Principles of Microeconomics Lecture – Cost Minimization
For positive output levels y, a firm’s average total cost of producing y units is
o
The returns-to-scale properties of a firm’s technology determine how average production costs change with
output level.
Our firm is presently producing y’ output units.
If a firm’s technology exhibits constant returns-to-scale, doubling its output level from y’ to 2y’ requires
doubling all input levels.
o Total production cost doubles.
o Average production cost does not change.
If a firm’s technology exhibits decreasing returns-to-scale then doubling its output level from y’ to 2y’
requires more than doubling all input levels.
o Total production cost more than doubles.
o Average production cost increases.
In the long-run a firm can vary all of its input levels.
Consider a firm that cannot change its input 2 level from x 2’ units.
The long-run cost-minimization problem is
o
o Subject to
The short-run cost-minimization problem is
o
o subject to
The short-run cost-min. problem is the long-run problem subject to the extra constraint that x 2 = x2’.
If the long-run choice for x2 was x2’ then the extra constraint x2 = x2’ is not really a constraint at all and so the
long-run and short-run total costs of producing y output units are the same.
But, if the long-run choice for x2 ¹ x2” then the extra constraint x2 = x2” prevents the firm in this short-run
from achieving its long-run production cost, causing the short-run total cost to exceed the long-run total cost
of producing y output units.
Short-run total cost exceeds long-run total cost except for the output level where the short-run input level
restriction is the long-run input level choice.
This says that the long-run total cost curve always has one point in common with any particular short-run
total cost curve.
For positive output levels y, a firm’s average total cost of producing y units is
o
The returns-to-scale properties of a firm’s technology determine how average production costs change with
output level.
Our firm is presently producing y’ output units.
If a firm’s technology exhibits constant returns-to-scale, doubling its output level from y’ to 2y’ requires
doubling all input levels.
o Total production cost doubles.
o Average production cost does not change.
If a firm’s technology exhibits decreasing returns-to-scale then doubling its output level from y’ to 2y’
requires more than doubling all input levels.
o Total production cost more than doubles.
o Average production cost increases.
In the long-run a firm can vary all of its input levels.
Consider a firm that cannot change its input 2 level from x 2’ units.
The long-run cost-minimization problem is
o
o Subject to
The short-run cost-minimization problem is
o
o subject to
The short-run cost-min. problem is the long-run problem subject to the extra constraint that x 2 = x2’.
If the long-run choice for x2 was x2’ then the extra constraint x2 = x2’ is not really a constraint at all and so the
long-run and short-run total costs of producing y output units are the same.
But, if the long-run choice for x2 ¹ x2” then the extra constraint x2 = x2” prevents the firm in this short-run
from achieving its long-run production cost, causing the short-run total cost to exceed the long-run total cost
of producing y output units.
Short-run total cost exceeds long-run total cost except for the output level where the short-run input level
restriction is the long-run input level choice.
This says that the long-run total cost curve always has one point in common with any particular short-run
total cost curve.
