Transcript Appendix

PowerPoint Presentations for
Principles of Macroeconomics
Sixth Canadian Edition
by Mankiw/Kneebone/McKenzie
Adapted for the
Sixth Canadian Edition by
Marc Prud’homme
University of Ottawa
APPENDIX:
THE MATHEMATICS
OF MARKET
EQUILIBRIUM
Chapter 4
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Appendix
 In this appendix, simple mathematical methods are
used to help solve algebraically for a market’s
equilibrium price and quantity using supply and
demand curves.
 In Figure 4.8, we saw how the equilibrium price and
quantity for a good are determined by the
intersection of the supply and demand curves.
 Although they don’t have to be, for simplicity, these
curves are often drawn as linear (the “curves” are
actually straight lines!).
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Figure 4.8
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Appendix
 The general equation for a linear demand curve is as follows:
 QD is the quantity demanded.
 P is the price.
 The letters a and b are referred to as demand parameters.
 The parameter a can be viewed as incorporating all of
the things other than the own price of the good that affect
demand.
 The parameter b reflects the sensitivity of demand to changes
in its own price.
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Appendix
 For a linear demand curve, we can determine its
intercept with the price axis (the y-intercept) by setting
QD = 0 and solving the demand equation for P.
 Solving for P gives P = a/b.
 The intercept with the quantity axis (the x-intercept) is
determined by setting P = 0.
 Solving for QD gives QD = a.
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Appendix
 Figure 4A.1 plots the
demand curve for a
general linear
demand curve given
by the equation QD =
a - bP, identifying the
x- and y-intercepts
determined
previously.
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Appendix
 We saw in the appendix to Chapter 2 that the slope of a
linear demand curve is equal to the “rise over the run” as
we move along the line.
 The “rise” is the change in price measured along the
y-axis as we move from one point on the demand curve
to another
 The “run” is the change in quantity demanded
measured along the x-axis.
 So the slope of the demand curve is measured as
as we move from one point on the demand curve to
another.
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,
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Appendix
Using two points on the demand curve to derive the slope:
Gathering and cancelling:
Run
Rise
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Appendix
The “rise” over the “run”:
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Appendix
 The general equation for a linear supply curve is as follows:
 QS is the quantity supplied.
 P is the price.
 The letters c and d are referred to as supply parameters.
 The parameter c can be viewed as incorporating all of
the things other than the own price of the good that affect
supply.
 The parameter d reflects the sensitivity of supply to changes
in its own price.
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Appendix
 For a linear supply curve, we can determine its
intercept with the price axis (the y-intercept) by
setting QS = 0 and solving the demand equation for P.
 Solving for P gives P = - c/d.
 The intercept with the quantity axis (the x-intercept) is
determined by setting P = 0.
 Solving for QS gives QS = c.
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Appendix
 Figure 4A.1 plots the supply curve
for a general linear supply curve
given by the equation QS = c + dP,
identifying the x- and y-intercepts
determined previously.
 Because supply curves are
upward sloping, they can
intersect the x - or y-axis at either
a positive or negative number, so
the supply parameter c can be
either positive or negative
(although d is always positive).
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Appendix
Using two points on the supply curve to derive the slope
:
Gathering and cancelling:
Run
Rise
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Appendix
The “rise” over the “run”:
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Appendix
Equilibrium price is found by setting:
And solving for P:
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Appendix
 To determine the equilibrium quantity in the market,
substitute the equilibrium price into the equation for
quantity demanded and do some simple algebra to get:
Or:
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Appendix
 For example:
 The demand schedule for a good is given by:
 The supply schedule is given by:
 a = 20, b = 2, c = - 10, and d = 4.
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Appendix
 The equilibrium price is
 The equilibrium quantity is
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Appendix
 Alternatively:
 Set
:
 Solve for P:
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THE END
Chapter 4
Appendix
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