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Unformatted text preview: st line (see example below): Target Target Let’s solve for first by working with: Substitute in the constraint (3rd FOC): [ [ [ 27
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. [ [ [ [ [
⏟ [ You should show (and understand that):
● As
To get substitute ● As ● As ● As in: [
[ [ [ [ [
⏟ [ You should show (and understand that):
● As ● As ● As ● As These solutions for
are exactly what we have in the HW 14 final solutions (they “look” different but are in fact
exactly the same). Next, we could substitute
in the FOCs and solve for
but there’s a faster way: from the
envelope theorem we know that and it’ll be faster to derive it from the cost function9: [
⏟ ⏟ ⏟ Now: Hence: . As an exercise, you should confirm that: 9 This could be an excellent test question: we give you a nasty CMP and its cost function and ask you to solve for
solving the CMP you could compute
and then report
. . Rather than
28 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. Shortrun CMP with
Increasing Returns to and Constant Returns to functions strictly concave and Decreasing Returns to functions linear and functions strictly convex As then As then constant As then As then As then constant As then As then As then and approaches As then and then As an exercise, you should do a detailed analysis of this short run CMP.
6. “Estimating Short Run Cost Functions”
In this section we discuss how firms can cost and quantity data to “guesstimate” the functional form and “estimate” the
parameters of its short run cost function. For example, if a company believes that it has a linear cost function (stemming
from constant returns to variable inputs) then it can use data to estimate the parameters
in: In this case
and
(confirm this). On the other hand, if a company believes that it has a
quadratic cost function (stemming from decreasing returns to variable inputs) then it can use data to estimate the
parameters
in: In this case or (confirm this). We will show how to estimate short run cost functions through the HBS case The Prestige Telephone Company. 29
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. From the case recall that the Prestige Data Services (PDS) has never earned a profit (
Price of commercial data
service in $/hour;
Price of intercompany data service in $/hour;
# of commercial data service hours;
# of
intercompany data service hours):
From Exhibits 1 and 2 in The Prestige Telephone Company
Prices are $/hour January February March Intercompany Hours 206 181 223 Intercompany Price $400 $400 $400 Commercial Hours 123 135 138 Commercial Price $800 $800 $800 Total Revenue $190,584 $181,584 $212,285 Total Expenses $231,513 $229,925 $233,723 Net Income (Loss) $(41,472) $(40,341) $(21,438) There are several proposals to make PDS profitable (You should review your lectures slides and class notes to
understand the intuition behind each proposal; for example, why might raising price increase profits?): “Wait: PDS will eventually breakeven” What is Breakeven output? When will PDS Breakeven?
↑ by $200 ↓ by 30% Why might and w...
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This note was uploaded on 03/20/2014 for the course ECON 204 taught by Professor Ajazhussain during the Fall '09 term at University of Toronto Toronto.
 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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