The supply curve for product X is given by QXS 420 20PX a

The supply curve for product X is given by Q_X^S = -420 + 20P_X .

a. Find the inverse supply curve.

P =_______ +________ Q

b. How much surplus do producers receive when Q_x = 380? When Q_x = 1,060?

When Q_X = 380: $_________

When Q_X = 1,060: $________

Solution

inverse supply curve

QXS = -420 + 20PX

divide both sides by 20

QXS/20=-420 /20 + 20PX/20

0.05QXS=-21+PX

P=21+0.05Q

b.

First find the price for the 2 quantities:

21+ 0.05*380 = 40
21+ 0.05*1060 =74

The surplus can be defined as the difference between what the producers receive (= price) and the minimal that they want to receive for a given quantity (= inverse supply curve).

Draw the inverse supply function on a diagram and draw a horizontal line at P = 40. The area between this price line and the supply function is the surplus (it\'s a triangle)

Area of this triangle = [(40 - 21) * 380] / 2 = 3610

Area when Q = 1060
= [(74 - 21) * 1060] / 2=28090