Question

The supply curve for product X is given by QXS = -300 + 10PX .

a. Find the inverse supply curve. P = 30 + Q

b. How much surplus do producers receive when Qx = 300? When Qx = 800?

When QX = 300: $

When QX = 800: $

Answer 1

a. QXS = -300 + 10PX
So, 10PX = QXS + 300
So, PX = (QXS/10) + (300/10)
So, PX = 0.1QXS + 30
This is the inverse supply curve.

b. Price when QX = 0 is Pmin = 30
When Qx = 300; PX = 0.1(300) + 30 = 30 + 30 = 60
Producer surplus = area of triangle = (1/2)*(PX - Pmin)*Qx = (1/2)*(60 - 30)*(300) = (1/2)*30*300 = $4500

When Qx = 800; PX = 0.1(800) + 30 = 80 + 30 = 110
Producer surplus = area of triangle = (1/2)*(PX - Pmin)*Qx = (1/2)*(110 - 30)*(80) = (1/2)*80*800 = $32,000