Question

The supply curve for product X is given by QXS = -440 + 20PX .

a. Find the inverse supply curve. P = _____ + ______ Q

b. How much surplus do producers receive when

Qx = 420?

When Qx = 980?

When QX = 420: $

When QX = 980: $

Answer 1

The given supply curve QXS = -440 + 20PX

20PX =Q +440

PX =Q/20 +440/20

PX =Q/20 +22

a. The inverse supply curve. P = 22 + (1/20) Q

(b)

The producer surplus is the area below the price and above the supply curve.

When QX=420

P = 22 + (1/20) *Q

P = 22 + (1/20)* 420

P = 22 + 21

P=43

When Qx=0

P = 22 + (1/20) *0

P = 22 + (1/20) *0

P = 22 + 0

P=22

Producer surplus = Area of triangle

=1/2* B*H

=1/2*420*(43-22)

=0.5*420*21

=4410

When QX=980

P = 22 + (1/20) *Q

P = 22 + (1/20)* 980

P = 22 + 49

P=71

When Qx=0

P = 22 + (1/20) *0

P = 22 + (1/20) *0

P = 22 + 0

P=22

Producer surplus = Area of triangle

=1/2* B*H

=1/2*980*(71-22)

=0.5*980*49

=24,010

Producer surplus

When QX = 420: $4,410

When QX = 980: $24,010