12
12.1
Lecture 12: October 7, 2004
Duality
See G-12.1 Regarding the graph of the isoquant (f (z ) = q ) tangent to the isocost
(c(w , q ) = w z ), we have two regions. It is clear from the diagram that:
cfw_z : f (z ) q cfw_z : w z c(w , q ).
So the up
9
Lecture 9: September 28, 2004
9.1
More on Welfare Evaluation
Example 3.I.1. This example demonstrates the deadweight loss (DWL) associated
with a commodity tax versus having a lump sum tax that raised the same amount of
revenue.
Consider a commodity t
Let p1 = 1 and consider the two good UMP:
L = x1 + (x2 ) + (w x1 p1 x2 p2 ).
Then,
L
1 p1 = 0.
x1
= 1.
But since is the marginal utility of wealth, we have:
v (p, w)
= 1.
w
So under Q-linear preferences, Roys Identity reduces to:
x(p, w) =
6.1
p v (p,
4.2
Matrix Notation
Assuming the Walrasian Demand is a function (ie, if the utility function is strictly
quasi-concave), we have the demand vector:
x1 (p, w)
x2 (p, w)
x(p, w) =
.
.
.
.
xL (p, w)
Wealth Eects:
Dw x(p, w) =
Price Eects:
Dp x(p, w) =
Economics 603: Microeconomics
Larry Ausubel
Matthew Chesnes
Updated: Januray 1, 2005
1
Lecture 1: August 31, 2004
1.1
Preferences
Dene the set of possible consumption bundles (an nx1 vector) as X . X is the set of
alternatives.
Usually all elements of X