Question:
Russ purchases 5 sirloins weekly. Is this statement true or false: If the price of sirloin increases by $5 per piece, and assuming Russ’s preferences and income stay the same, he will spend $25 less on other items weekly.
Solution:
A key concept I stress in my microeconomics principles class is that the behavioral responses we see in the market are significantly influenced by pricing. Changes in price lead to changes in behavior.
This notion derives from consumer theory. Standard models suggest that individuals aim to maximize their utility by consuming each good until the marginal value of an additional unit is equal to its market price. When the price of a product rises—as in this scenario—the marginal value at the new equilibrium must also increase. In this context, the new marginal value must be $5 higher to align with the new price of sirloin.
As the marginal value diminishes with increased consumption of sirloin, Russ can only restore the balance between marginal value and price—essential for his optimum—by reducing his consumption. While we lack precise details about his income or preferences, it’s evident that he will purchase fewer sirloins than he did previously.
Therefore, the original question’s statement is false: Russ will cut back on his sirloin consumption in response to the price hike, hence it does not necessarily imply he has $25 less to allocate to other goods.
Examining with Metrics
This outcome can also be illustrated by reviewing Russ’s budget constraint. Let’s say Russ allocates his income, M, to buy sirloin, S, and a composite good referred to as “all other goods,” Y. His budget constraint would thus be portrayed as:
M=PSS+PYY
In this expression, PS and PY represent the prices of sirloin and all other goods, respectively.
The scenario indicates that the price of sirloin increases by $5, resulting in a new budget constraint:
M=(PS+5)S+PYY
As Russ’s income, M, and the price of other goods, PY, remain unchanged, the highest quantity of “all other goods” he could purchase if he opted not to buy any sirloin still equals M/PY. Therefore, the maximum quantity of other goods available for consumption has not altered.
However, the slope of his budget line has shifted: sirloin is now relatively more expensive, causing the budget line to pivot inward around that axis. This alteration in relative prices constrains Russ’s available combinations of sirloin and other goods, leading him to adjust to a new optimum with diminished sirloin and increased quantity of other goods.
In this context, Russ’s effective income has declined even if his nominal income remains intact. Nevertheless, since he adjusts his spending allocation between sirloin and other goods due to the price fluctuation, it isn’t accurate to conclude that he has $25 less to spend on alternative goods each week.
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Solution:
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