Department of Economics
Fall 2009
LeBow College of Business
Microeconomics 301
Drexel University
Professor Stehr
Class 5
Outline
1.
Derivation of demand functions
2.
Income and substitution effects of price change
3.
Social Security Payments and the CPI
Derivation of demand functions
Key Equations:
1) Tangency condition
Assuming no corner solution, the utility maximizing bundle occurs where the
indifference curve is tangent to the budget line which means MRS = Px / Py.
Recall that the MRS = MU
x
/ MU
y
.
The marginal utility of X is the additional utility derived from a little more consumption
of good X.
Mathematically, it can be expressed as the partial derivative of the utility
function with respect to X.
MU
x
=
δ
U /
δ
X
2) Budget constraint
The utility maximizing bundle lies on the budget constraint:
We can use these equations to derive the demand curve for the consumer.
Extended Example:
Suppose a consumer has utility function U = XY where X = the quantity of good X
consumed and Y = the quantity of good Y consumed and income = I.
a) Find expressions for MU
x
and MU
y
.
1
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marginal utility of Y is in fact equal to X.
(Hint: Suppose X
1
and Y
1
represent quantities
of X and Y.
The marginal utility of X is the increase in total utility that arises from
consuming one more unit of X, so the MUx may be obtained by subtracting U(X
1
,Y
1
)
from U(X
1
+1,Y
1
).
c) Derive the demand curve for X.
(Hint: Begin with the expression implying that the
MRS must equal the price ratio and solve for Y.
Substitute this expression for Y into the
equation for the budget constraint and solve the resulting equation for X.
You should
obtain an expression for X as a function of prices and income.
2
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 Spring '09
 Microeconomics, Consumer price index

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