Question

Suppose your goal is to produce 100 units of something as cost effectively as possible. There are 3 different methods which each have rising marginal costs, such that MC₁= 24q_{1 ,} MC₂= 4q₂, MC₃= 8q₃. How much should you use each method? (Hint: The equimarginal principle suggests that if the marginal costs for the methods used are not equal then you can save resources by shifting to the one with lower marginal costs.)

Answer 1

Production will be continued in every method until the marginal cost of each method becomes equal

First take the case of a first two methods

MC1 = MC2

24q1 = 4q2

This implies q2 = 6q1

Now take the case of second and third method

4q2 = 8q3

This implies q2 = 2q3

These two expressions indicate that 2q3 = 6q1 or q3 = 3q1

Now we have q1 + q2 + q3 = 100

q1 + 2*3q1 + 3q1 = 100

This implies q1 = 100/10 = 10 units

q2 = 6*10 = 60 units

And q3 = 3*10 = 30 units

First method should be used for 10 units

Second method should be used for 60 units

Third method should be used for 30 units