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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
Changes in Income: one effect
Income Effect(IE): Change in the demand for a good resulting from a change in income
- A shift in the budget line
Normal Good: Income Effect is positive (goes up)
Inferno Good: Income Effect is negative (goes down)
-Shift in the budget line does not affect optimality condition ie the ray
Change in Price: two effects
Income Effect – Income unchanged but purchasing power changes, so it’s as if income changed.
Substitution Effect – A change in price affects optimality condition ie affects relative amounts of x and y
consumed
Specifically Substitution Effect – The change in consumption of x and y caused by a change in relative
prices, Px/Py, which keeps the consumer indifferent.
Ie. Same indifference curve, and same level of utility
Example
U = xy, Px increases from Px1 to Px2, Py is constant
Overall effect of Px increasing is moving to a steeper budget line
Substitution Effect is the move up the indifference curve to a price they cant afford
Income Effect is the movement from the previous point to the steeper indifference curve point.
Decomposition Bundle – Bundle where consumers are as well off as point A, but they face the new
prices. (old utility curve, new prices) Decomposing Income and Substitution Effect
Step 1
Solve for initial bundle
Step 2
Solve for final bundle
Step 3
Solve for decomposition bundle
5-4
Step 1 – Initial Bundle
X = (1/1+1)72/9 Y = (1/1+1)72/1
X = 36/9 Y = 36
X = 4 (4,36)
Step 2 – Final Bundle
X = (1/1+1)72/4 Y = (1/1+1)72/1
X = 36/4 Y = 36
X = 9 (9,36)
Step 3 – Decomposition Bundle
U(B) = U(A)
XbYb = 4x36 (old utility)
MRS = y/x = Px2/Py = 4 (new prices)
y/x = 4
y = 4x
Sub in y = 4x
X(4x) = 4 x 36
X = 36
X = 6, y = 24. Sub in Y to make it equal 4 x 36
Bundle is (6,24) Substituion Effect is Income Effect is
X 4 6 = 2 X 6 9 = 3
Y 36 24 = -12 Y 24 36 = 12
Perfect Substitution
U = 2x + 3y Px1 = 2 Px2 = 1 Py = 1 I = 10
Step 1 (A)
MUx/Px1 = 2/2 = 1 < MUy/Py = 3/1 = 3
Therefore X = 0, Y = I/Py which is 10 in this case (0, 10)
Step 2 (C)
MUx/Px2 = 2/1 = 2 < MUy/Py = 3/1 = 3
Again, therefore X = 0, Y = I/Py which is 10 in this cas(0, 10)
In this case A = C bundle, No effect
Decomposition Bundle is equal to the same bundle (0,10) still.
Same example just change prices
U = 2x + 3y Px1 = 2 Px2 = 0.5 Py = 1 I = 10
Step 1 (A)
MUx/Px1 = 2/2 = 1 < MUy/Py = 3/1 = 3
Therefore X = 0, Y = I/Py which is 10 in this case (0, 10)
Step 2 (B)
MUx/Px2 = 2/0.5 = 4 > MUy/Py = 3/1 = 3 Therefore X = 20, Y = 0 MRS of X overcame the MRS of Y so (20, 0)
Step 3 (C)
U(B) = U(A)
2Xb + 3Yb = 2(0) + 3(10) = 30
2Xb + 3Yb = 30 (old utility)
Solved from above Yb = 0
2Xb + 3(0)= 30
X = 30/2 = 15
Decomposition Bundle is (15,0)
Substituion Effect is Income Effect is
X 0 15 = 15 X 15 20 = 5
Y 10 0 = -10 Y 0 0 = 0
Practice:
1) U=2x + 3y, I = 10, Py = 1, Px1 = 0.5, Px2 = 4
2) U = min{2x,y}, I = 12, Py = 1, Px1 = 2, Px2 = 1. Degenerate
Market Demand: Sum of individual demands
Ie Two individuals, with demands: q1 = 10 – 2P
q2 = 20 – 5P
What is the market demand?
Choke Price: Price at which individual demand is 0
If q

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