Budget Constraints qStart to Build a Theory of Consumer Choice ...

Microeconomics
Dr. Dmitri M. Medvedovski
The Consumer’s Problem
●Attain the highest possible level of utility
–Scale utility mountain
●The available budget constitutes the constraint
●Think of the budget as a fence on the mountain
●Find the highest place on the fence
The Budget Constraint
●The consumer has a sum of money to spend each period, M
This money is spread across many goods, X i
●Thus the expenditure on the first good, X 1
, is
●And similarly for all other goods
Graphical Construction of the Budget Constraint
The Budget Line in Mathematical Terms
●Imagine the consumer spends all income on good Y
●The maximum amount of Y that can be purchased is M/(P Y
)
●If all income is spent on good X then the maximum quantity is M/(P X
)
●Join these two points to make a straight line
●Any combination on the line exhausts the entire budget M
The Slope of the Budget Constraint
●The slope is the ratio of the two prices: derive: (M/Py)/(M/Px)
●-P Y
/P X
The Consumer Choice
●Attain highest possible utility
●Don’t violate the budget constraint
●
Budget: I = P 1 X 1 + P 2 X 2 , where X 1 and X 2 are goods.
X 2
50
I
P 2
I
P 1
= X 1
+ P 2
P 1
X 2
40
30
20
Slope = -1 = − P 2
P 1
I
X 1
= I P 1
− P 2
P 1
X 2
10
10 20 30 40 50
X 1
P 1
constant
slope
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