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BSEN 401 Lecture Notes - Budget Constraint, Opportunity Cost

Business and Environment
Course Code
BSEN 401
William Huddleston

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- Suppose that the consumer (household) consumes only two goods (X and Y).
Given the Prices of the two goods (PX, PY) and the consumer’s income (m), the possible
quantities purchasable by the consumer (Xo, Yo) are constrained by
PXXo + PYYo m
e.g., Suppose that a student has a budget for coffee and milk of $100/month. If the price of
Coffee (X say) is $1/cup and the price of Milk (Y) is $2/litre, the budget constraint is
$1*QC + $2*QM $100
Note: We can define one of the goods (Y say) as a composite commodity, representing all goods
other than X.
Budget Line:
Definition: The maximum combination of two commodities purchasable by a consumer given
the prices of the two commodities and the consumer’s money income
Rearranging the budget equation for the assumption that all income is spent gives the Budget line
Yo = m/PY PX/PY *X0
e.g. The budget line for Coffee and Milk with Milk as the Y commodity is
QM = $100/$2 $1/$2*QC = 50 0.5QC
Since the Opportunity Cost of X = -dY/dX
(Recall: Opportunity Cost = the best foregone option)
Opportunity Cost of X = -dY/dX = PX/PY (= -slope of the budget line)
(=> dY = -PX/PY *dX)
e.g. The opportunity cost of a unit of Coffee = -(-0.5) = 0.5 Milk
i.e., one unit of Coffee costs ½ litre of Milk
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