Unformatted text preview: d the optimal bundle of inputs, we
see that the “optimal” isocost line then passes through the “optimal” bundle of inputs: “Optimal”
isocost line Target
Output Fixed 0 The total cost is
If
from to then because the company has to produce with capital fixed at
, it must continue to use the same amount of labor albeit at a higher total cost
(see graph below
where the new isocost line passes through the original optimal bundle): 17
ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Initial
isocost line
New
isocost line Target
Output Fixed 0 We will examine the impact of changes in other parameters on the optimal solution and cost below. ● Since [ ⏟ ⏟ we see that with increasing returns to labor, labor usage, , and cost have a strictly concave relationship with output; with constant returns to labor, labor usage,
, and cost have a linear
relationship with output; with decreasing returns to labor, labor usage,
, and cost have a strictly convex relationship
with output. This is one of the most important concepts in ECO 204 and in fact can be stated as a general result: Since
constant, the “functional form” of the cost function must be the same as that of the
vice versa) which implies: Here are some examples (recall that in
corresponds to constant returns to labor, and , function (and corresponds to increasing returns to labor,
corresponds to decreasing returns to labor): 18
ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Cost Functions: for CobbDouglas Production Function ● Now we’ll use the CobbDouglas short run CMP to state some general results about the cost, total fixed cost, total
variable cost, marginal cost, average cost, average fixed cost and average fixed cost function and explore the connection
between “returns” and “economies of scale”. First, note that for any short run cost function: ( )
⏟ Notice that as . Hence, the “shape” of the curve is intimately intertwined with the “shape” of the
curve which in turn is linked to “returns”. Recall that “returns” tell us what happens to output when all variable
inputs are increased by the same factor { For the CobbDouglas short run CMP we have:
19
ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ⏟ ⏟ ( ) ( { )
( ) In fact we can also show that:
(
{ ( )
( What is the relationship between and )
) ? Notice:
⏟ Therefore:
( ) (
( )
) Finally, what can we say about “returns” and the “shape” of the
curve which in turn reflects “economies of scale”?
Recall that
the concept of economies of scale tells us what happens to average cost (which now equals average f...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics, Economics of production, Sayed Ajaz Hussain

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