Transcript Managerial Economics & Business Strategy

Managerial Economics &
Business Strategy
Chapter 1
The Fundamentals of Managerial
Economics
Let’s try some homework (number 3)
• Suppose that the total benefit and total cost from an activity
are, respectively, given by the following equations:
• B(Q) = 150+28Q-5Q2 and C(Q) = 100+8Q
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Write out the equation for net benefits
What are the net benefits when Q=1? Q=5?
Write out the equation for marginal net benefits
What are the marginal net benefits when Q=1? Q=5?
What level of Q maximizes net benefits?
At the value of Q that maximizes net benefits, what is the value of
marginal net benefits?
Conclusion
• Make sure you include all costs and benefits
when making decisions (opportunity cost).
• When decisions span time, make sure you
are comparing apples to apples (PV
analysis).
• Optimal economic decisions are made at the
margin (marginal analysis).
Appendix A
Calculus of Maximizing Net Benefits
…And other useful Math stuff
Variables and Functions
• Variable
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“Something” that can assume different values
Can be measured
• What does optimal mean??
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Best outcome possible given circumstances
• Doesn’t have to be the BIGGEST
– Maximum profits but Minimum Cost
• Function
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Mathematical depiction of the key components of a variable
TR = f(Q)
• Which is the independent variable?
–Q
• Which is the dependent variable?
– TR
What are the pieces?
Y  a  bX
• Dependent Variable
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Y
• Independent Variable
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X
• Y-intercept
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a
• Slope
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b
• What is slope???
Marginal Analysis
• Looks at the change in the dependent variable that
results from a unit change in the independent
variable
Price
DP
Profit
DQ
D Revenue
D Cost
D Profit
Why use Calculus??
• Looks at rates of change in a continuous function
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Assume economic variables are related to each other in a
continuous fashion but are valid only at stated discrete intervals
• Calculus, first of all, is wrongly named. It should
never have been given that name. A far truer and
more meaningful name is “SLOPE-FINDING”. –
Eli Pine’s How to enjoy Calculus
• Slope of a linear function
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Constant
Y = mX + b
• Nice but…our functions are typically continuous
Derivatives
• The derivative of Y with
respect to X
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Slope of the tangent line to the
point in question on the curve
d is used to mean changes in Y
relative to very SMALL changes
in X
D is used to look at changes
BETWEEN two points
dY
dX
Derivative RULES
Y  bX
• Constants
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ALWAYS ZERO!!!
• What is the derivative of 10?
– Zero
• Power Functions
Y  10X
3
n
dY
( n 1)
 nbX
dX
dY
2
 30 X
dX
More Rules
• Sums and Differences
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The derivative of the sum
(difference) is equal to the sum
(difference) of the derivatives of
the individual terms
If U=g(x) and V=h(x) then…
Y  3X  4 X
2
3
dY dU dV


dX dX dX
dY
2
 6 X  12 X
dX
And more…
• Products
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The derivative of the product of
two expressions is equal to the
first term multiplied by the
derivative of the second, PLUS the
second term times the derivative of
the first
Y  5 X (7  X )
2
dY
dV
dU
U
V
dX
dX
dX
dY
2
 10X (7  X )  5 X
dX
dY
 70X  10X 2  5 X 2
dX
dY
 70X  15X 2
dX
And more…
• Quotient
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Denominator MULTIPLIED by
derivative of the numerator
MINUS numerator MULTIPLIED
by the derivative of the
denominator ALL DIVIVED BY
the denominator squared
5X  9
Y
2
10 X
dY V (dU dX )  U (dV dX )

2
dX
V
dY 10X (5)  (5 X  9)(20X )

2 2
dX
(10X )
2
dY 50X  100X  180X

4
dX
100X
dY 5 X  10X  18

3
dX
10X
dY 18  5 X
Divide by 10X

3
dX
10X
2
2
Total Revenue
• TR = 7Q – 0.01Q2
• What is the Marginal Revenue function?
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MR = 7 - 0.02Q
• TC = 100 – 8Q + 10Q2
• What is the Marginal Cost function?
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MC = -8 + 20Q