Chapter 3 Econ Behav
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1
Budegt Set (also called menu)
the set of all
outcomes I can achieve with my resources
outcomes I can achieve with my resources
2
Endowment
resources you have available
3
Prices
how much of your endowment is needed
to acquire one unit of each good
to acquire one unit of each good
4
slope of budget frontier
Px/Py
5
optimal choice
price ratio = MRS
6
Utility function
A function that converts inputs
from good space to utility space
-transforms cardinal values into ordinal values
from good space to utility space
-transforms cardinal values into ordinal values
7
Ordinal numbers
transforms cardinal values into ordinal values, like utility
8
Utility Function Example
My utility function: U(E,B) = 4* E*B^2
What is the utility of 4 eggs and 3 bacon strips? *High utility is good
My utility function: U(E,B) = 4* E*B^2
What is the utility of 4 eggs and 3 bacon strips? *High utility is good
144
9
X~Y -> U(X)=U(Y)
Means all points along an indifference curve have the same utility value.
• All points on higher indifference curves have greater utility and all point on lower indifference curves have less utility
• All points on higher indifference curves have greater utility and all point on lower indifference curves have less utility
10
Finding the optimal choice
Endowment = Px*X + Py*Y
– Variables are X and Y; Endowment, Px and Py are given
• Solve this for either X or Y and plug it into the
utility function
• Take derivative, set equal to zero, and solve
– Variables are X and Y; Endowment, Px and Py are given
• Solve this for either X or Y and plug it into the
utility function
• Take derivative, set equal to zero, and solve
11
Finding optimal choice example:
I have $8 with which to buy fruit for the week. I can buy apples ($2.00/lb.) and bananas ($1.00/lb.) U(A,B) = A*B – What should I buy?
I have $8 with which to buy fruit for the week. I can buy apples ($2.00/lb.) and bananas ($1.00/lb.) U(A,B) = A*B – What should I buy?
Endowment: $8
Pa = $2 and Pb = $1
Budget equation: 8 = 2*A + 1*B
Solve for either A or B (we’ll do B): B = 8 –2A
Plug this value for B into the utility function
U(A) = A *(8 –2A) = 8A –2A^2
Any constant is dropped out of the derivative
derivative = 2A^2 -> 2*2A->4A
New equation -> 8-4A
Set equal to zero and solve for A
4A = 8 so A = 2
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