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Lecture

# Classroom Lecture Notes - Kings

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Western University

Economics

Economics 2150A/B

Hugh Cassidy

Fall

Description

Chapter 5.1
Optimal Choice and Demand
We have solved for optimum given exogenous variables. (Px, Py, I)
Demand: how does the optimal (demanded) quantity of a good change as some exogenous variables
change?
Price Consumption Curve: Set of optimal bundles as price of good changes, holding other exogenous
variables constant. U = xy I =12, Py=1 hold these fixed. Px1 = 4 Px2 = 3, Px3 =2
MRS = 1/1 x y/x = Px/Py = Px/1 y = PxX
Y = 4x, 12 = 4x + y 12 = 4x + 4x12 = 8x x = 3/2, y = 4x = 6
(3/2, 6)
Y = 3x, 12 = 3x + 3x = 6x x = 2, y = 6 (2,6)
Y = 2x, 12 = 2x + 2x = 4x x = 3, y = 6 (3,6)
Straight Line across 6 is the Price Consumption curve, Y – int = 12, X –int = 3, 4, and 6. Straight lines to
them all. Look in textbook
Demand Curve: optimal quantity of a good as a function of its price, holding all other variables constant,
bowed towards the origin.
Income Consumption Curve: A set of optimal bundles as the income changes, holding all other
exogenous variables constant. Look in textbook for example
Engel Curve: Optimal quantity of a good as a function of income, holding all other exogenous variables
constant. Look in textbook for example
Normal Good: A good whose optimal quantity increases as income increases
Inferior Good: A good whose optimal quantity decreases as income increases
Giffen Good: A good whose optimal quantity increases as price increases Solving for Engel/Demand curve
- Same procedure as solving for the optimum, but without substituting for exogenous variables
c d
1) Cobb -Douglas. U = X Y , MRS = c/d x y/x Set MRS = Px/Py
c/d x y/x x = Px/Py
y = d/c x XPx/Py Sub into equation below
I = PxX + PyY
I = PxX + Py(d/c x XPx/Py)
I = PxX + (d/c x XPx)
I = XPx( 1 + d/c) = XPx(c+d/c)
X = (c/c+d) I / Px
Y = (d/c+d) I / Py
Example
2
U = x y c = 2 d= 1
Demand for X = (2/2+1) I / Px Y = ( 1/1+2) I / Py
X = (2/3) I / Px
Demand curve for X at I = 12
X = 2/3 (12) / Px
X = 8 / Px
Px = 8/x, now you can graph it
Engel Curve for X at Px = 1
X = 2/3 I/ Px
X = 2/3 I / 1
X = 2/3 I
I = 3/2 X, now you can graph it.
If I changes to 24. New demand curve X = 2/3 24 / Px = 16/Px. The demand curve shifts up. Perfect Compliments
U = min{ax, by}
Optimality condition: ax = by
Y = a/b x X
Budget Constraint I = PxX + PyY
I = PxX + Py(a/b x X)
I = X(Px + a

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