Question

Suppose a product can be produced using virgin ore at a marginal cost given by MC1 = 0.5q1 and with recycled materials at a marginal cost given by MC2 = 5 + 0.1q2. If the inverse demand curve were given by p = 20 – 0.5(q1+ q2), how many units of the product would be produced with virgin ore and how many units with recycled materials?

Answer 1

Given MC1=0.5q1 marginal cost of virgin ore ;MC2=5+0.1q2 marginal cost recycled material

Inverse demand curve p=20-0.5(q1+q2)

For virgin ore

MC1=P

0.5q1=20-0.5(q1+q2)

0.5q1=20-0.5q1-0.5q2

0.5q2=20-0.5q1-0.5q1

0.5q2=20-q1

q1=20-0.5q2-------equation 1

For recycled material

MC2=P

5+0.1q2=20-0.5(q1+q2)

5+0.1q2=20-0.5q1-0.5q2

0.5q2+0.1q2=20-5-0.5q1----equation 2

Subsutitute equation 1 im

0.6q2=15-0.5(20-0.5q2)

0.6q2=15-10+0.25q2

0.6q2-0.25q2=5

0.35q2=5

q2=5/0.35=14.28 units

q1=20-0.5(14.28)=20-7.14=12.86 units

For virgin ore= 14 units and recycled material=13units