = 25) the price or MC is,

Price = 6 × 25 + 0.75

        = 150.75

Now, the minimum accepted price should be searched where (y = 0).

Price = 6 × 0 + 0.75 = 0.75

Hence,

PS = 0.5 × Difference in price × Difference in y

     = 0.5 × (150.75 – 0.75) × (25 – 0)

     = 0.5 × 150 × 25

       = 1,875 [Answer]

Note: 0.5 is the part of formula.