The supply curve for product X is given by QXS 460 10PX a

The supply curve for product X is given by QXS = -460 + 10PX .

a. Find the inverse supply curve.

P = + Q

b. How much surplus do producers receive when Qx = 480? When Qx = 1,200?

When QX = 480: $

When QX = 1,200: $

Solution

Q_XS = -460 + 10 P_X

a) P = (Q+460)/10 => P = 0.1Q +46

b)

46+ 0.10*480 = 94
46+ 0.10*1200 = 166

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 = 94. The area between this price line and the supply function is the surplus (it\'s a triangle)

Area of this triangle = [(94 - 46) * 480] / 2 = 11520

Area when Q = 960
= [(166 - 46) * 1200] / 2

=72000