Question

The firm has the following marginal cost function:

MC(y) = 3 + .25y

what is the change in producer surplus when the price of y changes from $ 20 to $ 50?

Answer 1

Marginal cost function is considered as a supply function, i.e., P = MC

=> P = 3 + 0.25Y

Where P is price of Y.

Put P = 20

=> 20 = 3 + 0.25Y

=> 20 -3 = 0.25Y

=> Y = 17 / 0.25

=> Y = 68

When P =20, then Y = 68

and

P = 3 + 0.25Y

Put P = 50

=> 50 = 3 + 0.25Y

=> 50 - 3 = 0.25Y

=> Y = 47 / 0.25

=> Y = 188

When P = 50, then Y is 188

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Producer surplus (when P =20) = Area of ΔABC

=> Producer surplus (when P=20) = 0.5 (AB) (BC)

=> Producer surplus (when P=20) = 0.5 (20-3) (68 -0)

=> Producer surplus (when P=20) = 578.

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Producer surplus (when P=50) = Area of ΔADE

=> Producer surplus (when P=50) = 0.5 (AD) (DE)

=> Producer surplus (when P =50) = 0.5 (50 - 3) (188-0)

=> Producer surplus (when P =50) = 4418

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The producer surplus increase from 578 to 4418 when price of Y increases from 20 to 50.

Change in producer surplus when Price of Y changes from 20 to 50 = 4418 - 578

=> Change in producer surplus when Price of Y changes from 20 to 50 = 3840